https://wiki.swarma.org/api.php?action=feedcontributions&user=Vicky&feedformat=atom集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]2024-03-28T16:40:19Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E7%94%9F%E7%89%A9%E7%BD%91%E7%BB%9C&diff=21869生物网络2021-02-18T06:41:58Z<p>Vicky:</p>
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<div>本词条由Ryan初步翻译,由和光同尘审校<br />
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{{Network Science}}<br />
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{{refimprove|date=October 2011}}<br />
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A '''biological network''' is any [[network science|network]] that applies to [[biological system]]s. A network is any system with sub-units that are linked into a whole, such as species units linked into a whole [[food web]]. Biological networks provide a [[graph theory|mathematical representation]] of connections found in [[ecological network|ecological]], [[phylogenetic network|evolutionary]], and [[physiological]] studies, such as [[neural networks]].<ref name="Proulx05">{{cite journal | last1=Proulx | first1=S. R. | last2=Promislow | first2=D. E. L. | last3=Phillips | first3=P. C. | title=Network thinking in ecology and evolution | journal=Trends in Ecology and Evolution | volume=20 | issue=6 | pages=345–353 | year=2005 | doi=10.1016/j.tree.2005.04.004 | url=http://eeb19.biosci.arizona.edu/Faculty/Dornhaus/courses/materials/papers/Proulx%20Promislow%20Phillips%20networks%20ecol%20evol.pdf | pmid=16701391 | url-status=dead | archiveurl=https://web.archive.org/web/20110815122330/http://eeb19.biosci.arizona.edu/Faculty/Dornhaus/courses/materials/papers/Proulx%20Promislow%20Phillips%20networks%20ecol%20evol.pdf | archivedate=2011-08-15 }}</ref> The analysis of biological networks with respect to human diseases has led to the field of [[network medicine]].<ref>{{cite journal | last1 = Barabási | first1 = A. L. | last2 = Gulbahce | first2 = N. | last3 = Loscalzo | first3 = J. | year = 2011 | title = Network medicine: a network-based approach to human disease | url = | journal = Nature Reviews Genetics | volume = 12 | issue = 1| pages = 56–68 | doi=10.1038/nrg2918 | pmid=21164525 | pmc=3140052}}</ref><ref>{{Cite journal|last=Habibi|first=Iman|last2=Emamian|first2=Effat S.|last3=Abdi|first3=Ali|date=2014-10-07|title=Advanced Fault Diagnosis Methods in Molecular Networks|journal=PLOS ONE|volume=9|issue=10|pages=e108830|doi=10.1371/journal.pone.0108830|issn=1932-6203|pmc=4188586|pmid=25290670|bibcode=2014PLoSO...9j8830H}}</ref><br />
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A biological network is any network that applies to biological systems. A network is any system with sub-units that are linked into a whole, such as species units linked into a whole food web. Biological networks provide a mathematical representation of connections found in ecological, evolutionary, and physiological studies, such as neural networks. The analysis of biological networks with respect to human diseases has led to the field of network medicine.<br />
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我们称'''<font color="#ff8000">生物系统 biological systems</font>'''中的各个网络为'''<font color="#ff8000"> 生物网络 biological network</font>'''。网络是具有可连接成一个整体的子单元的系统,如由单个物种连接成的'''<font color="#ff8000">食物链网 food web</font>'''。生物网络为人们在生态学、进化学和生理学研究中发现的联系提供了数学表达方式,例如'''<font color="#ff8000"> 神经网络 neural networks</font>'''这一说法的出现。<ref name="Proulx05">{{cite journal | last1=Proulx | first1=S. R. | last2=Promislow | first2=D. E. L. | last3=Phillips | first3=P. C. | title=Network thinking in ecology and evolution | journal=Trends in Ecology and Evolution | volume=20 | issue=6 | pages=345–353 | year=2005 | doi=10.1016/j.tree.2005.04.004 | url=http://eeb19.biosci.arizona.edu/Faculty/Dornhaus/courses/materials/papers/Proulx%20Promislow%20Phillips%20networks%20ecol%20evol.pdf | pmid=16701391 | url-status=dead | archiveurl=https://web.archive.org/web/20110815122330/http://eeb19.biosci.arizona.edu/Faculty/Dornhaus/courses/materials/papers/Proulx%20Promislow%20Phillips%20networks%20ecol%20evol.pdf | archivedate=2011-08-15 }}</ref>生物网络分析方法同样应用于人类疾病研究,这开创了'''<font color="#ff8000">网络医学 network medicine'''</font>'''<ref>{{cite journal | last1 = Barabási | first1 = A. L. | last2 = Gulbahce | first2 = N. | last3 = Loscalzo | first3 = J. | year = 2011 | title = Network medicine: a network-based approach to human disease | url = | journal = Nature Reviews Genetics | volume = 12 | issue = 1| pages = 56–68 | doi=10.1038/nrg2918 | pmid=21164525 | pmc=3140052}}</ref><ref>{{Cite journal|last=Habibi|first=Iman|last2=Emamian|first2=Effat S.|last3=Abdi|first3=Ali|date=2014-10-07|title=Advanced Fault Diagnosis Methods in Molecular Networks|journal=PLOS ONE|volume=9|issue=10|pages=e108830|doi=10.1371/journal.pone.0108830|issn=1932-6203|pmc=4188586|pmid=25290670|bibcode=2014PLoSO...9j8830H}}</ref><br />
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==Network biology and bioinformatics==<br />
网络生物学和生物信息学<br />
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Complex biological systems may be represented and analyzed as computable networks. For example, ecosystems can be modeled as networks of interacting species or a protein can be modeled as a network of amino acids. Breaking a protein down farther, [[amino acids]] can be represented as a network of connected [[atom]]s, such as [[carbon]], [[nitrogen]], and [[oxygen]]. [[vertex (graph theory)|Nodes]] and [[vertex (graph theory)|edges]] are the basic components of a network. Nodes represent units in the network, while edges represent the interactions between the units. Nodes can represent a wide array of biological units, from individual organisms to individual neurons in the brain. Two important properties of a network are [[vertex (graph theory)|degree]] and [[betweenness centrality]]. Degree (or connectivity, a distinct usage from that used in [[Connectivity (graph theory)|graph theory]]) is the number of edges that connect a node, while betweenness is a measure of how central a node is in a network.<ref name="Proulx">{{cite journal |author= Proulx, S.R. |title= Network thinking in ecology and evolution |journal= Trends in Ecology and Evolution |year= 2005 |volume= 20 |issue= 6 |pages= 345–353 |doi=10.1016/j.tree.2005.04.004 |pmid=16701391|display-authors=etal}}</ref> Nodes with high betweenness essentially serve as bridges between different portions of the network (i.e. interactions must pass through this node to reach other portions of the network). In social networks, nodes with high degree or high betweenness may play important roles in the overall composition of a network.<br />
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Complex biological systems may be represented and analyzed as computable networks. For example, ecosystems can be modeled as networks of interacting species or a protein can be modeled as a network of amino acids. Breaking a protein down farther, amino acids can be represented as a network of connected atoms, such as carbon, nitrogen, and oxygen. Nodes and edges are the basic components of a network. Nodes represent units in the network, while edges represent the interactions between the units. Nodes can represent a wide array of biological units, from individual organisms to individual neurons in the brain. Two important properties of a network are degree and betweenness centrality. Degree (or connectivity, a distinct usage from that used in graph theory) is the number of edges that connect a node, while betweenness is a measure of how central a node is in a network. Nodes with high betweenness essentially serve as bridges between different portions of the network (i.e. interactions must pass through this node to reach other portions of the network). In social networks, nodes with high degree or high betweenness may play important roles in the overall composition of a network.<br />
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复杂的生物系统能用可运算网络来表示和分析。例如,生态系统可以被模拟为相互作用的物种网络,一个蛋白质可以被模拟为氨基酸网络。如果进一步分解蛋白质,氨基酸还可以表示为一个由相互连接的原子构成的网络,例如碳、氮和氧。'''<font color="#ff8000"> 节点 nodes</font>'''和'''<font color="#ff8000">边 edges</font>'''是网络的基本组成部分。节点表示网络中的单元,边表示单元之间的相互作用。节点可以代表广泛的生物单元——从单个的生物体到大脑中单个的'''<font color="#ff8000">神经元 neurons</font>'''。网络的两个重要性质是'''<font color="#ff8000">度 degree</font>'''和'''<font color="#ff8000"> 介数中心性 betweenness centrality</font>'''。度(或连通性,并非'''<font color="#ff8000">图论 graph theory</font>'''中所使用的)是连接一个节点的边的数量,而介数中心性是衡量一个顶点在网络中有多么靠近中心位置<ref name="Proulx">{{cite journal |author= Proulx, S.R. |title= Network thinking in ecology and evolution |journal= Trends in Ecology and Evolution |year= 2005 |volume= 20 |issue= 6 |pages= 345–353 |doi=10.1016/j.tree.2005.04.004 |pmid=16701391|display-authors=etal}}</ref>。本质上,具有高介数的节点充当的是网络不同部分之间的桥梁(即网络各个部分的交互必须通过这个节点发生)。在社会网络中,具有较高度值和较高介数的节点可以在网络的整体组成中发挥重要作用。<br />
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As early as the 1980s, researchers started viewing [[DNA]] or [[genome]]s as the dynamic storage of a language system with precise computable finite [[state (computer science)|states]] represented as a [[finite state machine]].<ref>{{cite book |author= Searls, D. |title= Artificial intelligence and molecular biology |publisher= MIT Press |year= 1993 |location= Cambridge, MA}}</ref> Recent [[complex system]]s research has also suggested some far-reaching commonality in the organization of information in problems from biology, [[computer science]], and [[physics]], such as the [[Bose–Einstein condensate]] (a special state of matter).<ref>{{cite journal |author1=Bianconi, G. |author2=Barabasi A. |lastauthoramp=yes |title= Bose-Einstein condensation in complex networks |journal= Phys. Rev. Lett. |year= 2001 |volume= 86 |issue= 24 |pages= 5632–5635 |doi=10.1103/physrevlett.86.5632|pmid=11415319 |arxiv=cond-mat/0011224|bibcode=2001PhRvL..86.5632B|hdl=2047/d20000696 }}</ref><br />
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As early as the 1980s, researchers started viewing DNA or genomes as the dynamic storage of a language system with precise computable finite states represented as a finite state machine. Recent complex systems research has also suggested some far-reaching commonality in the organization of information in problems from biology, computer science, and physics, such as the Bose–Einstein condensate (a special state of matter).<br />
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早在20世纪80年代,研究人员就开始将 DNA 或'''<font color="#ff8000">基因组genomes</font>'''视为一个可存储动态信息的语言系统——因其具有可精确运算的有限状态,所以被看做一个'''<font color="#ff8000">有限状态机finite state machine</font>'''<ref>{{cite book |author= Searls, D. |title= Artificial intelligence and molecular biology |publisher= MIT Press |year= 1993 |location= Cambridge, MA}}</ref>。近期的'''<font color="#ff8000">复杂系统 complex system</font>'''研究还表明,从信息组织的角度来看,一些'''<font color="#ff8000">生物学biology</font>'''、'''<font color="#ff8000">计算机科学 computer science</font>'''和'''<font color="#ff8000">物理学 physics</font>'''等领域的问题存在一些极有价值的共性,例如'''<font color="#ff8000">玻色-爱因斯坦凝聚态Bose–Einstein condensate </font>''' (一种特殊的物质状态) <ref>{{cite journal |author1=Bianconi, G. |author2=Barabasi A. |lastauthoramp=yes |title= Bose-Einstein condensation in complex networks |journal= Phys. Rev. Lett. |year= 2001 |volume= 86 |issue= 24 |pages= 5632–5635 |doi=10.1103/physrevlett.86.5632|pmid=11415319 |arxiv=cond-mat/0011224|bibcode=2001PhRvL..86.5632B|hdl=2047/d20000696 }}</ref>。<br />
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Bioinformatics has increasingly shifted its focus from individual [[gene]]s, proteins, and [[search algorithm]]s to large-scale networks often denoted as [[omics|-omes]] such as [[biome]], [[interactome]], [[genome]] and [[proteome]]. Such theoretical studies have revealed that biological networks share many features with other networks such as the [[Internet]] or [[social network]]s, e.g. their [[network topology]].<br />
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Bioinformatics has increasingly shifted its focus from individual genes, proteins, and search algorithms to large-scale networks often denoted as -omes such as biome, interactome, genome and proteome. Such theoretical studies have revealed that biological networks share many features with other networks such as the Internet or social networks, e.g. their network topology.<br />
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生物信息学已逐渐将关注点从单个基因、蛋白质和搜索算法转移到像'''<font color="#ff8000">生物组 biome</font>'''、'''<font color="#ff8000">交互组 interactome</font>'''、基因组和'''<font color="#ff8000">蛋白组 proteome</font>'''这样的大规模网络。这些理论研究揭示了生物网络与其他网络——如互联网或社交网络——有许多共同特征,例如他们的'''<font color="#ff8000">网络拓扑结构 network topology</font>'''。<br />
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==Networks in biology==<br />
生物学中的网络<br />
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===Protein–protein interaction networks===<br />
蛋白质-蛋白质互作网络<br />
{{main article|interactome}}<br />
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Many [[protein–protein interaction]]s (PPIs) in a cell form ''protein interaction networks'' (PINs) where proteins are ''nodes'' and their interactions are ''edges''.<ref>{{Cite journal|last=Habibi|first=Iman|last2=Emamian|first2=Effat S.|last3=Abdi|first3=Ali|date=2014-01-01|title=Quantitative analysis of intracellular communication and signaling errors in signaling networks|journal=BMC Systems Biology|volume=8|pages=89|doi=10.1186/s12918-014-0089-z|issn=1752-0509|pmc=4255782|pmid=25115405}}</ref> PINs are the most intensely analyzed networks in biology. There are dozens of PPI detection methods to identify such interactions. The [[Y2H|yeast two-hybrid system]] is a commonly used experimental technique for the study of binary interactions.<ref>{{cite journal |author= Mashaghi, A. |title= Investigation of a protein complex network |journal= European Physical Journal |year= 2004 |volume= 41 |issue= 1 |pages= 113–121 |doi=10.1140/epjb/e2004-00301-0|display-authors=etal|arxiv= cond-mat/0304207|bibcode= 2004EPJB...41..113M}}</ref><br />
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Many protein–protein interactions (PPIs) in a cell form protein interaction networks (PINs) where proteins are nodes and their interactions are edges. PINs are the most intensely analyzed networks in biology. There are dozens of PPI detection methods to identify such interactions. The yeast two-hybrid system is a commonly used experimental technique for the study of binary interactions.<br />
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在细胞中,大量的'''<font color="#ff8000">蛋白质间相互作用 protein-protein interactions(PPIs)</font>'''形成了'''<font color="#ff8000">蛋白质相互作用网络 protein interaction networks(PINs)</font>''',其中蛋白质是节点,它们的相互作用是边<ref>{{Cite journal|last=Habibi|first=Iman|last2=Emamian|first2=Effat S.|last3=Abdi|first3=Ali|date=2014-01-01|title=Quantitative analysis of intracellular communication and signaling errors in signaling networks|journal=BMC Systems Biology|volume=8|pages=89|doi=10.1186/s12918-014-0089-z|issn=1752-0509|pmc=4255782|pmid=25115405}}</ref>。蛋白质互作网络是生物学中人们分析的最深入的网络。现有几十种基于PPIs的检测方法被用于识别蛋白质间的相互作用,'''<font color="#ff8000">酵母双杂交系统 yeast two-hybrid System</font>'''是一种研究二元相互作用的常用实验技术<ref>{{cite journal |author= Mashaghi, A. |title= Investigation of a protein complex network |journal= European Physical Journal |year= 2004 |volume= 41 |issue= 1 |pages= 113–121 |doi=10.1140/epjb/e2004-00301-0|display-authors=etal|arxiv= cond-mat/0304207|bibcode= 2004EPJB...41..113M}}</ref><br />
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Recent studies have indicated conservation of molecular networks through deep evolutionary time.<ref>{{cite journal |author= Sharan, R. |title= Conserved patterns of protein interaction in multiple species |journal= Proceedings of the National Academy of Sciences of the United States of America |year= 2005 |volume= 102 |issue= 6 |pages= 1974–1979 |doi=10.1073/pnas.0409522102|pmid= 15687504 |display-authors=etal|pmc= 548573|bibcode= 2005PNAS..102.1974S}}</ref> Moreover, it has been discovered that proteins with high degrees of connectedness are more likely to be essential for survival than proteins with lesser degrees.<ref>{{cite journal |author= Jeong, H. |title= Lethality and centrality in protein networks |journal= Nature |year= 2001 |volume= 411 |issue= 6833 |pages= 41–42 |doi=10.1038/35075138 |pmid=11333967|display-authors=etal|bibcode= 2001Natur.411...41J |arxiv= cond-mat/0105306 }}</ref> This suggests that the overall composition of the network (not simply interactions between protein pairs) is important for the overall functioning of an organism.<br />
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Recent studies have indicated conservation of molecular networks through deep evolutionary time. Moreover, it has been discovered that proteins with high degrees of connectedness are more likely to be essential for survival than proteins with lesser degrees. This suggests that the overall composition of the network (not simply interactions between protein pairs) is important for the overall functioning of an organism.<br />
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近年来的研究表明,'''<font color="#ff8000">分子网络 molecular networks</font>'''在深层进化过程中是保守的(在进化过程中的改变较少)<ref>{{cite journal |author= Sharan, R. |title= Conserved patterns of protein interaction in multiple species |journal= Proceedings of the National Academy of Sciences of the United States of America |year= 2005 |volume= 102 |issue= 6 |pages= 1974–1979 |doi=10.1073/pnas.0409522102|pmid= 15687504 |display-authors=etal|pmc= 548573|bibcode= 2005PNAS..102.1974S}}</ref>。此外,相较于低度值的蛋白质,具有高度值的蛋白质对物种的生存可能更加重要<ref>{{cite journal |author= Jeong, H. |title= Lethality and centrality in protein networks |journal= Nature |year= 2001 |volume= 411 |issue= 6833 |pages= 41–42 |doi=10.1038/35075138 |pmid=11333967|display-authors=etal|bibcode= 2001Natur.411...41J |arxiv= cond-mat/0105306 }}</ref>。这表明网络如何组成(不仅仅是简单的蛋白质之间的相互作用)对于有机体的整体功能具有重要影响。<br />
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===Gene regulatory networks (DNA–protein interaction networks)===<br />
基因调控网络(DNA-蛋白质交互网络)<br />
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{{main article| Gene regulatory network}}<br />
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The activity of genes is regulated by [[transcription factors]], proteins that typically bind to [[DNA]]. Most transcription factors bind to multiple binding sites in a [[genome]]. As a result, all cells have complex [[gene regulatory networks]]. For instance, the [[human genome]] encodes on the order of 1,400 DNA-binding transcription factors that regulate the expression of more than 20,000 human genes.<ref>{{cite journal |author= Vaquerizas, J.-M. |title= A census of human transcription factors: function, expression and evolution |journal= Nature Reviews Genetics |year= 2009 |volume= 10 |issue= 4 |pages= 252–263 |pmid= 19274049 |doi=10.1038/nrg2538|display-authors=etal}}</ref> Technologies to study gene regulatory networks include [[ChIP-chip]], [[ChIP-seq]], [[CliP-seq]], and others.<br />
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The activity of genes is regulated by transcription factors, proteins that typically bind to DNA. Most transcription factors bind to multiple binding sites in a genome. As a result, all cells have complex gene regulatory networks. For instance, the human genome encodes on the order of 1,400 DNA-binding transcription factors that regulate the expression of more than 20,000 human genes. Technologies to study gene regulatory networks include ChIP-chip, ChIP-seq, CliP-seq, and others.<br />
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与DNA结合的蛋白质中,负责管理基因的'''<font color="#ff8000">转录因子 transcription factors</font>'''是十分典型的一类。大多数转录因子可以与基因组中的位点结合。因此,所有的细胞都有复杂的'''<font color="#ff8000">基因调控网络 gene regulatory Networks</font>'''。例如,人类基因组编码出1400个左右可与DNA结合的转录因子,它们调节超20000个人类基因的表达。研究基因调控网络的技术包括 ChIP-chip、 ChIP-seq、 CliP-seq 等。<br />
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===Gene co-expression networks (transcript–transcript association networks)===<br />
基因共表达网络(转录-转录关联网络)<br />
{{main article| Gene co-expression networks}}<br />
--~~~Gene co-expression networks 基因共表达网络 <br />
Gene co-expression networks can be interpreted as association networks between variables that measure transcript abundances. These networks have been used to provide a systems biologic analysis of DNA microarray data, RNA-seq data, miRNA data etc.<br />
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Gene co-expression networks can be interpreted as association networks between variables that measure transcript abundances. These networks have been used to provide a systems biologic analysis of DNA microarray data, RNA-seq data, miRNA data etc.<br />
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'''<font color="#ff8000">基因共表达网络 Gene co-expression networks </font>'''是一种变量之间的关系网络,用于衡量'''<font color="#ff8000">转录丰度transcript abundances</font>'''。这些网络被用来为'''<font color="#ff8000">DNA微阵列数据DNA microarray data</font>'''、 '''<font color="#ff8000">RNA-seq数据 RNA-seq data</font>'''、 '''<font color="#ff8000">miRNA数据 miRNA data</font>'''等分析提供系统生物学支持。<br />
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[[Weighted correlation network analysis|weighted gene co-expression network analysis]] is widely used to identify co-expression modules and intramodular hub genes. Co-expression modules may correspond to cell types or pathways. Highly connected intramodular hubs can be interpreted as representatives of their respective module.<br />
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weighted gene co-expression network analysis is widely used to identify co-expression modules and intramodular hub genes. Co-expression modules may correspond to cell types or pathways. Highly connected intramodular hubs can be interpreted as representatives of their respective module.<br />
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'''<font color="#ff8000">加权基因表达网络分析 weighted gene co-expression network analysis </font>'''被广泛应用于鉴定'''<font color="#ff8000">共表达模块co-expression modules</font>'''以及模块内的核心基因。共表达模块可能会对应细胞类型或病症通路。模块内四通八达的枢纽可以被视作本模块内其他基因的代表,显示出这些基因共有的特点。<br />
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===Metabolic networks===<br />
代谢网络<br />
{{main article|metabolic network}}<br />
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The chemical compounds of a living cell are connected by biochemical reactions which convert one compound into another. The reactions are catalyzed by [[enzymes]]. Thus, all compounds in a cell are parts of an intricate biochemical network of reactions which is called [[metabolic network]]. It is possible to use network analyses to infer how selection acts on metabolic pathways.<ref name="Proulx" /><br />
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The chemical compounds of a living cell are connected by biochemical reactions which convert one compound into another. The reactions are catalyzed by enzymes. Thus, all compounds in a cell are parts of an intricate biochemical network of reactions which is called metabolic network. It is possible to use network analyses to infer how selection acts on metabolic pathways.<br />
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化合物在活细胞中会发生大量生物化学反应,这使得化合物发生转变。这些反应是由'''<font color="#ff8000">酶 enzymes</font>'''催化的。因此,细胞中所有的化合物都是一个复杂生化反应网络的一部分,该网络被称为'''<font color="#ff8000">代谢网络 metabolic network</font>'''。我们可以使用网络分析方法来推断“筛选”是如何影响代谢通路的<ref name="Proulx" />。<br />
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===Signaling networks===<br />
信号网络<br />
{{main article|Cell signaling}}<br />
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Signals are transduced within cells or in between cells and thus form complex signaling networks. For instance, in the [[MAPK/ERK pathway]] is transduced from the cell surface to the cell nucleus by a series of protein–protein interactions, phosphorylation reactions, and other events. Signaling networks typically integrate [[interactome|protein–protein interaction networks]], [[gene regulatory networks]], and [[metabolic network]]s.<br />
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Signals are transduced within cells or in between cells and thus form complex signaling networks. For instance, in the MAPK/ERK pathway is transduced from the cell surface to the cell nucleus by a series of protein–protein interactions, phosphorylation reactions, and other events. Signaling networks typically integrate protein–protein interaction networks, gene regulatory networks, and metabolic networks.<br />
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信号在细胞内或细胞之间传递,形成了复杂的信号网络。例如,'''<font color="#ff8000">MAPK/ERK 通路 MAPK/ERK pathway</font>'''通过一系列蛋白质之间的相互作用、'''<font color="#ff8000">磷酸化反应 phosphorylation reactions</font>'''和其他事件将信号从细胞表面传递到'''<font color="#ff8000">细胞核cell nucleus</font>'''内。'''<font color="#ff8000">信号网络 signaling networks</font>'''通常包含蛋白质相互作用网络、'''<font color="#ff8000">基因调控网络 gene regulatory networks</font>'''和'''<font color="#ff8000">代谢网络 metabolic networks</font>'''。<br />
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===Neuronal networks===<br />
神经网络<br />
{{main article| Biological neural network}}<br />
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The complex interactions in the [[brain]] make it a perfect candidate to apply network theory. [[Neuron]]s in the brain are deeply connected with one another and this results in complex networks being present in the structural and functional aspects of the brain.<ref>{{cite journal |author1=Bullmore, E. |author2=O. Sporns |lastauthoramp=yes |title= Complex brain networks: graph theoretical analysis of structural and functional systems |journal= Nature Reviews Neuroscience |year= 2009 |volume= 10 |issue= 3 |pages= 186–198 |doi=10.1038/nrn2575 |pmid=19190637}}</ref> For instance, [[small-world network]] properties have been demonstrated in connections between cortical areas of the primate brain<ref>{{cite journal |author= Stephan, K.E. |title= Computational analysis of functional connectivity between areas of primate cerebral cortex |journal= [[Philosophical Transactions of the Royal Society B]]|year= 2000 |volume= 355 |issue= 1393 |pages= 111–126 |doi=10.1098/rstb.2000.0552|pmid= 10703047 |display-authors=etal|pmc= 1692715}}</ref> or during swallowing in humans.<ref>{{Cite journal|date=2016-12-01|title=Functional connectivity patterns of normal human swallowing: difference among various viscosity swallows in normal and chin-tuck head positions|journal=Brain Research|volume=1652|pages=158–169|doi=10.1016/j.brainres.2016.09.041|pmid=27693396|pmc=5102805|issn=0006-8993|last1=Jestrović|first1=Iva|last2=Coyle|first2=James L|last3=Perera|first3=Subashan|last4=Sejdić|first4=Ervin}}</ref> This suggests that cortical areas of the brain are not directly interacting with each other, but most areas can be reached from all others through only a few interactions.<br />
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The complex interactions in the brain make it a perfect candidate to apply network theory. Neurons in the brain are deeply connected with one another and this results in complex networks being present in the structural and functional aspects of the brain. For instance, small-world network properties have been demonstrated in connections between cortical areas of the primate brain or during swallowing in humans. This suggests that cortical areas of the brain are not directly interacting with each other, but most areas can be reached from all others through only a few interactions.<br />
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大脑中的神经元之间有着复杂的相互作用,这使其成为网络理论应用的绝佳场合。大脑中的神经元联系紧密,其相互交织形成的复杂网络是人脑结构和功能的基础<ref>{{cite journal |author1=Bullmore, E. |author2=O. Sporns |lastauthoramp=yes |title= Complex brain networks: graph theoretical analysis of structural and functional systems |journal= Nature Reviews Neuroscience |year= 2009 |volume= 10 |issue= 3 |pages= 186–198 |doi=10.1038/nrn2575 |pmid=19190637}}</ref>。例如,灵长类动物大脑皮层各区域之间的连接<ref>{{cite journal |author= Stephan, K.E. |title= Computational analysis of functional connectivity between areas of primate cerebral cortex |journal= [[Philosophical Transactions of the Royal Society B]]|year= 2000 |volume= 355 |issue= 1393 |pages= 111–126 |doi=10.1098/rstb.2000.0552|pmid= 10703047 |display-authors=etal|pmc= 1692715}}</ref>或者人类吞咽时神经网络的行为都具有'''<font color="#ff8000">小世界网络small-world network </font>'''属性<ref>{{Cite journal|date=2016-12-01|title=Functional connectivity patterns of normal human swallowing: difference among various viscosity swallows in normal and chin-tuck head positions|journal=Brain Research|volume=1652|pages=158–169|doi=10.1016/j.brainres.2016.09.041|pmid=27693396|pmc=5102805|issn=0006-8993|last1=Jestrović|first1=Iva|last2=Coyle|first2=James L|last3=Perera|first3=Subashan|last4=Sejdić|first4=Ervin}}</ref>。这表明大脑皮层各区域并不直接相互作用,大部分通过少量节点区域相互沟通。<br />
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===Food webs===<br />
食物链网络<br />
{{main article|Food web}}<br />
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All organisms are connected to each other through feeding interactions. That is, if a species eats or is eaten by another species, they are connected in an intricate [[food web]] of predator and prey interactions. The stability of these interactions has been a long-standing question in ecology.<ref>{{cite journal |author= MacArthur, R.H. |author-link= Robert MacArthur|title= Fluctuations in animal populations and a measure of community stability |journal= Ecology |year= 1955 |volume= 36 |issue= 3 |pages= 533–536 |doi=10.2307/1929601|jstor= 1929601}}</ref> That is to say, if certain individuals are removed, what happens to the network (i.e. does it collapse or adapt)? Network analysis can be used to explore food web stability and determine if certain network properties result in more stable networks. Moreover, network analysis can be used to determine how selective removals of species will influence the food web as a whole.<ref>{{cite journal |author= Dunne, J.A. |title= Network structure and biodiversity loss in food webs: robustness increases with connectance |journal= Ecology Letters |year= 2002 |volume= 5 |issue= 4 |pages= 558–567 |doi=10.1046/j.1461-0248.2002.00354.x|display-authors=etal}}</ref> This is especially important considering the potential species loss due to global climate change.<br />
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All organisms are connected to each other through feeding interactions. That is, if a species eats or is eaten by another species, they are connected in an intricate food web of predator and prey interactions. The stability of these interactions has been a long-standing question in ecology. That is to say, if certain individuals are removed, what happens to the network (i.e. does it collapse or adapt)? Network analysis can be used to explore food web stability and determine if certain network properties result in more stable networks. Moreover, network analysis can be used to determine how selective removals of species will influence the food web as a whole. This is especially important considering the potential species loss due to global climate change.<br />
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生物可以通过进食相互作用产生关联<ref>{{cite journal |author= MacArthur, R.H. |author-link= Robert MacArthur|title= Fluctuations in animal populations and a measure of community stability |journal= Ecology |year= 1955 |volume= 36 |issue= 3 |pages= 533–536 |doi=10.2307/1929601|jstor= 1929601}}</ref>。也就是说,不管一个生物成为食物还是找到食物,它都会处于一个复杂的'''<font color="#ff8000">食物网 food web</font>'''中——在网中捕食者与被捕食者相互作用。这些相互作用的稳定性长期困扰着生态学家们。具体来说,人们想知道,某些个体被移除后会发生什么(即它是崩溃还是适应) ?网络分析方法可以用来研究食物网的稳定性,并确定某些网络特性是否会让网络更稳定。此外,网络分析方法还可以用来研究物种的选择性迁移如何影响整个食物网<ref>{{cite journal |author= Dunne, J.A. |title= Network structure and biodiversity loss in food webs: robustness increases with connectance |journal= Ecology Letters |year= 2002 |volume= 5 |issue= 4 |pages= 558–567 |doi=10.1046/j.1461-0248.2002.00354.x|display-authors=etal}}</ref>。考虑到全球气候变化可能导致大量物种消失,运用网络分析方法来研究食物链网的特性是十分重要的。<br />
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===Between-species interaction networks===<br />
物种间交互网络<br />
{{main article|social relation}}<br />
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In biology, pairwise interactions have historically been the focus of intense study. With the recent advances in [[network science]], it has become possible to scale up pairwise interactions to include individuals of many species involved in many sets of interactions to understand the structure and function of larger [[ecological network]]s.<ref>{{cite journal |author= Bascompte, J. |title= Disentangling the web of life |journal= Science |year= 2009 |volume=325 |issue= 5939 |pages= 416–419 |doi=10.1126/science.1170749 |pmid=19628856|bibcode=2009Sci...325..416B }}</ref> The use of [[Social network analysis|network analysis]] can allow for both the discovery and understanding how these complex interactions link together within the system’s network, a property which has previously been overlooked. This powerful tool allows for the study of various types of interactions (from [[competitive]] to [[cooperative]]) using the same general framework.<ref>{{cite journal |author= Krause, J. |title= Animal social networks: an introduction |journal= Behav. Ecol. Sociobiol. |year= 2009 |volume= 63 |issue= 7 |pages= 967–973 |doi=10.1007/s00265-009-0747-0|display-authors=etal}}</ref> For example, plant-[[pollinator]] interactions are mutually beneficial and often involve many different species of pollinators as well as many different species of plants. These interactions are critical to plant reproduction and thus the accumulation of resources at the base of the [[food chain]] for primary consumers, yet these interaction networks are threatened by [[Human impact on the environment|anthropogenic]] change. The use of network analysis can illuminate how [[pollination network]]s work and may in turn inform conservation efforts.<ref name="Memmott, J., et al. 2004 2605-261">{{cite journal |author= Memmott, J. |title= Tolerance of pollination networks to species extinctions |journal= [[Philosophical Transactions of the Royal Society B]] |year= 2004 |volume= 271 |issue= 1557 |pages= 2605–261 |doi=10.1098/rspb.2004.2909|pmid= 15615687 |pmc= 1691904 |display-authors=etal}}</ref> Within pollination networks, nestedness (i.e., specialists interact with a subset of species that generalists interact with), redundancy (i.e., most plants are pollinated by many pollinators), and [[modularity (networks)|modularity]] play a large role in network stability.<ref name="Memmott, J., et al. 2004 2605-261"/><ref name="Olesen, J., et al. 2007 19891–19896">{{cite journal |author= Olesen, J. |title= The modularity of pollination networks |journal= PNAS |year= 2007 |volume= 104 |issue= 50 |pages= 19891–19896 |doi=10.1073/pnas.0706375104|pmid= 18056808 |pmc= 2148393 |display-authors=etal|bibcode= 2007PNAS..10419891O }}</ref> These network properties may actually work to slow the spread of disturbance effects through the system and potentially buffer the pollination network from anthropogenic changes somewhat.<ref name="Olesen, J., et al. 2007 19891–19896"/> More generally, the structure of species interactions within an ecological network can tell us something about the diversity, richness, and robustness of the network.<ref>{{cite journal |author= Campbell, V. |title= Experimental design and the outcome and interpretation of diversity-stability relations |journal= Oikos |year= 2011 |volume= 120 |issue= 3 |pages= 399–408 |doi=10.1111/j.1600-0706.2010.18768.x|display-authors=etal}}</ref> Researchers can even compare current constructions of species interactions networks with historical reconstructions of ancient networks to determine how networks have changed over time.<ref>{{cite journal |author= Lotze, H. |title= Historical changes in marine resources, food-web structure and ecosystem functioning in the Adriatic Sea, Mediterranean |journal= Ecosystems |year= 2011 |volume= 14 |issue= 2 |pages= 198–222 |doi=10.1007/s10021-010-9404-8|display-authors=etal}}</ref> Recent research into these complex species interactions networks is highly concerned with understanding what factors (e.g., diversity) lead to network stability.<ref>{{cite journal |author= Romanuk, T. |title= Maintenance of positive diversity-stability relations along a gradient of environmental stress |journal= PLoS ONE |year= 2010 |volume= 5 |issue= 4 |pages= e10378 |doi=10.1371/journal.pone.0010378|display-authors=etal |pmid=20436913 |pmc=2860506|bibcode=2010PLoSO...510378R }}</ref><br />
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In biology, pairwise interactions have historically been the focus of intense study. With the recent advances in network science, it has become possible to scale up pairwise interactions to include individuals of many species involved in many sets of interactions to understand the structure and function of larger ecological networks. The use of network analysis can allow for both the discovery and understanding how these complex interactions link together within the system’s network, a property which has previously been overlooked. This powerful tool allows for the study of various types of interactions (from competitive to cooperative) using the same general framework. For example, plant-pollinator interactions are mutually beneficial and often involve many different species of pollinators as well as many different species of plants. These interactions are critical to plant reproduction and thus the accumulation of resources at the base of the food chain for primary consumers, yet these interaction networks are threatened by anthropogenic change. The use of network analysis can illuminate how pollination networks work and may in turn inform conservation efforts. Within pollination networks, nestedness (i.e., specialists interact with a subset of species that generalists interact with), redundancy (i.e., most plants are pollinated by many pollinators), and modularity play a large role in network stability. These network properties may actually work to slow the spread of disturbance effects through the system and potentially buffer the pollination network from anthropogenic changes somewhat. Researchers can even compare current constructions of species interactions networks with historical reconstructions of ancient networks to determine how networks have changed over time. Recent research into these complex species interactions networks is highly concerned with understanding what factors (e.g., diversity) lead to network stability.<br />
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在生物学中,'''<font color="#ff8000">成对相互作用 pairwise interactions </font>'''历来是研究重点。随着近几年网络科学的发展,我们可以进一步丰富成对相互作用这一概念,其外延甚至能涵盖有许多物种参与的多组相互作用,进而帮助我们理解'''<font color="#ff8000">生态网络 ecological networks </font>'''的结构和功能<ref>{{cite journal |author= Bascompte, J. |title= Disentangling the web of life |journal= Science |year= 2009 |volume=325 |issue= 5939 |pages= 416–419 |doi=10.1126/science.1170749 |pmid=19628856|bibcode=2009Sci...325..416B }}</ref>。运用网络分析方法可以帮助我们理解这些复杂的交互是如何连接成网络的——这是一个之前经常被忽略的过程。这个强大的工具让处于同一普适框架下的各类型的相互作用(从竞争到合作)研究成为可能<ref>{{cite journal |author= Krause, J. |title= Animal social networks: an introduction |journal= Behav. Ecol. Sociobiol. |year= 2009 |volume= 63 |issue= 7 |pages= 967–973 |doi=10.1007/s00265-009-0747-0|display-authors=etal}}</ref>。例如,植物与传粉者之间的相互作用是互惠互利的,这通常会涉及到许多不同种类的传粉者以及许多不同种类的植物。这些相互作用对植物生殖和食物链底层初级消费者的资源积累来说至关重要,然而这些相互作用网络正受到人为变化的威胁。网络分析方法的使用可以说明授粉网络是如何工作的,反过来也可以为相关植物保护工作提供必要信息<ref name="Memmott, J., et al. 2004 2605-261">{{cite journal |author= Memmott, J. |title= Tolerance of pollination networks to species extinctions |journal= [[Philosophical Transactions of the Royal Society B]] |year= 2004 |volume= 271 |issue= 1557 |pages= 2605–261 |doi=10.1098/rspb.2004.2909|pmid= 15615687 |pmc= 1691904 |display-authors=etal}}</ref>。在授粉网络中,'''<font color="#ff8000">内嵌性 nestedness</font>''' (某一领域的植物被少数昆虫授粉,剩下的昆虫只对少数几种植物授粉)、'''<font color="#ff8000">冗余性redundancy</font>''' (大多数植物是由许多授粉者授粉的)和'''<font color="#ff8000">模块性 modularity</font>'''(特定的物种之间有着紧密的连接,由此形成一个个团簇,也可称之为“模块”)在网络稳定性中扮演着重要角色<ref name="Memmott, J., et al. 2004 2605-261"/><ref name="Olesen, J., et al. 2007 19891–19896">{{cite journal |author= Olesen, J. |title= The modularity of pollination networks |journal= PNAS |year= 2007 |volume= 104 |issue= 50 |pages= 19891–19896 |doi=10.1073/pnas.0706375104|pmid= 18056808 |pmc= 2148393 |display-authors=etal|bibcode= 2007PNAS..10419891O }}</ref>。实际上,这些网络属性不仅可以减缓干扰效应在系统中的传播,还可能会缓冲授粉网络受到的人造变化的影响<ref>{{cite journal |author= Campbell, V. |title= Experimental design and the outcome and interpretation of diversity-stability relations |journal= Oikos |year= 2011 |volume= 120 |issue= 3 |pages= 399–408 |doi=10.1111/j.1600-0706.2010.18768.x|display-authors=etal}}</ref>。研究人员甚至可以将物种相互作用网络的现有结构与过去结构进行比较,以确定网络在时间尺度上是如何演化的<ref>{{cite journal |author= Lotze, H. |title= Historical changes in marine resources, food-web structure and ecosystem functioning in the Adriatic Sea, Mediterranean |journal= Ecosystems |year= 2011 |volume= 14 |issue= 2 |pages= 198–222 |doi=10.1007/s10021-010-9404-8|display-authors=etal}}</ref>。最近对这些复杂物种相互作用网络的研究集中于分析是什么因素(如'''<font color="#ff8000">多样性diversity</font>''')造就了网络的稳定性<ref>{{cite journal |author= Romanuk, T. |title= Maintenance of positive diversity-stability relations along a gradient of environmental stress |journal= PLoS ONE |year= 2010 |volume= 5 |issue= 4 |pages= e10378 |doi=10.1371/journal.pone.0010378|display-authors=etal |pmid=20436913 |pmc=2860506|bibcode=2010PLoSO...510378R }}</ref>。<br />
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===Within-species interaction networks===<br />
物种内交互网络<br />
{{main article|social relation}}<br />
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Network analysis provides the ability to quantify associations between individuals, which makes it possible to infer details about the network as a whole at the species and/or population level.<ref>{{cite journal |author= Croft, D.P |title= Social networks in the guppy (Poecilia reticulate) |journal= [[Philosophical Transactions of the Royal Society B]] |year= 2004 |volume= 271 |issue= Suppl |pages= S516–S519 |doi=10.1098/rsbl.2004.0206|pmid= 15801620 |pmc= 1810091 |display-authors=etal}}</ref> One of the most attractive features of the network paradigm would be that it provides a single conceptual framework in which the social organisation of animals at all levels (individual, dyad, group, population) and for all types of interaction (aggressive, cooperative, sexual etc.) can be studied.<ref>{{Cite journal|last=Krause, Lusseau, James|first=Jens, David, Richard|date=1 May 2009|title=Animal social networks: an introduction|url=https://www.researchgate.net/publication/226996156_Animal_social_networks_An_introduction|journal=Behavioral Ecology and Sociobiology|volume=63|pages=967-973|doi=10.1007/s00265-009-0747-0|via=}}</ref><br />
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Network analysis provides the ability to quantify associations between individuals, which makes it possible to infer details about the network as a whole at the species and/or population level. One of the most attractive features of the network paradigm would be that it provides a single conceptual framework in which the social organisation of animals at all levels (individual, dyad, group, population) and for all types of interaction (aggressive, cooperative, sexual etc.) can be studied.<br />
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网络分析方法可以量化个体之间的关联,我们由此得以在物种和/或种群水平推断整个网络的细节<ref>{{cite journal |author= Croft, D.P |title= Social networks in the guppy (Poecilia reticulate) |journal= [[Philosophical Transactions of the Royal Society B]] |year= 2004 |volume= 271 |issue= Suppl |pages= S516–S519 |doi=10.1098/rsbl.2004.0206|pmid= 15801620 |pmc= 1810091 |display-authors=etal}}</ref>。网络范式最吸引人的特征之一就是,它提供了一个统一的概念框架,各层次(单,双,组,群)的动物和各类型的互动中(攻击,合作,性等等)都被囊括其中<ref>{{Cite journal|last=Krause, Lusseau, James|first=Jens, David, Richard|date=1 May 2009|title=Animal social networks: an introduction|url=https://www.researchgate.net/publication/226996156_Animal_social_networks_An_introduction|journal=Behavioral Ecology and Sociobiology|volume=63|pages=967-973|doi=10.1007/s00265-009-0747-0|via=}}</ref><br />
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Researchers interested in [[ethology]] across a multitude of taxa, from insects to primates, are starting to incorporate network analysis into their research. Researchers interested in social insects (e.g., ants and bees) have used network analyses to better understand division of labor, task allocation, and foraging optimization within colonies;<ref>{{cite journal |author= Dornhaus, A. |title= Benefits of recruitment in honey bees: Effects of ecology and colony size in an individual-based model |journal= Behavioral Ecology |year= 2006 |volume=17 |issue= 3 |pages= 336–344 |doi=10.1093/beheco/arj036|display-authors=etal|doi-access= free }}</ref><ref>{{cite journal |author= Linksvayer, T. |title= Developmental evolution in social insects: Regulatory networks from genes to societies |journal= Journal of Experimental Zoology Part B: Molecular and Developmental Evolution |year= 2012 |volume=318 |issue= 3 |pages= 159–169 |doi=10.1002/jez.b.22001|pmid= 22544713 |display-authors=etal}}</ref><ref>{{cite journal |author= Mullen, R. |title= A review of ant algorithms |journal= Expert Systems with Applications |year= 2009 |volume=36 |issue= 6 |pages= 9608–9617 |doi=10.1016/j.eswa.2009.01.020|display-authors=etal}}</ref> Other researchers are interested in how certain network properties at the group and/or population level can explain individual level behaviors. Studies have demonstrated how animal social network structure can be influenced by factors ranging from characteristics of the environment to characteristics of the individual, such as developmental experience and personality. At the level of the individual, the patterning of social connections can be an important determinant of [[Fitness (biology)|fitness]], predicting both survival and reproductive success. At the population level, network structure can influence the patterning of ecological and evolutionary processes, such as [[frequency-dependent selection]] and disease and information transmission.<ref>{{Cite journal|last=Croft, Darden, Wey|first=Darren P., Safi K., Tina W.|date=2016|title=Current directions in animal social networks|url=https://www.researchgate.net/publication/310819524_Current_directions_in_animal_social_networks|journal=Current Opinion in Behavioral Sciences|volume=12|pages=52-58|doi=10.1016/j.cobeha.2016.09.001|via=|hdl=10871/23348|hdl-access=free}}</ref> For instance, a study on [[Wire-tailed manakin|wire-tailed manakins]] (a small passerine bird) found that a male’s [[degree (graph theory)|degree]] in the network largely predicted the ability of the male to rise in the social hierarchy (i.e. eventually obtain a territory and matings).<ref>{{cite journal |author= Ryder, T.B. |title= Social networks in the lek-mating wire-tailed manakin (''Pipra filicauda'') |journal= [[Philosophical Transactions of the Royal Society B]] |year= 2008 |volume= 275 |issue= 1641 |pages= 1367–1374 |doi=10.1098/rspb.2008.0205 |pmid=18381257 |pmc=2602714|display-authors=etal}}</ref> In [[bottlenose dolphin]] groups, an individual’s degree and [[betweenness centrality]] values may predict whether or not that individual will exhibit certain behaviors, like the use of side flopping and upside-down lobtailing to lead group traveling efforts; individuals with high betweenness values are more connected and can obtain more information, and thus are better suited to lead group travel and therefore tend to exhibit these signaling behaviors more than other group members.<ref>{{cite journal |author= Lusseau, D. |title= Evidence for social role in a dolphin social network |journal= Evolutionary Ecology |year= 2007 |volume=21 |issue= 3 |pages= 357–366 |doi=10.1007/s10682-006-9105-0|arxiv= q-bio/0607048 }}</ref> <br />
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Researchers interested in ethology across a multitude of taxa, from insects to primates, are starting to incorporate network analysis into their research. Researchers interested in social insects (e.g., ants and bees) have used network analyses to better understand division of labor, task allocation, and foraging optimization within colonies; Other researchers are interested in how certain network properties at the group and/or population level can explain individual level behaviors. Studies have demonstrated how animal social network structure can be influenced by factors ranging from characteristics of the environment to characteristics of the individual, such as developmental experience and personality. At the level of the individual, the patterning of social connections can be an important determinant of fitness, predicting both survival and reproductive success. At the population level, network structure can influence the patterning of ecological and evolutionary processes, such as frequency-dependent selection and disease and information transmission. For instance, a study on wire-tailed manakins (a small passerine bird) found that a male’s degree in the network largely predicted the ability of the male to rise in the social hierarchy (i.e. eventually obtain a territory and matings). In bottlenose dolphin groups, an individual’s degree and betweenness centrality values may predict whether or not that individual will exhibit certain behaviors, like the use of side flopping and upside-down lobtailing to lead group traveling efforts; individuals with high betweenness values are more connected and can obtain more information, and thus are better suited to lead group travel and therefore tend to exhibit these signaling behaviors more than other group members. <br />
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从昆虫到灵长类动物,对'''<font color="#ff8000">动物行为学 ethology</font>'''感兴趣的研究人员开始将网络分析纳入到研究之中。对社会性昆虫(如蚂蚁和蜜蜂)感兴趣的研究人员利用网络分析来更好地理解群体内昆虫的分工、任务分配和'''<font color="#ff8000">最优化觅食 foraging optimization</font>'''<ref>{{cite journal |author= Dornhaus, A. |title= Benefits of recruitment in honey bees: Effects of ecology and colony size in an individual-based model |journal= Behavioral Ecology |year= 2006 |volume=17 |issue= 3 |pages= 336–344 |doi=10.1093/beheco/arj036|display-authors=etal|doi-access= free }}</ref><ref>{{cite journal |author= Linksvayer, T. |title= Developmental evolution in social insects: Regulatory networks from genes to societies |journal= Journal of Experimental Zoology Part B: Molecular and Developmental Evolution |year= 2012 |volume=318 |issue= 3 |pages= 159–169 |doi=10.1002/jez.b.22001|pmid= 22544713 |display-authors=etal}}</ref><ref>{{cite journal |author= Mullen, R. |title= A review of ant algorithms |journal= Expert Systems with Applications |year= 2009 |volume=36 |issue= 6 |pages= 9608–9617 |doi=10.1016/j.eswa.2009.01.020|display-authors=etal}}</ref>; 其他研究人员感兴趣的点则在于群体和/或种群水平的某些网络特性如何影响个体行为。研究表明,环境特征和个体特征——如经验发展和人格等因素——会影响动物的社会网络结构。在个体层面上,社会联系的模式是个体适应性的一个关键因素,可能决定着个体生存和繁殖的成功概率。在种群水平上,网络结构可以影响生态和进化过程的模式,如频率依赖性选择、疾病、信息的传递<ref>{{Cite journal|last=Croft, Darden, Wey|first=Darren P., Safi K., Tina W.|date=2016|title=Current directions in animal social networks|url=https://www.researchgate.net/publication/310819524_Current_directions_in_animal_social_networks|journal=Current Opinion in Behavioral Sciences|volume=12|pages=52-58|doi=10.1016/j.cobeha.2016.09.001|via=|hdl=10871/23348|hdl-access=free}}</ref>。例如,一项针对线尾 (一种小型雀形目鸟)的研究发现,网络中雄性个体的度值在很大程度上预测了雄性在社会等级中进阶的能力(即最终获得领地和交配机会的能力) <ref>{{cite journal |author= Ryder, T.B. |title= Social networks in the lek-mating wire-tailed manakin (''Pipra filicauda'') |journal= [[Philosophical Transactions of the Royal Society B]] |year= 2008 |volume= 275 |issue= 1641 |pages= 1367–1374 |doi=10.1098/rspb.2008.0205 |pmid=18381257 |pmc=2602714|display-authors=etal}}</ref>。在宽吻海豚群体中,个体的度值和介数中心性可以预测个体是否会表现出某些行为,比如使用侧翻和潜入水中尾巴举向空中来表达自己领导团队迁移的意愿; 介数值较高的个体与外界有更多的关联,可以获得更多信息,因此更适合领导团队迁行,因此比其他团队成员相比,它们更倾向于去传递这些信号<ref>{{cite journal |author= Lusseau, D. |title= Evidence for social role in a dolphin social network |journal= Evolutionary Ecology |year= 2007 |volume=21 |issue= 3 |pages= 357–366 |doi=10.1007/s10682-006-9105-0|arxiv= q-bio/0607048 }}</ref>。<br />
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[[Social network analysis]] can also be used to describe the social organization within a species more generally, which frequently reveals important proximate mechanisms promoting the use of certain behavioral strategies. These descriptions are frequently linked to ecological properties (e.g., resource distribution). For example, network analyses revealed subtle differences in the group dynamics of two related equid [[fission-fusion society|fission-fusion]] species, [[Grevy’s zebra]] and [[onager]]s, living in variable environments; Grevy’s zebras show distinct preferences in their association choices when they fission into smaller groups, whereas onagers do not.<ref>{{cite journal |author= Sundaresan, S. |title= Network metrics reveal differences in social organization between two fission-fusion species, Grevy's zebra and onager |journal= Oecologia |year= 2007 |volume= 151 |issue= 1 |pages= 140–149 |doi=10.1007/s00442-006-0553-6|pmid= 16964497 |display-authors=etal|bibcode= 2007Oecol.151..140S }}</ref> Similarly, researchers interested in primates have also utilized network analyses to compare social organizations across the diverse [[primate]] order, suggesting that using network measures (such as [[centrality]], [[assortativity]], [[modularity (networks)|modularity]], and betweenness) may be useful in terms of explaining the types of social behaviors we see within certain groups and not others.<ref>{{cite journal |author1=Kasper, C. |author2=Voelkl, B. |title= A social network analysis of primate groups |journal= Primates |year= 2009 |volume= 50 |issue=4 |pages= 343–356 |doi=10.1007/s10329-009-0153-2|pmid=19533270 }}</ref> <br />
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Social network analysis can also be used to describe the social organization within a species more generally, which frequently reveals important proximate mechanisms promoting the use of certain behavioral strategies. These descriptions are frequently linked to ecological properties (e.g., resource distribution). For example, network analyses revealed subtle differences in the group dynamics of two related equid fission-fusion species, Grevy’s zebra and onagers, living in variable environments; Grevy’s zebras show distinct preferences in their association choices when they fission into smaller groups, whereas onagers do not. Similarly, researchers interested in primates have also utilized network analyses to compare social organizations across the diverse primate order, suggesting that using network measures (such as centrality, assortativity, modularity, and betweenness) may be useful in terms of explaining the types of social behaviors we see within certain groups and not others. <br />
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'''<font color="#ff8000">社会网络分析 social network analysis </font>'''也可以用来广泛描述物种内的社会组织,它经常揭示出那些能够促进某些行为策略使用的重要邻近机制。这些描述经常与生态属性(例如资源分配)联系在一起。例如,网络分析方法揭示了生活在变化环境中的两个相关等裂变融合物种——格雷维斑马和骑驴——的群体动力学的细微差异; 格雷维斑马在分裂为较小的群体时,在同伴选择上表现出明显的偏好,而骑驴则不然<ref>{{cite journal |author= Sundaresan, S. |title= Network metrics reveal differences in social organization between two fission-fusion species, Grevy's zebra and onager |journal= Oecologia |year= 2007 |volume= 151 |issue= 1 |pages= 140–149 |doi=10.1007/s00442-006-0553-6|pmid= 16964497 |display-authors=etal|bibcode= 2007Oecol.151..140S }}</ref>。同样,对灵长类动物感兴趣的研究人员也利用网络分析方法来比较不同灵长类动物的社会组织,这表明以网络的视角进行测量(如集中性、协调性、模块性和中介性)可能有助于我们理解在某些特定群体中看到的社会行为<ref>{{cite journal |author1=Kasper, C. |author2=Voelkl, B. |title= A social network analysis of primate groups |journal= Primates |year= 2009 |volume= 50 |issue=4 |pages= 343–356 |doi=10.1007/s10329-009-0153-2|pmid=19533270 }}</ref> <br />
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Finally, social network analysis can also reveal important fluctuations in animal behaviors across changing environments. For example, network analyses in female [[chacma baboon]]s (''Papio hamadryas ursinus'') revealed important dynamic changes across seasons which were previously unknown; instead of creating stable, long-lasting social bonds with friends, baboons were found to exhibit more variable relationships which were dependent on short-term contingencies related to group level dynamics as well as environmental variability.<ref>{{cite journal |author= Henzi, S. |title= Cyclicity in the structure of female baboon social networks |journal= Behavioral Ecology and Sociobiology |year= 2009 |volume= 63 |issue= 7 |pages= 1015–1021 |doi=10.1007/s00265-009-0720-y|display-authors=etal}}</ref> Changes in an individual's social network environment can also influence characteristics such as 'personality': for example, social spiders that huddle with bolder neighbours tend to increase also in boldness.<ref>{{cite journal |author= Hunt, ER. |title= Social interactions shape individual and collective personality in social spiders |journal= Proceedings of the Royal Society B |year= 2018 |volume= 285 |issue= 1886 |pages= 20181366 |doi=10.1098/rspb.2018.1366|pmid= 30185649 |pmc= 6158534 |display-authors=etal}}</ref> This is a very small set of broad examples of how researchers can use network analysis to study animal behavior. Research in this area is currently expanding very rapidly, especially since the broader development of animal borne tags and [[computer vision]] that can be used to automate the collection of social associations.<ref>{{Cite journal|last=Krause J, Krause S, Arlinghaus R, Psorakis I, Roberts S, Rutz C|first=|date=2013|title=Reality mining of animal social systems.|url=https://risweb.st-andrews.ac.uk/portal/en/researchoutput/reality-mining-of-animal-social-systems(570e21d0-527e-4275-8926-c4b479c55ee4).html|journal=Trends in Ecology and Evolution|volume=28|pages=541-551|doi=10.1016/j.tree.2013.06.002|via=}}</ref> Social network analysis is a valuable tool for studying animal behavior across all animal species, and has the potential to uncover new information about animal behavior and social ecology that was previously poorly understood.<br />
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Finally, social network analysis can also reveal important fluctuations in animal behaviors across changing environments. For example, network analyses in female chacma baboons (Papio hamadryas ursinus) revealed important dynamic changes across seasons which were previously unknown; instead of creating stable, long-lasting social bonds with friends, baboons were found to exhibit more variable relationships which were dependent on short-term contingencies related to group level dynamics as well as environmental variability. Changes in an individual's social network environment can also influence characteristics such as 'personality': for example, social spiders that huddle with bolder neighbours tend to increase also in boldness. This is a very small set of broad examples of how researchers can use network analysis to study animal behavior. Research in this area is currently expanding very rapidly, especially since the broader development of animal borne tags and computer vision that can be used to automate the collection of social associations. Social network analysis is a valuable tool for studying animal behavior across all animal species, and has the potential to uncover new information about animal behavior and social ecology that was previously poorly understood.<br />
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最后,社会网络分析还可以揭示动物行为在环境变化时的关键波动。例如,对雌性沙卡马狒狒的网络分析揭示了该群体中重要的跨季动态变化; 研究结果发现,狒狒之间没有建立稳定、持久的社会联系。恰恰相反,它们之间的关系是多变的。这些关系取决于动态群体层面发生的短期偶然事件以及环境的变化<ref>{{cite journal |author= Henzi, S. |title= Cyclicity in the structure of female baboon social networks |journal= Behavioral Ecology and Sociobiology |year= 2009 |volume= 63 |issue= 7 |pages= 1015–1021 |doi=10.1007/s00265-009-0720-y|display-authors=etal}}</ref>。个体社交网络环境的变化也会影响个体的性格特点。例如,与胆大的邻居挤在一起的蜘蛛也会更加大胆<ref>{{cite journal |author= Hunt, ER. |title= Social interactions shape individual and collective personality in social spiders |journal= Proceedings of the Royal Society B |year= 2018 |volume= 285 |issue= 1886 |pages= 20181366 |doi=10.1098/rspb.2018.1366|pmid= 30185649 |pmc= 6158534 |display-authors=etal}}</ref>。关于运用网络分析方法研究动物行为的实践,以上展示的是一小部分研究成果。这一领域的研究目前正在迅速扩展。特别是随着'''<font color="#ff8000">动物身体标记技术 animal borne tags</font>'''和'''<font color="#ff8000">计算机视觉技术computer vision</font>'''的发展,个体社会关系的收集变得更加自动化<ref>{{Cite journal|last=Krause J, Krause S, Arlinghaus R, Psorakis I, Roberts S, Rutz C|first=|date=2013|title=Reality mining of animal social systems.|url=https://risweb.st-andrews.ac.uk/portal/en/researchoutput/reality-mining-of-animal-social-systems(570e21d0-527e-4275-8926-c4b479c55ee4).html|journal=Trends in Ecology and Evolution|volume=28|pages=541-551|doi=10.1016/j.tree.2013.06.002|via=}}</ref>。社会网络分析是研究物种行为的有效工具,并且有可能帮助我们发现鲜为人知的与动物行为和社会生态相关的新信息。<br />
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==See also==<br />
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* [[List of omics topics in biology]]<br />
生物学中的组学<br />
* [[Biological network inference]]<br />
生物网络推理<br />
* [[Applied Statistics]]<br />
应用统计学<br />
* [[Biostatistics]]<br />
生物统计学<br />
* [[Computational Biology]]<br />
计算生物学<br />
* [[Systems biology]]<br />
系统生物学<br />
* [[Weighted correlation network analysis]] <br />
权重相关性网络分析<br />
* [[Interactome]]<br />
交互组<br />
* [[Network medicine]]<br />
网络医学<br />
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== External links ==<br />
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* [http://www.nettab.org Network Tools and Applications in Biology] (NETTAB) workshops.<br />
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==References==<br />
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{{Reflist}}<br />
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==Books==<br />
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*E. Estrada, "The Structure of Complex Networks: Theory and Applications", Oxford University Press, 2011, {{ISBN|978-0-199-59175-6}}<br />
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*J. Krause, R. James, D. Franks, D. Croft, "Animal Social Networks", Oxford University Press, 2015, {{ISBN|978-0199679041}}<br />
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==External links==<br />
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* [https://web.archive.org/web/20110920220214/http://www.networkbio.org/ Networkbio.org], The site of the series of Integrative Network Biology (INB) meetings. For the 2012 event also see www.networkbio.org<br />
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* [http://networkbiology.org Networkbiology.org], NetworkBiology wiki site.<br />
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* [http://www.lindinglab.org LindingLab.org], Technical University of Denmark (DTU) studies Network Biology and Cellular Information Processing, and is also organizing the Denmark branch of the annual "[http://www.lindinglab.org/events ''Integrative Network Biology and Cancer'']" symposium series.<br />
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* [http://nrnb.org NRNB.org], The National Resource for Network Biology. A US National Institute of Health (NIH) Biomedical Technology Research Center dedicated to the study of biological networks.<br />
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*[http://networkrepository.com/asn.php Network Repository] The first interactive data and network data repository with real-time visual analytics.<br />
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*[https://bansallab.github.io/asnr/ Animal Social Network Repository(ASNR)] The first multi-taxonomic repository that collates 790 social networks from more than 45 species, including those of mammals, reptiles, fish, birds, and insects <br />
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*[http://konect.uni-koblenz.de/networks/ KONECT – Koblenz network collection.]<br />
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[[Category:Biological techniques and tools]]<br />
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Category:Biological techniques and tools<br />
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类别: 生物技术和工具<br />
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[[Category:Bioinformatics]]<br />
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Category:Bioinformatics<br />
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类别: 生物信息学<br />
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[[Category:Systems biology]]<br />
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Category:Systems biology<br />
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分类: 系统生物学<br />
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[[Category:Networks]]<br />
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Category:Networks<br />
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类别: 网络<br />
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<small>This page was moved from [[wikipedia:en:Biological network]]. Its edit history can be viewed at [[生物网络/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21868互信息2021-02-18T01:49:02Z<p>Vicky:/* 应用 Applications */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
<br />
Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>也展示了如何对除互信息之外的许多其他信息理论性质进行贝叶斯估计。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>这一内容,并进行了扩展<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
请参阅<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>最近的一篇论文,该论文基于先验知识对互信息本身进行估计。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in less extreme factorizations; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对非极端因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变种 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变种。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
<br />
<br />
==== 多元统计独立性 Multivariate statistical independence ====<br />
<br />
The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
<br />
The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
<br />
<br />
多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
<br />
<br />
==== 应用 Applications ====<br />
<br />
For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
<br />
For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
<br />
对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
<br />
<br />
<br />
<br />
<br />
One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
<br />
<br />
One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
<br />
目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
<br />
Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
<br />
Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
<br />
互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
<br />
=== 定向信息 Directed information ===<br />
<br />
[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
<br />
Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
<br />
'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
<br />
<br />
:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
<br />
= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
<br />
<br />
<br />
Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
<br />
Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
<br />
注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
<br />
=== 归一化变量 Normalized variants ===<br />
<br />
Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
<br />
Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
<br />
互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
<br />
:<math><br />
<br />
C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
<br />
~~~~\mbox{和}~~~~ <br />
<br />
C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
<br />
</math><br />
<br />
<br />
<br />
The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
<br />
The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
<br />
这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
<br />
:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
<br />
<br />
<br />
<br />
which attains a minimum of zero when the variables are independent and a maximum value of<br />
<br />
which attains a minimum of zero when the variables are independent and a maximum value of<br />
<br />
当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
<br />
<br />
:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
<br />
<br />
<br />
<br />
when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
<br />
when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
<br />
当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
<br />
<br />
<br />
<br />
<br />
Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
<br />
Another symmetrical measure is the symmetric uncertainty , given by<br />
<br />
另一个对称度量是''对称不确定度'',由下式表示:<br />
<br />
<br />
:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
<br />
<br />
<br />
<br />
<br />
which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
<br />
which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
<br />
它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
<br />
<br />
<br />
<br />
<br />
If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
<br />
If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
<br />
如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
<br />
:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
<br />
<br />
<br />
This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
<br />
<br />
This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
<br />
这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
<br />
:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
<br />
= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
<br />
= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
<br />
<br />
<br />
<br />
There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
<br />
<br />
<br />
There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
<br />
有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
<br />
</math><br />
<br />
<br />
=== 加权变量 Weighted variants ===<br />
<br />
In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
<br />
在互信息的传统表述中:<br />
<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) <br />
<br />
= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
<br />
each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
<br />
<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
<br />
<br />
<br />
<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
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<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
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=== 线性相关 Linear correlation ===<br />
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Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
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== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
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<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
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在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
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* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
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现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
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* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
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RNA secondary structure prediction from a multiple sequence alignment.<br />
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从多序列比对预测RNA二级结构。<br />
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* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
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Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
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功能连锁基因成对存在与消失的系统发育模式预测。<br />
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* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
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* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
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时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
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* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
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* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
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Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
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ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
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* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
<br />
* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
<br />
<br />
* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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<br />
* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
<br />
| first4 = S.<br />
<br />
| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
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| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21867互信息2021-02-18T01:48:32Z<p>Vicky:/* 应用 Applications */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>也展示了如何对除互信息之外的许多其他信息理论性质进行贝叶斯估计。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>这一内容,并进行了扩展<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
请参阅<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>最近的一篇论文,该论文基于先验知识对互信息本身进行估计。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in less extreme factorizations; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对非极端因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变种 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变种。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
<br />
<br />
==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
<br />
<br />
One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
<br />
Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
<br />
= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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<br />
<br />
:<math><br />
<br />
\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
<br />
</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
<br />
在互信息的传统表述中:<br />
<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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<br />
<br />
each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
<br />
each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的'''<font color="#ff8000">兰德指数 Rand index</font>'''相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
<br />
* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
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* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
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| first4 = S.<br />
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| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
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| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21866互信息2021-02-18T01:43:03Z<p>Vicky:/* 变形 Variations */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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<font color="#32cd32"> </font><br />
互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>也展示了如何对除互信息之外的许多其他信息理论性质进行贝叶斯估计。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>这一内容,并进行了扩展<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
请参阅<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>最近的一篇论文,该论文基于先验知识对互信息本身进行估计。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in less extreme factorizations; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对非极端因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变种 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变种。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
<br />
<br />
==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
<br />
<br />
One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
<br />
Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
<br />
= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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<br />
<br />
:<math><br />
<br />
\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
<br />
</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
<br />
在互信息的传统表述中:<br />
<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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<br />
<br />
each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
<br />
each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
<br />
* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
<br />
<br />
* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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<br />
* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
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| first4 = S.<br />
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| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
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| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21666互信息2021-02-07T11:36:14Z<p>Vicky:/* 独立性假设 Independence assumptions */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>也展示了如何对除互信息之外的许多其他信息理论性质进行贝叶斯估计。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>这一内容,并进行了扩展<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
请参阅<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>最近的一篇论文,该论文基于先验知识对互信息本身进行估计。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in less extreme factorizations; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对非极端因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变形 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变形。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
<br />
<br />
==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
<br />
<br />
One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
<br />
Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
<br />
= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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<br />
<br />
:<math><br />
<br />
\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
<br />
</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
<br />
在互信息的传统表述中:<br />
<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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<br />
<br />
each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
<br />
each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
<br />
* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
<br />
<br />
* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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<br />
* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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<br />
* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
<br />
| first4 = S.<br />
<br />
| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
<br />
| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21648互信息2021-02-07T09:38:49Z<p>Vicky:/* 互信息的贝叶斯估计 Bayesian estimation of mutual information */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>也展示了如何对除互信息之外的许多其他信息理论性质进行贝叶斯估计。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>这一内容,并进行了扩展<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
请参阅<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>最近的一篇论文,该论文基于先验知识对互信息本身进行估计。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in '''<font color="#32CD32">less extreme factorizations</font>'''; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对较不极端的因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变形 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变形。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
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==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
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Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
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= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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:<math><br />
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\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
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</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
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在互信息的传统表述中:<br />
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:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
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each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
<br />
* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
<br />
<br />
* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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<br />
* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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<br />
* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
<br />
| first4 = S.<br />
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| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
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| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21647互信息2021-02-07T09:11:02Z<p>Vicky:/* 互信息的贝叶斯估计 Bayesian estimation of mutual information */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>也展示了如何对除互信息之外的许多其他信息理论性质进行贝叶斯估计。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>这一内容,并进行了扩展<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
最近的一篇论文<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>中基于一个专门针对互信息本身估计的先验知识。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in '''<font color="#32CD32">less extreme factorizations</font>'''; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对较不极端的因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变形 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变形。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
<br />
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==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
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Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
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= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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:<math><br />
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\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
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</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
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在互信息的传统表述中:<br />
<br />
<br />
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:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
<br />
each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
<br />
* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
<br />
<br />
* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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<br />
* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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<br />
* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
<br />
| first4 = S.<br />
<br />
| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
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| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21646互信息2021-02-07T08:48:03Z<p>Vicky:/* 互信息的贝叶斯估计 Bayesian estimation of mutual information */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是很容易理解的。<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
关于这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>,它还展示了如何对贝叶斯估计进行除互信息之外的许多其他信息理论性质。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>内容,并扩展了<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
最近的一篇论文<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>中基于一个专门针对互信息本身估计的先验知识。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in '''<font color="#32CD32">less extreme factorizations</font>'''; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对较不极端的因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变形 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变形。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
<br />
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==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
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Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
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= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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:<math><br />
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\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
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</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
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在互信息的传统表述中:<br />
<br />
<br />
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:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
<br />
each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
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* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
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* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| first2 = P.<br />
| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
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| first4 = S.<br />
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| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
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| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%BA%92%E4%BF%A1%E6%81%AF&diff=21645互信息2021-02-07T08:40:53Z<p>Vicky:/* 定义 Definition */</p>
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<div>已由[[用户:Yillia Jing]]进行初步翻译,已由[[用户:Flipped]]进行审校。{{Information theory}}<br />
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[[File:Entropy-mutual-information-relative-entropy-relation-diagram.svg|thumb|256px|right|[[Venn diagram]] showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the [[joint entropy 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。]] <br />
--[[用户:趣木木|趣木木]]([[用户讨论:趣木木|讨论]])图片应该按照[图1:英文+中文]<br />
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<math>H(X,Y)</math>. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] <math>H(X)</math>, with the red being the [[conditional entropy]] <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the [[mutual information]] <math>\operatorname{I}(X;Y)</math>. 这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual information(MI) '''</font><math>\operatorname{I}(X;Y)</math>)。]]<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables <math>X</math> and <math>Y</math>. The area contained by both circles is the joint entropy <math>H(X,Y)</math>. The circle on the left (red and violet) is the individual entropy <math>H(X)</math>, with the red being the conditional entropy <math>H(X|Y)</math>. The circle on the right (blue and violet) is <math>H(Y)</math>, with the blue being <math>H(Y|X)</math>. The violet is the mutual information <math>\operatorname{I}(X;Y)</math>.<br />
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Venn diagram showing additive and subtractive relationships various information measures associated with correlated variables 𝑋 and 𝑌. The area contained by both circles is the joint entropy H(𝑋,𝑌). The circle on the left (red and violet) is the individual entropy H(𝑋), with the red being the conditional entropy H(𝑋|𝑌). The circle on the right (blue and violet) is H(𝑌), with the blue being H(𝑌|𝑋). The violet is the mutual information I(𝑋;𝑌).<br />
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这里的维恩图显示了各种信息间的交并补运算关系,这些信息都可以用来度量变量<math>X</math>和<math>Y</math>的各种相关性。图中所有面积(包括两个圆圈)表示二者的<font color="#ff8000"> '''联合熵 Joint Entropy'''</font><math>H(X,Y)</math>。左侧的整个圆圈表示变量<math>X</math>的<font color="#ff8000"> '''独立熵 Individual Entropy'''</font><math>H(X)</math>,红色(差集)部分表示X的<font color="#ff8000"> '''条件熵 Conditional Entropy'''</font><math>H(X|Y)</math>。右侧的整个圆圈表示变量<math>Y</math>的独立熵<math>H(Y)</math>,蓝色(差集)部分表示X的条件熵<math>H(Y|X)</math>。两个圆中间的交集部分(紫色的部分)表示二者的<font color="#ff8000">'''互信息 Mutual Information,(MI)'''</font><math>\operatorname{I}(X;Y)</math>)。<br />
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In [[probability theory]] and [[information theory]], the '''mutual information''' ('''MI''') of two [[random variable]]s is a measure of the mutual [[Statistical dependence|dependence]] between the two variables. More specifically, it quantifies the "amount of information" (in [[unit of measurement|unit]]s such as [[shannon (unit)|shannon]]s, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of [[Entropy (information theory)|entropy]] of a random variable, a fundamental notion in information theory that quantifies the expected "[[Information content|amount of information]]" held in a random variable.<br />
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In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two variables. More specifically, it quantifies the "amount of information" (in units such as shannons, commonly called bits) obtained about one random variable through observing the other random variable. The concept of mutual information is intricately linked to that of entropy of a random variable, a fundamental notion in information theory that quantifies the expected "amount of information" held in a random variable.<br />
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在<font color="#ff8000"> '''概率论 Probability Theory'''</font>和<font color="#ff8000"> '''信息论 Information Theory'''</font>理论中,两个随机变量的互信息是两个变量之间相互依赖程度的度量。更具体地说,通过观察一个随机变量而可以获得的关于另一个随机变量的“信息量”,互信息将其量化(单位如''香农 Shannons'',通常称为比特)。互信息的概念与随机变量的熵之间有着错综复杂的联系,熵是信息论中的一个基本概念,它量化了随机变量中所包含的预期“信息量”。<br />
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Not limited to real-valued random variables and linear dependence like the [[correlation coefficient]], MI is more general and determines how different the [[joint distribution]] of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the [[expected value]] of the [[pointwise mutual information]] (PMI).<br />
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Not limited to real-valued random variables and linear dependence like the correlation coefficient, MI is more general and determines how different the joint distribution of the pair <math>(X,Y)</math> is to the product of the marginal distributions of <math>X</math> and <math>Y</math>. MI is the expected value of the pointwise mutual information (PMI).<br />
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不仅限于实值随机变量和线性相关性(如相关系数),互信息表示的关系其实更加普遍,它决定了一对变量<math>(X,Y)</math>的联合分布与<math>X</math>和<math>Y</math>的<font color="#ff8000">'''边缘分布 Marginal Distributions'''</font>之积的不同程度。互信息是'''点互信息 Pointwise Mutual Information,PMI'''的期望值。<br />
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Mutual Information is also known as [[information gain]].<br />
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Mutual Information is also known as information gain.<br />
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互信息也称为<font color="#ff8000">'''信息增益 Information Gain'''</font>。<br />
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== 定义 Definition ==<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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Let <math>(X,Y)</math> be a pair of random variables with values over the space <math>\mathcal{X}\times\mathcal{Y}</math>. If their joint distribution is <math>P_{(X,Y)}</math> and the marginal distributions are <math>P_X</math> and <math>P_Y</math>, the mutual information is defined as<br />
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设一对随机变量<math>(X,Y)</math>的参数空间为<math>\mathcal{X}\times\mathcal{Y}</math>。若它们之间的联合分布为<math>P_{(X,Y)}</math>,边缘分布分别为<math>P_X</math>和<math>P_Y</math>,则它们之间的互信息定义为:<br />
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[[文件:MI pic1.png|左|缩略图]]<br />
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where <math>D_{\mathrm{KL}}</math> is the [[Kullback–Leibler divergence]].<br />
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其中<math>D_{\mathrm{KL}}</math>表示<font color="#ff8000">'''相对熵 Relative Entropy,又称Kullback-Leibler/KL散度'''(以下统称KL散度)</font>。<br />
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Notice, as per property of the [[Kullback–Leibler divergence]], that <math>I(X;Y)</math> is equal to zero precisely when the joint distribution coincides with the product of the marginals, i.e. when <math>X</math> and <math>Y</math> are independent (and hence observing <math>Y</math> tells you nothing about <math>X</math>). In general <math>I(X;Y)</math> is non-negative, it is a measure of the price for encoding <math>(X,Y)</math> as a pair of independent random variables, when in reality they are not.<br />
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需要注意的是,根据KL散度的性质,当两个随机变量的联合分布与其分别的边缘分布的乘积相等时,如当<math>X</math>和<math>Y</math>是相互独立时(因此观察y不会得到x的信息),<math>I(X;Y)</math>等于零(因此已知<math>Y</math>的信息并不能得到任何关于<math>X</math>的信息)。一般来说,<math>I(X;Y)</math>是非负的,因为它是将<math>(X,Y)</math>作为一对独立随机变量来编码进而进行价值度量的,但实际上它们并不一定是非负的。<br />
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== 关于离散分布的PMF In terms of PMFs for discrete distributions ==<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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The mutual information of two jointly discrete random variables <math>X</math> and <math>Y</math> is calculated as a double sum:<br />
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两个联合分布的离散型随机变量X和Y的互信息计算表现为双和的形式:<ref name=cover1991>{{cite book|last1=Cover|first1=T.M.|last2=Thomas|first2=J.A.|title=Elements of Information Theory|url=https://archive.org/details/elementsofinform0000cove|url-access=registration|date=1991|isbn=978-0-471-24195-9|edition=Wiley}}</ref>{{rp|20}}<br />
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[[文件:MI pic2.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is the [[joint distribution|joint probability ''mass'' function]] of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the [[marginal probability]] mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is the joint probability mass function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability mass functions of <math>X</math> and <math>Y</math> respectively.<br />
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<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合概率质量函数 Probability Mass Functions</font>''',而<math>p_X</math>和<math>p_Y</math>分别是数学<math>X</math>和<math>Y</math>的'''<font color="#ff8000">边缘概率质量函数 Marginal Probability Mass Functions</font>'''。<br />
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== 连续分布的PDF In terms of PDFs for continuous distributions ==<br />
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In the case of jointly continuous random variables, the double sum is replaced by a [[double integral]]:<ref name=cover1991 />{{rp|251}}<br />
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In the case of jointly continuous random variables, the double sum is replaced by a double integral:<br />
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在联合分布的随机变量为连续型的情况下,公式中的二重求和用二重积分代替: <ref name=cover1991 />{{rp|251}}<br />
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[[文件:MI pic3.png|居中|缩略图]]<br />
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where <math>p_{(X,Y)}</math> is now the joint probability ''density'' function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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where <math>p_{(X,Y)}</math> is now the joint probability density function of <math>X</math> and <math>Y</math>, and <math>p_X</math> and <math>p_Y</math> are the marginal probability density functions of <math>X</math> and <math>Y</math> respectively.<br />
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式中,<math>p_{(X,Y)}</math>是<math>X</math>和<math>Y</math>的联合概率密度函数,而<math>p_X</math>和<math>p_Y</math>分别是<math>X</math>和<math>Y</math>的边缘概率密度函数。<br />
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If the [[Logarithm|log base]] 2 is used, the units of mutual information are [[bit|bits]].<br />
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If the log base 2 is used, the units of mutual information are bits.<br />
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如果以2为底取对数,则互信息的单位为''位 bit''。<br />
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== 动机 Motivation ==<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the [[information entropy|entropy]] of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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Intuitively, mutual information measures the information that <math>X</math> and <math>Y</math> share: It measures how much knowing one of these variables reduces uncertainty about the other. For example, if <math>X</math> and <math>Y</math> are independent, then knowing <math>X</math> does not give any information about <math>Y</math> and vice versa, so their mutual information is zero. At the other extreme, if <math>X</math> is a deterministic function of <math>Y</math> and <math>Y</math> is a deterministic function of <math>X</math> then all information conveyed by <math>X</math> is shared with <math>Y</math>: knowing <math>X</math> determines the value of <math>Y</math> and vice versa. As a result, in this case the mutual information is the same as the uncertainty contained in <math>Y</math> (or <math>X</math>) alone, namely the entropy of <math>Y</math> (or <math>X</math>). Moreover, this mutual information is the same as the entropy of <math>X</math> and as the entropy of <math>Y</math>. (A very special case of this is when <math>X</math> and <math>Y</math> are the same random variable.)<br />
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直观地说,互信息衡量了<math>X</math> 和 <math>Y</math>的信息共享程度:当已知其中一个变量后,它可以衡量了另一个变量减少的不确定性。例如,若<math>X</math>和<math>Y</math>是相互独立的,那么已知<math>X</math>不会得到关于<math>Y</math>的任何信息,反之亦然,因此它们之间的互信息为零。而另一种极端情况就是,若<math>X</math>是<math>Y</math>的确定函数,而<math>Y</math>也是<math>X</math>的确定函数,则<math>X</math>传递的所有信息都与<math>Y</math>共享:即已知<math>X</math>就可以知道<math>Y</math>的值,反之亦然。因此,在这种情况下,互信息与仅包含在<math>Y</math>(或<math>X</math>)中的不确定性相同,即<math>Y</math>(或<math>X</math>)的熵相同。此外,这种情况下互信息与<math>X</math>的熵,<math>Y</math>的熵相同。(一个非常特殊的情况是当<math>X</math>和<math>Y</math>是相同的随机变量。)<br />
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Mutual information is a measure of the inherent dependence expressed in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math> under the assumption of independence. Mutual information therefore measures dependence in the following sense: <math>\operatorname{I}(X;Y)=0</math> [[if and only if]] <math>X</math> and <math>Y</math> are independent random variables. This is easy to see in one direction: if <math>X</math> and <math>Y</math> are independent, then <math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>, and therefore:<br />
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Mutual information is a measure of the inherent dependence expressed in the joint distribution of 𝑋 and 𝑌 relative to the joint distribution of 𝑋 and 𝑌 under the assumption of independence. Mutual information therefore measures dependence in the following sense: I(𝑋;𝑌)=0 if and only if 𝑋 and 𝑌 are independent random variables. This is easy to see in one direction: if 𝑋 and 𝑌 are independent, then 𝑝(𝑋,𝑌)(𝑥,𝑦)=𝑝𝑋(𝑥)⋅𝑝𝑌(𝑦), and therefore:<br />
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--[[用户:flipped| flipped]]([[用户讨论: flipped |第一句话有一点点不理解<br />
in the [[joint distribution]] of <math>X</math> and <math>Y</math> relative to the joint distribution of <math>X</math> and <math>Y</math>]])<br />
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<font color="#32cd32"> </font><br />
互信息是在独立假设下,<math>X</math> 和<math>Y</math>的联合分布相对于其内在相关性的度量。因此互信息是在以下条件下定义相关性的:当且仅当<math>X</math和<math>Y</math>是独立随机变量时,<math>\operatorname{I}(X;Y)=0</math>。这很容易得出:如果<math>X</math和<math>Y</math>是独立的,那么<math>p_{(X,Y)}(x,y)=p_X(x) \cdot p_Y(y)</math>,因此:<br />
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<math> \log{ \left( \frac{p_{(X,Y)}(x,y)}{p_X(x)\,p_Y(y)} \right) } = \log 1 = 0 .</math><br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and [[Symmetric function|symmetric]] (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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Moreover, mutual information is nonnegative (i.e. <math>\operatorname{I}(X;Y) \ge 0</math> see below) and symmetric (i.e. <math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math> see below).<br />
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此外,互信息是非负的(例如:(<math>\operatorname{I}(X;Y) \ge 0</math>,见下文)和对称的(即<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math>,见下文)。<br />
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== 与其他量的关系 Relation to other quantities ==<br />
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=== 非负性 Nonnegativity ===<br />
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Using [[Jensen's inequality]] on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<ref name=cover1991 />{{rp|28}}<br />
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Using Jensen's inequality on the definition of mutual information we can show that <math>\operatorname{I}(X;Y)</math> is non-negative, i.e.<br />
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利用'''<font color="#ff8000">琴生不等式 Jensen's Inequality</font>'''对互信息的定义进行推导,我们可以证明<math>\operatorname{I}(X;Y)</math>是非负的,即: <ref name=cover1991 />{{rp|28}}<br />
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<math>\operatorname{I}(X;Y) \ge 0</math><br />
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=== 对称性 Symmetry===<br />
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<math>\operatorname{I}(X;Y) = \operatorname{I}(Y;X)</math><br />
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=== 条件熵与联合熵的关系 Relation to conditional and joint entropy ===<br />
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Mutual information can be equivalently expressed as:<br />
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Mutual information can be equivalently expressed as:<br />
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互信息也可以等价地表示为:<br />
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[[文件:MI pic4.png|居中|缩略图]]<br />
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where <math>H(X)</math> and <math>H(Y)</math> are the marginal [[information entropy|entropies]], <math>H(X|Y)</math> and <math>H(Y|X)</math> are the [[conditional entropy|conditional entropies]], and <math>H(X,Y)</math> is the [[joint entropy]] of <math>X</math> and <math>Y</math>.<br />
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其中<math>H(X)</math>和<math>H(Y)</math>是'''<font color="#ff8000">边际熵 Marginal Entropy</font>''',<math>H(X|Y)</math>和<math>H(Y|X)</math>表示'''<font color="#ff8000">条件熵 Conditional Entropy</font>''',<math>H(X,Y)</math>是<math>X</math>和<math>Y</math>的'''<font color="#ff8000">联合熵 Joint Entropy</font>'''。<br />
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Notice the analogy to the union, difference, and intersection of two sets: in this respect, all the formulas given above are apparent from the Venn diagram reported at the beginning of the article.<br />
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注意两个集合的并集、差集和交集的类比:在这方面,上面给出的所有公式都可以从文章开头的维恩图中看出。<br />
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In terms of a communication channel in which the output <math>Y</math> is a noisy version of the input <math>X</math>, these relations are summarised in the figure:<br />
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对于输出<math>Y</math>是输入<math>X</math>的噪声版本的通信通道而言,这些关系如图中总结所示:<br />
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[[File:Figchannel2017ab.svg|thumb| The relationships between information theoretic quantities 信息论量之间的关系]]<br />
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Because <math>\operatorname{I}(X;Y)</math> is non-negative, consequently, <math>H(X) \ge H(X|Y)</math>. Here we give the detailed deduction of <math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math> for the case of jointly discrete random variables:<br />
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因为<math>\operatorname{I}(X;Y)</math>是非负的,因此<math>H(X) \ge H(X|Y)</math>。这里我们给出了联合离散随机变量情形下,结论<math>\operatorname{I}(X;Y)=H(Y)-H(Y|X)</math>的详细推导过程:<br />
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[[文件:MI pic5.png|居中|800px]]<br />
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The proofs of the other identities above are similar. The proof of the general case (not just discrete) is similar, with integrals replacing sums.<br />
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同理,上述其他恒等式的证明方法都是相似的。一般情况(不仅仅是离散情况)的证明是类似的,用积分代替求和。<br />
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Intuitively, if entropy <math>H(Y)</math> is regarded as a measure of uncertainty about a random variable, then <math>H(Y|X)</math> is a measure of what <math>X</math> does ''not'' say about <math>Y</math>. This is "the amount of uncertainty remaining about <math>Y</math> after <math>X</math> is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in <math>Y</math>, minus the amount of uncertainty in <math>Y</math> which remains after <math>X</math> is known", which is equivalent to "the amount of uncertainty in <math>Y</math> which is removed by knowing <math>X</math>". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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Intuitively, if entropy 𝐻(𝑌) is regarded as a measure of uncertainty about a random variable, then 𝐻(𝑌|𝑋) is a measure of what 𝑋 does not say about 𝑌. This is "the amount of uncertainty remaining about 𝑌 after 𝑋 is known", and thus the right side of the second of these equalities can be read as "the amount of uncertainty in 𝑌, minus the amount of uncertainty in 𝑌 which remains after 𝑋 is known", which is equivalent to "the amount of uncertainty in 𝑌 which is removed by knowing 𝑋". This corroborates the intuitive meaning of mutual information as the amount of information (that is, reduction in uncertainty) that knowing either variable provides about the other.<br />
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理论上来说,如果熵<math>H(Y)</math>被视为随机变量不确定性的度量,那么<math>H(Y|X)</math>则是对<math>X</math>没有说明<math>Y</math>的程度的度量。也就是“已知<math>X</math>后,关于<math>Y</math>剩余的不确定性”的度量,因此这些等式中第二个等式的右侧可以解读为“<math>Y</math>的不确定性的量,减去已知<math>X</math>后的<math>Y</math>中仍然存在不确定性的量”,相当于“已知<math>X</math>后消除的<math>Y</math>中的不确定性量” .这证实了互信息的直观含义就是了解其中一个变量提供的关于另一个变量的信息量(即不确定性的减少量)。<br />
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Note that in the discrete case <math>H(X|X) = 0</math> and therefore <math>H(X) = \operatorname{I}(X;X)</math>. Thus <math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>, and one can formulate the basic principle that a variable contains at least as much information about itself as any other variable can provide.<br />
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注意,在离散情况下,<math>H(X|X) = 0</math>,因此<math>H(X) = \operatorname{I}(X;X)</math>。所以,<math>\operatorname{I}(X; X) \ge \operatorname{I}(X; Y)</math>,据此我们可以得到一个基本结论,那就是一个变量包含的信息量至少与任何其他变量所能提供的关于自身的信息量的一样多。<br />
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=== 与相对熵的关系 Relation to Kullback–Leibler divergence ===<br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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For jointly discrete or jointly continuous pairs <math>(X,Y)</math>, <br />
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对于联合的离散或连续分布变量对<math>(X,Y)</math>,<br />
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mutual information is the [[Kullback–Leibler divergence]] of the product of the [[marginal distribution]]s, <math>p_X \cdot p_Y</math>, from the [[joint distribution]] <math>p_{(X,Y)}</math>, that is,<br />
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mutual information is the Kullback–Leibler divergence of the product of the marginal distributions, 𝑝𝑋⋅𝑝𝑌, from the joint distribution 𝑝(𝑋,𝑌), that is,<br />
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互信息是边缘分布乘积<math>p_X \cdot p_Y</math>的KL散度<math>D_{KL}</math>,也就是联合分布<math>p_{(X,Y)}</math>的乘积,即:<br />
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[[文件:MI pic6.png|居中|缩略图]]<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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Furthermore, let <math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math> be the conditional mass or density function. Then, we have the identity<br />
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进一步地,设<math>p_{X|Y=y}(x) = p_{(X,Y)}(x,y) / p_Y(y)</math>为条件质量或密度函数。那么,我们就可以给出:<br />
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[[文件:MI pic7.png|居中|缩略图]]<br />
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The proof for jointly discrete random variables is as follows:<br />
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The proof for jointly discrete random variables is as follows:<br />
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联合离散随机变量的证明如下:<br />
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[[文件:MI pic8.png|居中|缩略图]]<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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Similarly this identity can be established for jointly continuous random variables.<br />
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这个恒等式在联合、连续的随机变量情况下同样成立。<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the [[expected value|expectation]] of the Kullback–Leibler divergence of the [[univariate distribution]] <math>p_X</math> of <math>X</math> from the [[conditional distribution]] <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the [[Kullback–Leibler divergence|information gain]].<br />
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Note that here the Kullback–Leibler divergence involves integration over the values of the random variable <math>X</math> only, and the expression <math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> still denotes a random variable because <math>Y</math> is random. Thus mutual information can also be understood as the expectation of the Kullback–Leibler divergence of the univariate distribution <math>p_X</math> of <math>X</math> from the conditional distribution <math>p_{X|Y}</math> of <math>X</math> given <math>Y</math>: the more different the distributions <math>p_{X|Y}</math> and <math>p_X</math> are on average, the greater the information gain.<br />
<br />
请注意,此处的KL散度仅涉及对随机变量<math>X</math>的值进行积分,并且表达式<math>D_\text{KL}(p_{X|Y} \parallel p_X)</math> 仍然表示随机变量,因为y是随机的。因此,互信息也可以理解为X的单变量分布<math>p_X</math>与给定<math>Y</math>的<math>X</math>的条件分布<math>p_{X|Y}</math>的KL散度的期望:平均分布<math>p_{X|Y}</math>和<math>p_X</math>的分布差异越大,信息增益越大。<br />
<br />
=== 互信息的贝叶斯估计 Bayesian estimation of mutual information ===<br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
It is well-understood how to do Bayesian estimation of the mutual information of a joint distribution based on samples of that distribution. <br />
<br />
如何根据联合分布的样本对联合分布的互信息进行贝叶斯估计,是一个众所周知的问题<br />
<br />
The first work to do this, which also showed how to do Bayesian estimation of many other information-theoretic properties besides mutual information, was <ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>. Subsequent researchers have rederived <ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref><br />
and extended <ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>this analysis. <br />
<br />
<br />
关于这方面的第一项工作<ref>{{cite journal | last1 = Wolpert | first1 = D.H. | last2 = Wolf | first2 = D.R. | year = 1995 | title = Estimating functions of probability distributions from a finite set of samples | journal = Physical Review E | volume = 52 | issue = 6 | pages = 6841–6854 | doi = 10.1103/PhysRevE.52.6841 | pmid = 9964199 | citeseerx = 10.1.1.55.7122 | bibcode = 1995PhRvE..52.6841W }}</ref>,它还展示了如何对贝叶斯估计进行除互信息之外的许多其他信息理论性质。后来的研究人员重新推导了<ref>{{cite journal | last1 = Hutter | first1 = M. | year = 2001 | title = Distribution of Mutual Information | journal = Advances in Neural Information Processing Systems 2001 }}</ref>内容,并扩展了<ref>{{cite journal | last1 = Archer | first1 = E. | last2 = Park | first2 = I.M. | last3 = Pillow | first3 = J. | year = 2013 | title = Bayesian and Quasi-Bayesian Estimators for Mutual Information from Discrete Data | journal = Entropy| volume = 15 | issue = 12 | pages = 1738–1755 | doi = 10.3390/e15051738 | citeseerx = 10.1.1.294.4690 | bibcode = 2013Entrp..15.1738A }}</ref>分析。<br />
<br />
<br />
<br />
<br />
See <ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>for a recent paper based on a prior specifically tailored to estimation of mutual information per se. <br />
<br />
<br />
最近的一篇论文<ref>{{cite journal | last1 = Wolpert | first1 = D.H | last2 = DeDeo | first2 = S. | year = 2013 | title = Estimating Functions of Distributions Defined over Spaces of Unknown Size | journal = Entropy | volume = 15 | issue = 12 | pages = 4668–4699 | doi = 10.3390/e15114668 | arxiv = 1311.4548 | bibcode = 2013Entrp..15.4668W }}</ref>中基于一个专门针对互信息本身估计的先验知识。<br />
<br />
<br />
Besides, recently an estimation method accounting for continuous and multivariate outputs, <math>Y</math>, was proposed in <ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>.<br />
<br />
<br />
此外,最近文献<ref>{{citation| journal = [[PLOS Computational Biology]]|volume = 15|issue = 7|pages = e1007132|doi = 10.1371/journal.pcbi.1007132|pmid = 31299056|pmc = 6655862|title=Information-theoretic analysis of multivariate single-cell signaling responses|author1= Tomasz Jetka|author2= Karol Nienaltowski|author3= Tomasz Winarski| author4=Slawomir Blonski| author5= Michal Komorowski|year=2019|bibcode = 2019PLSCB..15E7132J|arxiv = 1808.05581}}</ref>提出了一种考虑连续多种输出变量𝑌的估计方法。<br />
<br />
=== 独立性假设 Independence assumptions ===<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing <math>p(x,y)</math> to the fully factorized [[outer product]] <math>p(x) \cdot p(y)</math>. In many problems, such as [[non-negative matrix factorization]], one is interested in less extreme factorizations; specifically, one wishes to compare <math>p(x,y)</math> to a low-rank matrix approximation in some unknown variable <math>w</math>; that is, to what degree one might have<br />
<br />
The Kullback-Leibler divergence formulation of the mutual information is predicated on that one is interested in comparing 𝑝(𝑥,𝑦) to the fully factorized outer product 𝑝(𝑥)⋅𝑝(𝑦). In many problems, such as non-negative matrix factorization, one is interested in '''<font color="#32CD32">less extreme factorizations</font>'''; specifically, one wishes to compare 𝑝(𝑥,𝑦) to a low-rank matrix approximation in some unknown variable 𝑤; that is, to what degree one might have<br />
<br />
互信息的KL散度公式是基于这样一个结论的:人们会更关注将<math>p(x,y)</math>与完全分解的'''<font color="#ff8000">外积 Outer Product</font>'''<math>p(x) \cdot p(y)</math>进行比较。在许多问题中,例如'''<font color="#ff8000">非负矩阵因式分解 Non-negative matrix factorization</font>''',人们对较不极端的因式分解感兴趣;具体地说,人们希望将<math>p(x,y)</math>与某个未知变量<math>w</math>中的低秩矩阵近似进行比较;也就是说,在多大程度上可能会有这样的结果:<br />
<br />
:<math>p(x,y)\approx \sum_w p^\prime (x,w) p^{\prime\prime}(w,y)</math><br />
<br />
<br />
<br />
Alternately, one might be interested in knowing how much more information <math>p(x,y)</math> carries over its factorization. In such a case, the excess information that the full distribution <math>p(x,y)</math> carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
Alternately, one might be interested in knowing how much more information 𝑝(𝑥,𝑦) carries over its factorization. In such a case, the excess information that the full distribution 𝑝(𝑥,𝑦) carries over the matrix factorization is given by the Kullback-Leibler divergence<br />
<br />
另一方面,人们可能有兴趣了解在因式分解过程中, <math>p(x,y)</math>携带了多少信息。在这种情况下,全分布<math>p(x,y)</math>通过矩阵因式分解所携带的多余信息由KL散度给出<br />
<br />
:<math>\operatorname{I}_{LRMA} = \sum_{y \in \mathcal{Y}} \sum_{x \in \mathcal{X}}<br />
<br />
{p(x,y) \log{ \left(\frac{p(x,y)}{\sum_w p^\prime (x,w) p^{\prime\prime}(w,y)}<br />
<br />
\right) }},<br />
</math><br />
<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
The conventional definition of the mutual information is recovered in the extreme case that the process <math>W</math> has only one value for <math>w</math>.<br />
<br />
在过程<math> W </math>中,<math>w</math>只有一个值的极端情况下,可以使用传统的互信息定义。<br />
<br />
== 变形 Variations ==<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
Several variations on mutual information have been proposed to suit various needs. Among these are normalized variants and generalizations to more than two variables.<br />
<br />
为了适应不同的需要,已经提出了几种互信息的变形。其中包括变量归一化和对两个以上变量的泛化。<br />
<br />
<br />
<br />
<br />
<br />
=== 度量 Metric ===<br />
<br />
Many applications require a [[metric (mathematics)|metric]], that is, a distance measure between pairs of points. The quantity<br />
<br />
Many applications require a metric, that is, a distance measure between pairs of points. The quantity<br />
<br />
许多应用需要一个度量,即点对之间的距离度量。这个量:<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\begin{align}<br />
<br />
d(X,Y) &= H(X,Y) - \operatorname{I}(X;Y) \\<br />
<br />
&= H(X) + H(Y) - 2\operatorname{I}(X;Y) \\<br />
<br />
&= H(X|Y) + H(Y|X)<br />
<br />
\end{align}<br />
<br />
</math><br />
<br />
<br />
satisfies the properties of a metric ([[triangle inequality]], [[non-negative|non-negativity]], [[identity of indiscernibles|indiscernability]] and symmetry). This distance metric is also known as the [[variation of information]].<br />
<br />
satisfies the properties of a metric (triangle inequality, non-negativity, indiscernability and symmetry). This distance metric is also known as the variation of information.<br />
<br />
满足度量的性质(三角不等式、非负性、不可除性和对称性)。这种距离度量也称为信息的变化。<br />
<br />
<br />
<br />
<br />
If <math>X, Y</math> are discrete random variables then all the entropy terms are non-negative, so <math>0 \le d(X,Y) \le H(X,Y)</math> and one can define a normalized distance<br />
<br />
If 𝑋,𝑌 are discrete random variables then all the entropy terms are non-negative, so 0≤𝑑(𝑋,𝑌)≤𝐻(𝑋,𝑌) and one can define a normalized distance<br />
<br />
如果<math>X, Y</math>是离散随机变量,那么所有熵项都是非负的,因此<math>0 \le d(X,Y) \le H(X,Y)</math>,可以定义一个标准化距离:<br />
<br />
<br />
<br />
:<math>D(X,Y) = \frac{d(X, Y)}{H(X, Y)} \le 1.</math><br />
<br />
<br />
<br />
<br />
The metric <math>D</math> is a universal metric, in that if any other distance measure places <math>X</math> and <math>Y</math> close-by, then the <math>D</math> will also judge them close.<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref>{{dubious|see talk page|date=November 2014}}<br />
<br />
The metric 𝐷 is a universal metric, in that if any other distance measure places 𝑋 and 𝑌 close-by, then the 𝐷 will also judge them close.<br />
<br />
度量<math>D</math>是一种通用度量,即如果任何其他距离度量将<math>X</math>和<math>Y</math>认为是近的,则<math>D</math>也将判断它们接近。<ref>{{cite journal|arxiv=q-bio/0311039|last1=Kraskov|first1=Alexander|title=Hierarchical Clustering Based on Mutual Information|last2=Stögbauer|first2=Harald|last3= Andrzejak|first3=Ralph G.|last4=Grassberger|first4=Peter|year=2003|bibcode=2003q.bio....11039K}}</ref><br />
<br />
<br />
<br />
<br />
Plugging in the definitions shows that<br />
<br />
Plugging in the definitions shows that<br />
<br />
从如下定义可以看出:<br />
<br />
<br />
<br />
<br />
<br />
:<math>D(X,Y) = 1 - \frac{\operatorname{I}(X; Y)}{H(X, Y)}.</math><br />
<br />
<br />
<br />
<br />
<br />
In a set-theoretic interpretation of information (see the figure for [[Conditional entropy]]), this is effectively the [[Jaccard index|Jaccard distance]] between <math>X</math> and <math>Y</math>.<br />
<br />
In a set-theoretic interpretation of information (see the figure for Conditional entropy), this is effectively the Jaccard distance between 𝑋 and 𝑌.<br />
<br />
在信息的集合论解释中(参见条件熵的图),这实际上就是<math>X</math>和<math>Y</math>之间的'''<font color="#ff8000">杰卡德距离 Jaccard Distance</font>'''。<br />
<br />
<br />
<br />
<br />
Finally,<br />
<br />
Finally,<br />
<br />
最后,<br />
<br />
<br />
<br />
:<math>D^\prime(X, Y) = 1 - \frac{\operatorname{I}(X; Y)}{\max\left\{H(X), H(Y)\right\}}</math><br />
<br />
<br />
is also a metric.<br />
<br />
is also a metric.<br />
<br />
也是一种度量标准。<br />
<br />
=== 条件互信息 Conditional mutual information ===<br />
<br />
{{Main|Conditional mutual information}}<br />
<br />
<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
Sometimes it is useful to express the mutual information of two random variables conditioned on a third.<br />
<br />
有时,在以第三个随机变量为条件的情况下,表示两个随机变量的互信息也是有意义的。<br />
<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent =<br />
<br />
|title=<br />
<br />
|equation = <br />
<br />
<math><br />
<br />
\operatorname{I}(X;Y|Z) = \mathbb{E}_Z [D_{\mathrm{KL}}( P_{(X,Y)|Z} \| P_{X|Z} \otimes P_{Y|Z} )]<br />
<br />
</math><br />
<br />
|cellpadding= 1<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
<br />
For jointly [[discrete random variable|discrete random variables]] this takes the form<br />
<br />
For jointly discrete random variables this takes the form<br />
<br />
对于联合离散随机变量,采用以下形式:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]},<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \sum_{z\in \mathcal{Z}} \sum_{y\in \mathcal{Y}} \sum_{x\in \mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)}.<br />
<br />
</math><br />
<br />
<br />
<br />
For jointly [[continuous random variable|continuous random variables]] this takes the form<br />
<br />
For jointly continuous random variables this takes the form<br />
<br />
对于联合连续随机变量,其形式为:<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
{p_Z(z)\, p_{X,Y|Z}(x,y|z) <br />
<br />
\log\left[\frac{p_{X,Y|Z}(x,y|z)}{p_{X|Z}\,(x|z)p_{Y|Z}(y|z)}\right]} dx dy dz,<br />
<br />
</math><br />
<br />
which can be simplified as<br />
<br />
which can be simplified as<br />
<br />
可以简化为<br />
<br />
:<math><br />
<br />
\operatorname{I}(X;Y|Z) = \int_{\mathcal{Z}} \int_{\mathcal{Y}} \int_{\mathcal{X}}<br />
<br />
p_{X,Y,Z}(x,y,z) \log \frac{p_{X,Y,Z}(x,y,z)p_{Z}(z)}{p_{X,Z}(x,z)p_{Y,Z}(y,z)} dx dy dz.<br />
<br />
</math><br />
<br />
<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
Conditioning on a third random variable may either increase or decrease the mutual information, but it is always true that<br />
<br />
第三个随机变量的条件作用可能增加或减少互信息,但下式始终是成立的:<br />
<br />
:<math>\operatorname{I}(X;Y|Z) \ge 0</math><br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other [[inequalities in information theory]].<br />
<br />
for discrete, jointly distributed random variables <math>X,Y,Z</math>. This result has been used as a basic building block for proving other inequalities in information theory.<br />
<br />
对于离散的、联合分布的随机变量<math>X,Y,Z</math>。这一结果被用作证明信息论中其他不等式的基本组成部分。<br />
<br />
=== 多元互信息 Multivariate mutual information ===<br />
<br />
{{Main|Multivariate mutual information}}<br />
<br />
<br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as [[total correlation]] (or multi-information) and [[interaction information]]. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) <ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref> who called these functions “interaction information”, and Hu Kuo Ting (1962) <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref> who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <ref name=e21090869>{{cite journal | last1 = Baudot | first1 = P. | last2 = Tapia | first2 = M. | last3 = Bennequin | first3 = D. | last4 = Goaillard | first4 = J.M. | year = 2019 | title = Topological Information Data Analysis | doi = 10.3390/e21090869 | journal = Entropy | volume = 21 | issue = 9| at = 869 | bibcode = 2019Entrp..21..869B | arxiv = 1907.04242 }}</ref><br />
<br />
Several generalizations of mutual information to more than two random variables have been proposed, such as total correlation (or multi-information) and interaction information. The expression and study of multivariate higher-degree mutual-information was achieved in two seemingly independent works: McGill (1954) who called these functions “interaction information”, and Hu Kuo Ting (1962) who also first proved the possible negativity of mutual-information for degrees higher than 2 and justified algebraically the intuitive correspondence to Venn diagrams <br />
<br />
目前提出了一些将互信息推广到两个以上随机变量的方法,如'''<font color="#ff8000">全相关 Total Correlation</font>'''(或'''<font color="#ff8000">多信息 Multi-Information</font>''')以及'''<font color="#ff8000">交互信息 Interaction Information</font>'''。多元高阶互信息的表达和研究是在两部看似无关的著作中实现的:McGill 麦吉尔(1954年)<ref>{{cite journal | last1 = McGill| first1 = W. | year = 1954 | title = Multivariate information transmission | journal = Psychometrika | volume = 19 | issue = 1 | pages = 97–116 | doi = 10.1007/BF02289159 }}</ref>将这些函数统称为“交互信息”,胡国亭(1962年)也<ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>首次证明了大于2度的互信息可能是负的,并在文献[10]中用代数的方法证明了互信息和维恩图的直观对应关系。<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;X_1) = H(X_1)<br />
<br />
</math><br />
<br />
<br />
<br />
<br />
and for <math>n > 1,</math><br />
<br />
and for 𝑛>1,<br />
<br />
而对于𝑛>1,有:<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}(X_1;\,...\,;X_n)<br />
<br />
= \operatorname{I}(X_1;\,...\,;X_{n-1}) <br />
<br />
- \operatorname{I}(X_1;\,...\,;X_{n-1}|X_n),<br />
<br />
</math><br />
<br />
<br />
<br />
where (as above) we define<br />
<br />
where (as above) we define<br />
<br />
综上所述,我们定义:<br />
<br />
<br />
:<math><br />
<br />
I(X_1;\ldots;X_{n-1}|X_{n}) = \mathbb{E}_{X_{n}} [D_{\mathrm{KL}}( P_{(X_1,\ldots,X_{n-1})|X_{n}} \| P_{X_1|X_{n}} \otimes\cdots\otimes P_{X_{n-1}|X_{n}} )].<br />
<br />
</math><br />
<br />
<br />
(This definition of multivariate mutual information is identical to that of [[interaction information]] except for a change in sign when the number of random variables is odd.)<br />
<br />
(This definition of multivariate mutual information is identical to that of interaction information except for a change in sign when the number of random variables is odd.)<br />
<br />
(这个多元互信息的定义与交互信息的定义相同,对于随机变量的数目为奇数时符号的变化除外。)<br />
<br />
<br />
<br />
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==== 多元统计独立性 Multivariate statistical independence ====<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that <math>X_1,X_2</math> if and only if <math>I(X_1;X_2)=0</math>, to arbitrary numerous variable. n variables are mutually independent if and only if the <math>2^n-n-1</math> mutual information functions vanish <math>I(X_1;...;X_k)=0</math> with <math>n \ge k \ge 2</math> (theorem 2 <ref name=e21090869/>). In this sense, the <math>I(X_1;...;X_k)=0</math> can be used as a refined statistical independence criterion.<br />
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The multivariate mutual-information functions generalize the pairwise independence case that states that 𝑋1,𝑋2 if and only if 𝐼(𝑋1;𝑋2)=0, to arbitrary numerous variable. n variables are mutually independent if and only if the 2𝑛−𝑛−1 mutual information functions vanish 𝐼(𝑋1;...;𝑋𝑘)=0 with 𝑛≥𝑘≥2 (theorem 2). In this sense, the 𝐼(𝑋1;...;𝑋𝑘)=0 can be used as a refined statistical independence criterion.<br />
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多元互信息函数将<math>I(X_1;X_2)=0</math>当且仅当<math>X_1,X_2</math>两两独立的情况推广到任意多变量。当且仅当<math>2^n-n-1</math>的互信息函数为<br />
<math>I(X_1;...;X_k)=0</math>且<math>n \ge k \ge 2</math>,n个变量相互独立(定理2<ref name=e21090869/>)。从这个意义上讲,<math>I(X_1;...;X_k)=0</math>可以用作一个精确的统计独立性标准。<br />
--[[用户:flipped| flipped]]([[用户讨论: flipped |第二句中的vanish不太理解]])<br />
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==== 应用 Applications ====<br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" <ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref> and Watkinson et al. applied it to genetic expression <ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>. For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression <ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>). It can be zero, positive, or negative <ref>{{cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>. The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints <ref name=s41598/>). <br />
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For 3 variables, Brenner et al. applied multivariate mutual information to neural coding and called its negativity "synergy" and Watkinson et al. applied it to genetic expression . For arbitrary k variables, Tapia et al. applied multivariate mutual information to gene expression . '''<font color="#32CD32">The positivity corresponds to relations generalizing the pairwise correlations, nullity corresponds to a refined notion of independence, and negativity detects high dimensional "emergent" relations and clusterized datapoints </font>'''. <br />
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对于3个变量,Brenner 布伦纳等人<ref>{{cite journal | last1 = Brenner | first1 = N. | last2 = Strong | first2 = S. | last3 = Koberle | first3 = R. | last4 = Bialek | first4 = W. | year = 2000 | title = Synergy in a Neural Code | doi = 10.1162/089976600300015259 | pmid = 10935917 | journal = Neural Comput | volume = 12 | issue = 7 | pages = 1531–1552 }}</ref>将多元互信息应用到神经编码中,并将其称为'''<font color="#ff8000">负面“协同作用” Negativity "Synergy"</font>''',接着Watkinson 沃特森等人<ref>{{cite journal | last1 = Watkinson | first1 = J. | last2 = Liang | first2 = K. | last3 = Wang | first3 = X. | last4 = Zheng | first4 = T.| last5 = Anastassiou | first5 = D. | year = 2009 | title = Inference of Regulatory Gene Interactions from Expression Data Using Three-Way Mutual Information | doi = 10.1111/j.1749-6632.2008.03757.x | pmid = 19348651 | journal = Chall. Syst. Biol. Ann. N. Y. Acad. Sci. | volume = 1158 | issue = 1 | pages = 302–313 | bibcode = 2009NYASA1158..302W | url = https://semanticscholar.org/paper/cb09223a34b08e6dcbf696385d9ab76fd9f37aa4 }}</ref>.将其应用到基因表达上。对于任意k个变量,Tapia 塔皮亚 等人<ref name=s41598>{{cite journal|last1=Tapia|first1=M.|last2=Baudot|first2=P.|last3=Formizano-Treziny|first3=C.|last4=Dufour|first4=M.|last5=Goaillard|first5=J.M.|year=2018|title=Neurotransmitter identity and electrophysiological phenotype are genetically coupled in midbrain dopaminergic neurons|doi= 10.1038/s41598-018-31765-z|pmid=30206240|pmc=6134142|journal=Sci. Rep.|volume=8|issue=1|pages=13637|bibcode=2018NatSR...813637T}}</ref> <ref name=e21090869/>将多元互信息应用于基因表达——它可以是0,正,或负。cite journal | last1 = Hu| first1 = K.T. | year = 1962 | title = On the Amount of Information | journal = Theory Probab. Appl. | volume = 7 | issue = 4 | pages = 439–447 | doi = 10.1137/1107041 }}</ref>'''<font color="#32CD32">正性对应于一般化成对相关性的关系,无效性对应于一个精确的独立性概念,负性检测高维“涌现”关系和聚合数据点</font>'''<ref name=s41598/>。<br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in [[feature selection]].<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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One high-dimensional generalization scheme which maximizes the mutual information between the joint distribution and other target variables is found to be useful in feature selection.<br />
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目前已经提出了一种能够最大化联合分布与其他目标变量之间的互信息的高维推广方案,该方法可用于'''<font color="#ff8000"> 特征选择 Feature Selection</font>'''。<ref>{{cite book|author1=Christopher D. Manning |author2=Prabhakar Raghavan |author3=Hinrich Schütze | title = An Introduction to Information Retrieval| publisher = [[Cambridge University Press]]| year = 2008| isbn = 978-0-521-86571-5 }}</ref><br />
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Mutual information is also used in the area of signal processing as a [[Similarity measure|measure of similarity]] between two signals. For example, FMI metric<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref> is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The [[Matlab]] code for this metric can be found at.<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref><br />
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Mutual information is also used in the area of signal processing as a measure of similarity between two signals. For example, FMI metric is an image fusion performance measure that makes use of mutual information in order to measure the amount of information that the fused image contains about the source images. The Matlab code for this metric can be found at.<br />
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互信息也用于信号处理领域,用来进行两个信号之间的'''<font color="#ff8000">相似性度量 Similarity Measure</font>'''。例如,FMI 度量<ref>{{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | doi = 10.1016/j.compeleceng.2011.07.012 | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 }}</ref>是一种图像融合性能度量,它利用互信息来度量融合图像包含的关于源图像的信息量。这个度量的 Matlab 代码可以找到<ref>{{cite web|url=http://www.mathworks.com/matlabcentral/fileexchange/45926-feature-mutual-information-fmi-image-fusion-metric|title=Feature Mutual Information (FMI) metric for non-reference image fusion - File Exchange - MATLAB Central|author=|date=|website=www.mathworks.com|accessdate=4 April 2018}}</ref>。<br />
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=== 定向信息 Directed information ===<br />
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[[Directed information]], <math>\operatorname{I}\left(X^n \to Y^n\right)</math>, measures the amount of information that flows from the process <math>X^n</math> to <math>Y^n</math>, where <math>X^n</math> denotes the vector <math>X_1, X_2, ..., X_n</math> and <math>Y^n</math> denotes <math>Y_1, Y_2, ..., Y_n</math>. The term ''directed information'' was coined by [[James Massey]] and is defined as<br />
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Directed information, I(𝑋𝑛→𝑌𝑛), measures the amount of information that flows from the process 𝑋𝑛 to 𝑌𝑛, where 𝑋𝑛 denotes the vector 𝑋1,𝑋2,...,𝑋𝑛 and 𝑌𝑛 denotes 𝑌1,𝑌2,...,𝑌𝑛. The term directed information was coined by James Massey and is defined as:<br />
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'''<font color="#ff8000">定向信息 Directed Information</font>'''<math>\operatorname{I}\left(X^n \to Y^n\right)</math>度量从<math>X^n</math>流向<math>Y^n</math>的过程中的信息量,其中<math>X^n</math>表示为向量<math>X_1, X_2, ..., X_n</math>,<math>Y^n</math>表示为<math>Y_1, Y_2, ..., Y_n</math>。定向信息这个术语是由 James Massey 创造的,它被定义为:<br />
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:<math>\operatorname{I}\left(X^n \to Y^n\right)<br />
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= \sum_{i=1}^n \operatorname{I}\left(X^i; Y_i|Y^{i-1}\right)</math>.<br />
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Note that if <math>n=1</math>, the directed information becomes the mutual information. Directed information has many applications in problems where [[causality]] plays an important role, such as [[Channel capacity|capacity of channel]] with feedback.<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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Note that if 𝑛=1, the directed information becomes the mutual information. Directed information has many applications in problems where causality plays an important role, such as capacity of channel with feedback.<br />
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注意,当<math>n=1</math>时,则定向信息成为互信息。定向信息在因果关系问题中有着广泛的应用,如反馈'''<font color="#ff8000">信道容量问题 Channel Capacity</font>'''。<ref>{{cite conference|last1=Massey|first1=James|title=Causality, Feedback And Directed Informatio|date=1990|book-title=Proc. 1990 Intl. Symp. on Info. Th. and its Applications, Waikiki, Hawaii, Nov. 27-30, 1990|citeseerx=10.1.1.36.5688}}</ref><ref>{{cite journal|last1=Permuter|first1=Haim Henry|last2=Weissman|first2=Tsachy|last3=Goldsmith|first3=Andrea J.|title=Finite State Channels With Time-Invariant Deterministic Feedback|journal=IEEE Transactions on Information Theory|date=February 2009|volume=55|issue=2|pages=644–662|doi=10.1109/TIT.2008.2009849|arxiv=cs/0608070}}</ref><br />
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=== 归一化变量 Normalized variants ===<br />
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Normalized variants of the mutual information are provided by the ''coefficients of constraint'',{{sfn|Coombs|Dawes|Tversky|1970}} [[uncertainty coefficient]]<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref> or proficiency:<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref><br />
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Normalized variants of the mutual information are provided by the coefficients of constraint, uncertainty coefficient or proficiency:<br />
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互信息的归一化变量由约束系数、不确定系数<ref name=pressflannery>{{Cite book|last1=Press|first1=WH|last2=Teukolsky |first2=SA|last3=Vetterling|first3=WT|last4=Flannery|first4=BP|year=2007|title=Numerical Recipes: The Art of Scientific Computing|edition=3rd|publisher=Cambridge University Press|location=New York|isbn=978-0-521-88068-8|chapter=Section 14.7.3. Conditional Entropy and Mutual Information|chapter-url=http://apps.nrbook.com/empanel/index.html#pg=758}}</ref>或熟练程度组成<ref name=JimWhite>{{Cite conference| last1= White |first1= Jim | last2= Steingold | first2=Sam | last3= Fournelle | first3=Connie | title = Performance Metrics for Group-Detection Algorithms | conference = Interface 2004 | url = http://www.interfacesymposia.org/I04/I2004Proceedings/WhiteJim/WhiteJim.paper.pdf}}</ref>: <br />
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:<math><br />
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C_{XY} = \frac{\operatorname{I}(X;Y)}{H(Y)}<br />
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~~~~\mbox{和}~~~~ <br />
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C_{YX} = \frac{\operatorname{I}(X;Y)}{H(X)}.<br />
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</math><br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following ''[[Redundancy (information theory)|redundancy]]''{{Citation needed|date=July 2008}} measure:<br />
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The two coefficients have a value ranging in [0, 1], but are not necessarily equal. In some cases a symmetric measure may be desired, such as the following redundancy measure:<br />
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这两个系数的值范围均为[0,1],但不一定是相等的。在某些情况下,可能需要一个对称的度量,例如下面的冗余度量:<br />
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:<math>R = \frac{\operatorname{I}(X;Y)}{H(X) + H(Y)}</math><br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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which attains a minimum of zero when the variables are independent and a maximum value of<br />
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当变量是独立的时候,它的最小值为零,最大值可以达到:<br />
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:<math>R_\max = \frac{\min\left\{H(X), H(Y)\right\}}{H(X) + H(Y)}</math><br />
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when one variable becomes completely redundant with the knowledge of the other. See also ''[[Redundancy (information theory)]]''. <br />
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when one variable becomes completely redundant with the knowledge of the other. See also Redundancy (information theory). <br />
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当一个变量与另一个变量的知识完全多余时。参见'''<font color="#ff8000">冗余 Redundancy</font>'''(信息论)。<br />
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Another symmetrical measure is the ''symmetric uncertainty'' {{harv|Witten|Frank|2005}}, given by<br />
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Another symmetrical measure is the symmetric uncertainty , given by<br />
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另一个对称度量是''对称不确定度'',由下式表示:<br />
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:<math>U(X, Y) = 2R = 2\frac{\operatorname{I}(X;Y)}{Ha(X) + H(Y)}</math><br />
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which represents the [[harmonic mean]] of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<ref name=pressflannery /><br />
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which represents the harmonic mean of the two uncertainty coefficients <math>C_{XY}, C_{YX}</math>.<br />
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它表示两个不确定系数<math>C_{XY}, C_{YX}</math>的'''<font color="#ff8000">调和平均数 Harmonic Mean</font>'''<ref name=pressflannery />。<br />
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If we consider mutual information as a special case of the [[total correlation]] or [[dual total correlation]], the normalized version are respectively,<br />
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If we consider mutual information as a special case of the total correlation or dual total correlation, the normalized version are respectively,<br />
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如果我们把互信息看作是'''<font color="#ff8000">总相关 Total Correlation</font>'''或'''<font color="#ff8000">对偶总相关 Dual Total Correlation</font>'''的特殊情况,则其标准化版本分别为,<br />
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:<math>\frac{\operatorname{I}(X;Y)}{\min\left[ H(X),H(Y)\right]}</math> and <math>\frac{\operatorname{I}(X;Y)}{H(X,Y)} \; .</math><br />
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This normalized version also known as '''Information Quality Ratio (IQR)''' which quantifies the amount of information of a variable based on another variable against total uncertainty:<ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref><br />
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This normalized version also known as Information Quality Ratio (IQR) which quantifies the amount of information of a variable based on another variable against total uncertainty:<br />
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这个标准化版本也被称为'''<font color="#ff8000">信息质量比率 Information Quality Ratio(IQR)</font>''' ,它根据另一个变量,相对于总的不确定性来量化另一个变量的信息量: <ref name=DRWijaya>{{Cite journal| last1= Wijaya |first1= Dedy Rahman | last2= Sarno| first2=Riyanarto| last3= Zulaika | first3=Enny| title = Information Quality Ratio as a novel metric for mother wavelet selection| journal = Chemometrics and Intelligent Laboratory Systems| journal = Chemometrics and Intelligent Laboratory Systems| volume = 160| pages = 59–71| doi = 10.1016/j.chemolab.2016.11.012|year= 2017 }}</ref> <br />
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:<math>IQR(X, Y) = \operatorname{E}[\operatorname{I}(X;Y)] <br />
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= \frac{\operatorname{I}(X;Y)}{H(X, Y)} <br />
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= \frac{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x)p(y)}}{\sum_{x \in X} \sum_{y \in Y} p(x, y) \log {p(x, y)}} - 1</math><br />
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There's a normalization<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref> which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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There's a normalization which derives from first thinking of mutual information as an analogue to [[covariance]] (thus [[Entropy (information theory)|Shannon entropy]] is analogous to [[variance]]). Then the normalized mutual information is calculated akin to the [[Pearson product-moment correlation coefficient|Pearson correlation coefficient]],<br />
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有一种归一化<ref name="strehl-jmlr02">{{cite journal| title = Cluster Ensembles – A Knowledge Reuse Framework for Combining Multiple Partitions| journal = The Journal of Machine Learning Research| pages = 583–617 | volume = 3 | year = 2003| last1 = Strehl | first1 = Alexander | last2 = Ghosh | first2 = Joydeep| doi=10.1162/153244303321897735| url=http://www.jmlr.org/papers/volume3/strehl02a/strehl02a.pdf}}</ref>起源于互信息的最初思想,看作是'''<font color="#ff8000">协方差 Covariance</font>'''的类比(因此香农熵类似于方差)。然后计算归一化互信息,类似于'''<font color="#ff8000">皮尔森相关系数 Pearson Product-moment</font>''':<br />
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:<math><br />
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\frac{\operatorname{I}(X;Y)}{\sqrt{H(X)H(Y)}}\; .<br />
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</math><br />
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=== 加权变量 Weighted variants ===<br />
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In the traditional formulation of the mutual information,<br />
<br />
In the traditional formulation of the mutual information,<br />
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在互信息的传统表述中:<br />
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:<math> \operatorname{I}(X;Y) <br />
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= \sum_{y \in Y} \sum_{x \in X} p(x, y) \log \frac{p(x, y)}{p(x)\,p(y)}, </math><br />
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each ''event'' or ''object'' specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent ''apart from'' their probability of occurrence. However, in some applications it may be the case that certain objects or events are more ''significant'' than others, or that certain patterns of association are more semantically important than others.<br />
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each event or object specified by <math>(x, y)</math> is weighted by the corresponding probability <math>p(x, y)</math>. This assumes that all objects or events are equivalent apart from their probability of occurrence. However, in some applications it may be the case that certain objects or events are more significant than others, or that certain patterns of association are more semantically important than others.<br />
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<math>(x, y)</math> 指定的每个事件或对象都由相应的概率<math>p(x, y)</math>进行加权。这假设所有的物体或事件除了发生的概率外都是相等的。然而,在某些应用场景中,某些特定的对象或事件可能比其他对象或事件更重要,或者某些特定的关联模式在语义上比其他模式更重要。<br />
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<br />
<br />
For example, the deterministic mapping <math>\{(1,1),(2,2),(3,3)\}</math> may be viewed as stronger than the deterministic mapping <math>\{(1,3),(2,1),(3,2)\}</math>, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values ({{harvnb|Cronbach|1954}}, {{harvnb|Coombs|Dawes|Tversky|1970}}, {{harvnb|Lockhead|1970}}), and is therefore not sensitive at all to the '''form''' of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following ''weighted mutual information'' {{harv|Guiasu|1977}}.<br />
<br />
For example, the deterministic mapping {(1,1),(2,2),(3,3)} may be viewed as stronger than the deterministic mapping {(1,3),(2,1),(3,2)}, although these relationships would yield the same mutual information. This is because the mutual information is not sensitive at all to any inherent ordering in the variable values, and is therefore not sensitive at all to the form of the relational mapping between the associated variables. If it is desired that the former relation—showing agreement on all variable values—be judged stronger than the later relation, then it is possible to use the following weighted mutual information.<br />
<br />
例如,确定性映射<math>\{(1,1),(2,2),(3,3)\}</math>可能被视为比确定性映射<math>\{(1,3),(2,1),(3,2)\}</math>更强,尽管这些关系产生的互信息是相同的。这是因为互信息对变量值的任何内在顺序都不敏感,因此对关联变量之间的关系映射形式一点也不敏感。如果希望对所有变量值的前一个关系比后一个关系强,则可以使用以下加权互信息的方法:<br />
<br />
<br />
:<math> \operatorname{I}(X;Y) = \sum_{y \in Y} \sum_{x \in X} w(x,y) p(x,y) \log \frac{p(x,y)}{p(x)\,p(y)}, </math><br />
<br />
<br />
<br />
which places a weight <math>w(x,y)</math> on the probability of each variable value co-occurrence, <math>p(x,y)</math>. This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant ''holistic'' or ''[[Prägnanz]]'' factors. In the above example, using larger relative weights for <math>w(1,1)</math>, <math>w(2,2)</math>, and <math>w(3,3)</math> would have the effect of assessing greater ''informativeness'' for the relation <math>\{(1,1),(2,2),(3,3)\}</math> than for the relation <math>\{(1,3),(2,1),(3,2)\}</math>, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref> and there are examples where the weighted mutual information also takes negative values.<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
<br />
<br />
which places a weight 𝑤(𝑥,𝑦) on the probability of each variable value co-occurrence, 𝑝(𝑥,𝑦). This allows that certain probabilities may carry more or less significance than others, thereby allowing the quantification of relevant holistic or Prägnanz factors. In the above example, using larger relative weights for 𝑤(1,1), 𝑤(2,2), and 𝑤(3,3) would have the effect of assessing greater informativeness for the relation {(1,1),(2,2),(3,3)} than for the relation {(1,3),(2,1),(3,2)}, which may be desirable in some cases of pattern recognition, and the like. This weighted mutual information is a form of weighted KL-Divergence, which is known to take negative values for some inputs,[24] and there are examples where the weighted mutual information also takes negative values.[25]<br />
<br />
##<br />
设每个变量值同时出现的概率<math>p(x,y)</math>的权重为<math>w(x,y)</math>。这使得某些特定概率可能比其他概率具有更多(或更少)的重要性,从而可以量化相关的整体或Prägnanz因素。在上面的例子中,对<math>w(1,1)</math>、<math>w(2,2)</math>和<math>w(3,3)</math>使用更大的相对权重,评估关系<math>\{(1,1),(2,2),(3,3)\}</math>比关系<math>\{(1,3),(2,1),(3,2)\}</math>具有更大的信息性,这在一些模式识别等情况下是可行的。这种加权互信息是加权KL散度的一种形式,通常对某些输入取负值,<ref name="weighted-kl">{{cite journal | last1 = Kvålseth | first1 = T. O. | year = 1991 | title = The relative useful information measure: some comments | url = | journal = Information Sciences | volume = 56 | issue = 1| pages = 35–38 | doi=10.1016/0020-0255(91)90022-m}}</ref>并且在一些例子中加权互信息也取负值。<ref>{{cite dissertation|title=Feature Selection Via Joint Likelihood|first=A. |last=Pocock|year=2012|url=http://www.cs.man.ac.uk/~gbrown/publications/pocockPhDthesis.pdf}}</ref><br />
<br />
=== 调整后的互信息 Adjusted mutual information ===<br />
<br />
{{Main|adjusted mutual information}}<br />
<br />
<br />
<br />
A probability distribution can be viewed as a [[partition of a set]]. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The [[adjusted mutual information]] or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the [[adjusted Rand index]] of two different partitions of a set.<br />
<br />
A probability distribution can be viewed as a partition of a set. One may then ask: if a set were partitioned randomly, what would the distribution of probabilities be? What would the expectation value of the mutual information be? The adjusted mutual information or AMI subtracts the expectation value of the MI, so that the AMI is zero when two different distributions are random, and one when two distributions are identical. The AMI is defined in analogy to the adjusted Rand index of two different partitions of a set.<br />
<br />
概率分布可以被看作是集合划分。可能有人会问: 如果一个集合被随机分割,概率的分布会是什么?互信息的期望值是什么?我们用'''<font color="#ff8000">调整后的互信息 Adjusted Mutual Information</font>'''或 AMI 减去 MI 的期望值,这样当两个不同的分布是随机的时候 AMI 为零,当两个分布是相同的时候 AMI 也为零。AMI的定义类似于一个集合的两个不同分区的'''<font color="#ff8000">调整后的Rand指数 Adjusted Rand Index</font>'''。<br />
<br />
=== 绝对互信息 Absolute mutual information ===<!-- This section is linked from Kolmogorov complexity --><br />
<br />
Using the ideas of [[Kolmogorov complexity]], one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
Using the ideas of Kolmogorov complexity, one can consider the mutual information of two sequences independent of any probability distribution:<br />
<br />
利用'''<font color="#ff8000">柯氏复杂性 Kolmogorov Complexity</font>'''的思想,我们可以考虑两个序列的互信息,这两个序列独立于任何概率分布序列:<br />
<br />
<br />
<br />
<br />
<br />
:<math><br />
<br />
\operatorname{I}_K(X;Y) = K(X) - K(X|Y).<br />
<br />
</math><br />
<br />
<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>) one requires the [[chain rule for Kolmogorov complexity]] {{Harvard citation|Li|Vitányi|1997}}. Approximations of this quantity via [[Data compression|compression]] can be used to define a [[Metric (mathematics)|distance measure]] to perform a [[hierarchical clustering]] of sequences without having any [[domain knowledge]] of the sequences {{Harvard citation|Cilibrasi|Vitányi|2005}}.<br />
<br />
To establish that this quantity is symmetric up to a logarithmic factor (I𝐾(𝑋;𝑌)≈I𝐾(𝑌;𝑋)) one requires the chain rule for Kolmogorov complexity.Approximations of this quantity via compression can be used to define a distance measure to perform a hierarchical clustering of sequences without having any domain knowledge of the sequences.<br />
<br />
为了确定这个量在对数因子<math>\operatorname{I}_K(X;Y) \approx \operatorname{I}_K(Y;X)</math>是对称的,需要'''<font color="#ff8000"> 柯氏复杂性的链式规则 Chain Rule for Kolmogorov Complexity</font>'''。通过压缩对这个量的近似值可以用来定义'''<font color="#ff8000">距离度量 Distance Measure</font>'''来执行序列的'''<font color="#ff8000">层次聚类 Hierarchical Clustering</font>''',而不需要序列的任何领域知识。<br />
<br />
=== 线性相关 Linear correlation ===<br />
<br />
<br />
<br />
<br />
Unlike correlation coefficients, such as the [[product moment correlation coefficient]], mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a [[bivariate normal distribution]] (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> {{harv|Gel'fand|Yaglom|1957}}.<br />
<br />
Unlike correlation coefficients, such as the product moment correlation coefficient, mutual information contains information about all dependence—linear and nonlinear—and not just linear dependence as the correlation coefficient measures. However, in the narrow case that the joint distribution for <math>X</math> and <math>Y</math> is a bivariate normal distribution (implying in particular that both marginal distributions are normally distributed), there is an exact relationship between <math>\operatorname{I}</math> and the correlation coefficient <math>\rho</math> .<br />
<br />
互信息不同于相关系数,如'''<font color="#ff8000">积矩相关系数 Product Moment Correlation Coefficient</font>''',互信息包含所有相关信息ーー线性和非线性ーー而不仅仅是相关系数的线性相关。然而,在<math>X</math>和<math>Y</math>的联合分布是'''<font color="#ff8000">二元正态分布 Bivariate Normal Distribution</font>'''(特别是边际分布都是正态分布)的狭义情况下,<math>\operatorname{I}</math>与相关系数<math>\rho</math>之间存在精确的关系。<br />
<br />
:<math>\operatorname{I} = -\frac{1}{2} \log\left(1 - \rho^2\right)</math><br />
<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
The equation above can be derived as follows for a bivariate Gaussian:<br />
<br />
对于双变量高斯分布,上面的公式可以推导如下:<br />
<br />
:<math>\begin{align}<br />
<br />
\begin{pmatrix}<br />
<br />
X_1 \\<br />
<br />
X_2<br />
<br />
\end{pmatrix} &\sim \mathcal{N} \left( \begin{pmatrix}<br />
<br />
\mu_1 \\<br />
<br />
\mu_2<br />
<br />
\end{pmatrix}, \Sigma \right),\qquad<br />
<br />
\Sigma = \begin{pmatrix}<br />
<br />
\sigma^2_1 & \rho\sigma_1\sigma_2 \\<br />
<br />
\rho\sigma_1\sigma_2 & \sigma^2_2<br />
<br />
\end{pmatrix} \\<br />
<br />
H(X_i) &= \frac{1}{2}\log\left(2\pi e \sigma_i^2\right) = \frac{1}{2} + \frac{1}{2}\log(2\pi) + \log\left(\sigma_i\right), \quad i\in\{1, 2\} \\<br />
<br />
H(X_1, X_2) &= \frac{1}{2}\log\left[(2\pi e)^2|\Sigma|\right] = 1 + \log(2\pi) + \log\left(\sigma_1 \sigma_2\right) + \frac{1}{2}\log\left(1 - \rho^2\right) \\<br />
<br />
\end{align}</math><br />
<br />
<br />
Therefore, <br />
<br />
Therefore, <br />
<br />
所以,<br />
<br />
:<math> <br />
<br />
\operatorname{I}\left(X_1; X_2\right) <br />
<br />
= H\left(X_1\right) + H\left(X_2\right) - H\left(X_1, X_2\right) <br />
<br />
<br />
= -\frac{1}{2}\log\left(1 - \rho^2\right)<br />
<br />
</math><br />
<br />
<br />
=== 对于离散数据 For discrete data ===<br />
<br />
When <math>X</math> and <math>Y</math> are limited to be in a discrete number of states, observation data is summarized in a [[contingency table]], with row variable <math>X</math> (or <math>i</math>) and column variable <math>Y</math> (or <math>j</math>). Mutual information is one of the measures of [[association (statistics)|association]] or [[correlation and dependence|correlation]] between the row and column variables. Other measures of association include [[Pearson's chi-squared test]] statistics, [[G-test]] statistics, etc. In fact, mutual information is equal to [[G-test]] statistics divided by <math>2N</math>, where <math>N</math> is the sample size.<br />
<br />
When 𝑋 and 𝑌 are limited to be in a discrete number of states, observation data is summarized in a contingency table, with row variable 𝑋 (or 𝑖) and column variable 𝑌 (or 𝑗). Mutual information is one of the measures of association or correlation between the row and column variables. Other measures of association include Pearson's chi-squared test statistics, G-test statistics, etc. In fact, mutual information is equal to G-test statistics divided by 2𝑁, where 𝑁 is the sample size.<br />
<br />
当<math>X</math>和<math>Y</math>被限制为离散状态时,观测数据汇总在'''<font color="#ff8000">列联表 Contingency Table</font>'''中,其中行变量<math>X</math>(或<math>i</math>)和列变量<math>Y</math>(或<math>j</math>)。互信息是行和列变量之间关联或相关性的度量之一。其他关联度量包括Pearson卡方检验统计量、'''<font color="#ff8000">G检验 G-Test</font>'''统计量等。事实上,互信息等于G检验统计量除以<math>2N</math>,其中<math>N</math>为样本量。<br />
<br />
== 应用 Applications ==<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing [[conditional entropy]]. Examples include:<br />
<br />
In many applications, one wants to maximize mutual information (thus increasing dependencies), which is often equivalent to minimizing conditional entropy. Examples include:<br />
<br />
在许多应用场景中,需要最大化互信息(从而增加依赖关系),这通常相当于最小化条件熵。例如:<br />
<br />
* In [[search engine technology]], mutual information between phrases and contexts is used as a feature for [[k-means clustering]] to discover semantic clusters (concepts).<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> For example, the mutual information of a bigram might be calculated as:<br />
<br />
在搜索引擎技术中,短语和上下文之间的互信息用作k均值聚类的功能,以发现语义聚类(概念)。<ref name=magerman>[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.78.4178&rep=rep1&type=pdf Parsing a Natural Language Using Mutual Information Statistics] by David M. Magerman and Mitchell P. Marcus</ref> 例如,一个二元组的互信息可以计算为:<br />
<br />
<br />
{{Equation box 1<br />
<br />
|indent=::<br />
<br />
|equation=<br />
<br />
<math>MI(x,y) = \log \frac{P_{X,Y}(x,y)}{P_X(x) P_Y(y)} \approx log \frac{\frac{f_{XY}}{B}}{\frac{f_X}{U} \frac{f_Y}{U}} </math><br />
<br />
|cellpadding= 6<br />
<br />
|border<br />
<br />
|border colour = #0073CF<br />
<br />
|background colour=#F5FFFA}}<br />
<br />
<br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<ref name=magerman/><br />
<br />
where <math>f_{XY}</math> is the number of times the bigram xy appears in the corpus, <math>f_{X}</math> is the number of times the unigram x appears in the corpus, B is the total number of bigrams, and U is the total number of unigrams.<br />
<br />
其中<math>f_{XY}</math>是 二元语法 XY 在语料库中出现的次数,<math>f_{X}</math>是一元模型x在语料库中出现的次数,B 是二元语法的总数,U 是一元模型的总数。<ref name=magerman/><br />
<br />
* In [[telecommunications]], the [[channel capacity]] is equal to the mutual information, maximized over all input distributions.<br />
<br />
<br />
In telecommunications, the channel capacity is equal to the mutual information, maximized over all input distributions.<br />
<br />
在电信中,信道容量等于互信息,在所有输入分配中最大化。<br />
<br />
* [[Discriminative model|Discriminative training]] procedures for [[hidden Markov model]]s have been proposed based on the [[maximum mutual information]] (MMI) criterion.<br />
<br />
Discriminative training procedures for hidden Markov models have been proposed based on the maximum mutual information (MMI) criterion.<br />
<br />
现在已经提出了基于最大互信息(MMI)准则的'''<font color="#ff8000">隐马尔可夫模型 Hidden Markov Model</font>'''判别训练方法。<br />
<br />
* [[Nucleic acid secondary structure|RNA secondary structure]] prediction from a [[multiple sequence alignment]].<br />
<br />
RNA secondary structure prediction from a multiple sequence alignment.<br />
<br />
从多序列比对预测RNA二级结构。<br />
<br />
<br />
* [[Phylogenetic profiling]] prediction from pairwise present and disappearance of functionally link [[gene]]s.<br />
<br />
Phylogenetic profiling prediction from pairwise present and disappearance of functionally link genes.<br />
<br />
功能连锁基因成对存在与消失的系统发育模式预测。<br />
<br />
* Mutual information has been used as a criterion for [[feature selection]] and feature transformations in [[machine learning]]. It can be used to characterize both the relevance and redundancy of variables, such as the [[minimum redundancy feature selection]].<br />
<br />
Mutual information has been used as a criterion for feature selection and feature transformations in machine learning. It can be used to characterize both the relevance and redundancy of variables, such as the minimum redundancy feature selection.<br />
<br />
在机器学习中,互信息作为特征选择和特征转换的准则。它可以用来表征变量的相关性和冗余性,例如最小冗余特征选择。<br />
<br />
<br />
* Mutual information is used in determining the similarity of two different [[cluster analysis|clusterings]] of a dataset. As such, it provides some advantages over the traditional [[Rand index]].<br />
<br />
Mutual information is used in determining the similarity of two different clusterings of a dataset. As such, it provides some advantages over the traditional Rand index.<br />
<br />
互信息用于确定数据集中两个不同聚类的相似性。因此,它与传统的Rand指数相比具有一定的优势。<br />
<br />
* Mutual information of words is often used as a significance function for the computation of [[collocation]]s in [[corpus linguistics]]. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within <math>N</math> words of another, goes up with <math>N</math>.<br />
<br />
Mutual information of words is often used as a significance function for the computation of collocations in corpus linguistics. This has the added complexity that no word-instance is an instance to two different words; rather, one counts instances where 2 words occur adjacent or in close proximity; this slightly complicates the calculation, since the expected probability of one word occurring within 𝑁 words of another, goes up with 𝑁.<br />
<br />
在'''<font color="#ff8000">语料库语言学 Corpus Linguistics</font>'''中,单词的互信息常常被用作搭配运算的重要函数。这增加了复杂性,即没有一个单词实例是两个不同单词的实例;相反,我们统计两个单词相邻或非常接近的实例;这稍微使计算复杂化,因为一个单词出现在另一个单词的<math>N</math>单词内的预期概率会增加。<br />
<br />
* Mutual information is used in [[medical imaging]] for [[image registration]]. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same [[coordinate system]] as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
Mutual information is used in medical imaging for image registration. Given a reference image (for example, a brain scan), and a second image which needs to be put into the same coordinate system as the reference image, this image is deformed until the mutual information between it and the reference image is maximized.<br />
<br />
在'''<font color="#ff8000">医学图像 medical imaging</font>'''中,利用互信息进行'''<font color="#ff8000">图像配准 Image Registration</font>'''。给定一个参考图像(例如,脑部扫描),以及需要将第二个图像放入与参考图像相同的'''<font color="#ff8000">坐标系 Coordinate System</font>'''中,该图像会发生变形,直到其与参考图像之间的互信息最大化。<br />
<br />
* Detection of [[phase synchronization]] in [[time series]] analysis<br />
<br />
Detection of phase synchronization in time series analysis<br />
<br />
时间序列分析中的'''<font color="#ff8000">相位同步 Phase Synchronization</font>'''检测。<br />
<br />
* In the [[infomax]] method for neural-net and other machine learning, including the infomax-based [[Independent component analysis]] algorithm<br />
<br />
In the infomax method for neural-net and other machine learning, including the infomax-based Independent component analysis algorithm.<br />
<br />
在'''<font color="#ff8000">信息极大化 Infomax</font>'''方法中用于神经网络等机器学习,包括基于信息极大化的'''<font color="#ff8000">独立成分分析 Independent Component Analysis</font>'''算法<br />
<br />
* Average mutual information in [[delay embedding theorem]] is used for determining the ''embedding delay'' parameter.<br />
<br />
Average mutual information in delay embedding theorem is used for determining the embedding delay parameter.<br />
<br />
利用'''<font color="#ff8000">延迟嵌入定理 Delay Embedding Theorem</font>'''中的平均互信息确定嵌入延迟参数。<br />
<br />
* Mutual information between [[genes]] in [[microarray|expression microarray]] data is used by the ARACNE algorithm for reconstruction of [[gene regulatory network|gene networks]].<br />
<br />
Mutual information between genes in expression microarray data is used by the ARACNE algorithm for reconstruction of gene networks.<br />
<br />
ARACNE算法利用表达微阵列数据中基因间的互信息来重构'''<font color="#ff8000">基因网络 Gene Networks</font>'''。<br />
<br />
<br />
* In [[statistical mechanics]], [[Loschmidt's paradox]] may be expressed in terms of mutual information.<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref> Loschmidt noted that it must be impossible to determine a physical law which lacks [[time reversal symmetry]] (e.g. the [[second law of thermodynamics]]) only from physical laws which have this symmetry. He pointed out that the [[H-theorem]] of [[Boltzmann]] made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in [[phase space]], then [[Liouville's theorem (Hamiltonian)|Liouville's theorem]] implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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In statistical mechanics, Loschmidt's paradox may be expressed in terms of mutual information.[27][28] Loschmidt noted that it must be impossible to determine a physical law which lacks time reversal symmetry (e.g. the second law of thermodynamics) only from physical laws which have this symmetry. He pointed out that the H-theorem of Boltzmann made the assumption that the velocities of particles in a gas were permanently uncorrelated, which removed the time symmetry inherent in the H-theorem. It can be shown that if a system is described by a probability density in phase space, then Liouville's theorem implies that the joint information (negative of the joint entropy) of the distribution remains constant in time. The joint information is equal to the mutual information plus the sum of all the marginal information (negative of the marginal entropies) for each particle coordinate. Boltzmann's assumption amounts to ignoring the mutual information in the calculation of entropy, which yields the thermodynamic entropy (divided by Boltzmann's constant).<br />
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在统计力学中,'''<font color="#ff8000">洛施密特悖论 Loschmidt's Paradox</font>'''可以用互信息来表示。<ref name=everett56>[[Hugh Everett]] [https://www.pbs.org/wgbh/nova/manyworlds/pdf/dissertation.pdf Theory of the Universal Wavefunction], Thesis, Princeton University, (1956, 1973), pp 1–140 (page 30)</ref><ref name=everett57>{{cite journal | last1 = Everett | first1 = Hugh | authorlink = Hugh Everett | year = 1957 | title = Relative State Formulation of Quantum Mechanics | url = http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | journal = Reviews of Modern Physics | volume = 29 | issue = 3 | pages = 454–462 | doi = 10.1103/revmodphys.29.454 | bibcode = 1957RvMP...29..454E | access-date = 2012-07-16 | archive-url = https://web.archive.org/web/20111027191052/http://www.univer.omsk.su/omsk/Sci/Everett/paper1957.html | archive-date = 2011-10-27 | url-status = dead }}</ref>洛施密特指出,只从具有这种对称性的物理定律中确定缺乏时间反转对称性的物理定律(例如'''<font color="#ff8000">热力学第二定律 Second Law of Thermodynamics</font>''')是不可能的。他指出,Boltzmann 玻尔兹曼的H-定理假设气体中粒子的速度是永久不相关的,这就消除了H-定理固有的时间对称性。可以证明,如果系统在相空间中用概率密度来描述,那么'''<font color="#ff8000">刘维尔定理 Liouville's Theorem</font>'''意味着分布的联合信息(联合熵的负)在时间上保持不变。联合信息等于互信息加上每个粒子坐标的所有边缘信息(负的边缘熵)之和。玻尔兹曼的假设相当于在熵的计算中忽略了互信息,从而得到了热力学熵(除以玻尔兹曼常数)。<br />
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* The mutual information is used to learn the structure of [[Bayesian network]]s/[[dynamic Bayesian network]]s, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:<ref>{{Google Code|globalmit|GlobalMIT}}</ref> learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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The mutual information is used to learn the structure of Bayesian networks/dynamic Bayesian networks, which is thought to explain the causal relationship between random variables, as exemplified by the GlobalMIT toolkit:[29] learning the globally optimal dynamic Bayesian network with the Mutual Information Test criterion.<br />
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互信息用于学习'''<font color="#ff8000">贝叶斯网络 Bayesian Network</font>'''/'''<font color="#ff8000">动态贝叶斯网络 Dynamic Bayesian Network</font>'''的结构,被认为是用来解释随机变量之间的因果关系,如GlobalMIT工具包<ref>{{Google Code|globalmit|GlobalMIT}}</ref>用互信息检验准则学习全局最优动态贝叶斯网络。<br />
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* Popular cost function in [[decision tree learning]].<br />
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Popular cost function in decision tree learning.<br />
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作为'''<font color="#ff8000">决策树学习 Decision Tree Learning</font>'''中常用的代价函数。<br />
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* The mutual information is used in [[cosmology]] to test the influence of large-scale environments on galaxy properties in the [[Galaxy Zoo]].<br />
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The mutual information is used in cosmology to test the influence of large-scale environments on galaxy properties in the Galaxy Zoo.<br />
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在'''<font color="# ff8000">星系 Galaxy Zoo</font>'''中,利用互信息在'''<font color="#ff8000">宇宙学 Cosmology</font>'''中测试大尺度环境对星系性质的影响。<br />
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* The mutual information was used in [[Solar Physics]] to derive the solar [[differential rotation]] profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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The mutual information was used in Solar Physics to derive the solar differential rotation profile, a travel-time deviation map for sunspots, and a time–distance diagram from quiet-Sun measurements.<br />
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在'''<font color="#ff8000">太阳物理学 Solar Physics</font>'''中,互信息被用于推导太阳差分自转剖面图、太阳黑子的旅行时间偏差图和从安静太阳测量的时间-距离图。<ref>{{cite journal|last1=Keys|first1=Dustin|last2=Kholikov|first2=Shukur|last3=Pevtsov|first3=Alexei A.|title=Application of Mutual Information Methods in Time Distance Helioseismology|journal=Solar Physics|date=February 2015|volume=290|issue=3|pages=659–671|doi=10.1007/s11207-015-0650-y|arxiv=1501.05597|bibcode=2015SoPh..290..659K}}</ref><br />
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* Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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Used in Invariant Information Clustering to automatically train neural network classifiers and image segmenters given no labelled data.<br />
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用于不变信息聚类,在没有标记数据的情况下自动训练神经网络分类器和图像分割器。<ref name=iic>[https://arxiv.org/abs/1807.06653 Invariant Information Clustering for Unsupervised Image Classification and Segmentation] by Xu Ji, Joao Henriques and Andrea Vedaldi</ref><br />
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== 参见 See also ==<br />
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* [[Pointwise mutual information 点态互信息]]<br />
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* [[Quantum mutual information 量子互信息]]<br />
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== 注释 Notes ==<br />
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<references /><br />
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== 参考资料 References ==<br />
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* {{cite journal|last1=Baudot|first1=P.|last2=Tapia|first2=M.|last3=Bennequin|first3=D.|last4=Goaillard|first4=J.M.|title=Topological Information Data Analysis|journal=Entropy|volume=21|issue=9|at=869|year=2019|doi= 10.3390/e21090869|bibcode=2019Entrp..21..869B|arxiv=1907.04242}}<br />
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<br />
<br />
* {{cite journal<br />
| last1 = Cilibrasi<br />
<br />
| first1 = R.<br />
| first2 = Paul<br />
| last2 = Vitányi<br />
| title = Clustering by compression<br />
| journal = IEEE Transactions on Information Theory<br />
| volume = 51<br />
<br />
| issue = 4<br />
<br />
| pages = 1523–1545<br />
| year = 2005<br />
| url = http://www.cwi.nl/~paulv/papers/cluster.pdf<br />
| doi = 10.1109/TIT.2005.844059<br />
<br />
| ref = harv<br />
<br />
| arxiv = cs/0312044}}<br />
<br />
<br />
* {{Cite book|last1=Cronbach|first1=L. J.|year=1954|chapter=On the non-rational application of information measures in psychology|editor1-first=Henry|editor1-last=Quastler|editor1-link=Henry Quastler|title=Information Theory in Psychology: Problems and Methods|publisher=Free Press|place=Glencoe, Illinois|pages=14–30|ref=harv}}<br />
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<br />
<br />
* {{cite book|last1=Coombs|first1=C. H.|last2=Dawes|first2=R. M.|last3=Tversky|first3=A.|year=1970|title=Mathematical Psychology: An Elementary Introduction|publisher=Prentice-Hall|location=Englewood Cliffs, New Jersey|ref=harv}}<br />
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* {{cite journal|first1=Kenneth Ward|last1=Church|first2=Patrick|last2=Hanks|title=Word association norms, mutual information, and lexicography|journal=Proceedings of the 27th Annual Meeting of the Association for Computational Linguistics|pages=76–83|year=1989|url=http://dl.acm.org/citation.cfm?id=89095|doi=10.3115/981623.981633|doi-access=free}}<br />
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* {{cite journal|first1=I.M.|last1=Gel'fand|first2=A.M.|last2=Yaglom|year=1957|title=Calculation of amount of information about a random function contained in another such function|journal= American Mathematical Society Translations: Series 2 |volume = 12 | pages = 199–246 |ref=harv}} English translation of original in ''Uspekhi Matematicheskikh Nauk'' '''12'''&nbsp;(1):&nbsp;3-52.<br />
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* {{cite book|last=Guiasu|first=Silviu|year=1977|title=Information Theory with Applications|publisher=McGraw-Hill, New York|isbn=978-0-07-025109-0|ref=harv}}<br />
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* {{cite book<br />
| last1 = Li<br />
| first1 = Ming<br />
| first2 = Paul<br />
<br />
| last2 = Vitányi<br />
| title = An introduction to Kolmogorov complexity and its applications<br />
<br />
| location = New York<br />
| publisher = [[Springer-Verlag]]<br />
|date=February 1997<br />
| isbn = 978-0-387-94868-3<br />
| ref=harv }}<br />
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* {{cite journal | last1 = Lockhead | first1 = G. R. | year = 1970 | title = Identification and the form of multidimensional discrimination space | url = | journal = Journal of Experimental Psychology | volume = 85 | issue = 1| pages = 1–10 | doi=10.1037/h0029508| pmid = 5458322 | ref = harv}}<br />
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* David J. C. MacKay. ''[http://www.inference.phy.cam.ac.uk/mackay/itila/book.html Information Theory, Inference, and Learning Algorithms]'' Cambridge: Cambridge University Press, 2003. {{isbn|0-521-64298-1}} (available free online)<br />
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* {{cite journal | last1 = Haghighat | first1 = M. B. A. | last2 = Aghagolzadeh | first2 = A. | last3 = Seyedarabi | first3 = H. | year = 2011 | title = A non-reference image fusion metric based on mutual information of image features | url = | journal = Computers & Electrical Engineering | volume = 37 | issue = 5| pages = 744–756 | doi=10.1016/j.compeleceng.2011.07.012}}<br />
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* [[Athanasios Papoulis]]. ''Probability, Random Variables, and Stochastic Processes'', second edition. New York: McGraw-Hill, 1984. ''(See Chapter 15.)''<br />
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* {{cite book|last1=Witten|first1=Ian H.|last2=Frank|first2=Eibe |lastauthoramp=yes |year=2005|title=Data Mining: Practical Machine Learning Tools and Techniques|publisher=Morgan Kaufmann, Amsterdam|isbn=978-0-12-374856-0|url=http://www.cs.waikato.ac.nz/~ml/weka/book.html|ref=harv}}<br />
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* {{cite journal|author=Peng, H.C. |author2=Long, F. |author3=Ding, C. |lastauthoramp=yes |title=Feature selection based on mutual information: criteria of max-dependency, max-relevance, and min-redundancy|journal=IEEE Transactions on Pattern Analysis and Machine Intelligence|volume=27|issue=8|pages=1226–1238|year=2005|url=http://research.janelia.org/peng/proj/mRMR/index.htm|doi=10.1109/tpami.2005.159|pmid=16119262|citeseerx=10.1.1.63.5765}}<br />
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* {{cite journal|author1=Andre S. Ribeiro |author2=Stuart A. Kauffman |author3=Jason Lloyd-Price |author4=Bjorn Samuelsson |author5=Joshua Socolar |last-author-amp=yes |year=2008|title=Mutual Information in Random Boolean models of regulatory networks|journal=Physical Review E|volume=77|issue=1|pages=011901 |arxiv=0707.3642|doi=10.1103/physreve.77.011901 |pmid=18351870 |bibcode=2008PhRvE..77a1901R}}<br />
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* {{cite journal<br />
| last1 = Wells<br />
| first1 = W.M. III<br />
| last2 = Viola<br />
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| last3 = Atsumi<br />
| first3 = H.<br />
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| last4 = Nakajima<br />
<br />
| first4 = S.<br />
<br />
| last5 = Kikinis<br />
| first5 = R.<br />
| title = Multi-modal volume registration by maximization of mutual information<br />
<br />
| journal = Medical Image Analysis<br />
| volume = 1<br />
| issue = 1<br />
| pages = 35–51<br />
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| year = 1996<br />
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| pmid = 9873920<br />
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| doi = 10.1016/S1361-8415(01)80004-9<br />
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| url = http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
| ref = harv<br />
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| access-date = 2010-08-05<br />
| archive-url = https://web.archive.org/web/20080906201633/http://www.ai.mit.edu/people/sw/papers/mia.pdf<br />
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| archive-date = 2008-09-06<br />
| url-status = dead<br />
}}<br />
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* {{cite journal | last1 = Pandey | first1 = Biswajit | last2 = Sarkar | first2 = Suman | year = 2017 | title = How much a galaxy knows about its large-scale environment?: An information theoretic perspective | url = | journal = Monthly Notices of the Royal Astronomical Society Letters| volume = 467 | issue = 1| page = L6 | doi=10.1093/mnrasl/slw250| arxiv = 1611.00283| bibcode = 2017MNRAS.467L...6P}}<br />
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[[Category:Information theory]]<br />
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Category:Information theory<br />
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范畴: 信息论<br />
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[[Category:Entropy and information]]<br />
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Category:Entropy and information<br />
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类别: 熵和信息<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Mutual information]]. Its edit history can be viewed at [[互信息/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21644行为经济学2021-02-07T08:18:11Z<p>Vicky:/* Financial models 金融模型 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型,补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论,即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman“将心理学研究的见解整合到经济科学中,特别是在不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是身体在面对任务时的非特异性反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>软家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
。<br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
。<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
。<br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
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Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
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'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
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和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
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== Notable people 著名人物==<br />
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=== Economics 经济学===<br />
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{{div col|colwidth=20em}}<br />
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* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
<br />
* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
<br />
* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
<br />
* [[Larry Summers]]<br />
<br />
* [[Richard Thaler]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
<br />
* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
<br />
* [[Robert Vishny]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
<br />
{{div col end}}<br />
<br />
<br />
== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
<br />
{{div col|colwidth=30em}}<br />
<br />
* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
<br />
* [[Behavioralism]] 行为主义<br />
<br />
* [[Behavioral analysis of markets]] 市场的行为分析<br />
<br />
* [[Behavioral operations research]] 行为运筹学<br />
<br />
*[[Big Five personality traits]] 大五人格<br />
<br />
* [[Confirmation bias]] 确认偏差<br />
<br />
* [[Cultural economics]] 文化经济学<br />
<br />
* [[Culture change]] 文化变迁<br />
<br />
* [[Economic sociology]] 经济社会学<br />
<br />
* [[Emotional bias]] 情绪偏差<br />
<br />
* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
<br />
* [[Hindsight bias]] 后见之明偏差<br />
<br />
* ''[[Homo reciprocans]]'' “人属”<br />
<br />
* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
<br />
* [[List of cognitive biases]] 认知偏差列表<br />
<br />
* [[Market sentiment]] 市场情绪<br />
<br />
* [[Methodological individualism]] 方法论个人主义<br />
<br />
* [[Nudge theory]] “助推”理论<br />
<br />
* [[Observational techniques]] 可观察的技术<br />
<br />
* [[Praxeology]] 人类行为学<br />
<br />
* [[Priority heuristic]] 齐当别启发式<br />
<br />
* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
<br />
* [[Repugnancy costs]] 厌恶成本<br />
<br />
* [[Socioeconomics]] 社会经济学<br />
<br />
* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
<br />
* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
<br />
* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
<br />
* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
<br />
* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
<br />
* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
<br />
* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
<br />
* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
<br />
* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
<br />
* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
<br />
* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
<br />
* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
<br />
* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
<br />
* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
<br />
* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
<br />
* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
<br />
* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
<br />
*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
<br />
* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
<br />
*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
<br />
<br />
<br />
== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
<br />
== External links ==<!-- This section is linked from Behavioral finance --><br />
<br />
外部链接! -- 这一部分链接来自行为金融学 -- <br />
<br />
{{wikiquote}}<br />
<br />
* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
<br />
* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
<br />
* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
<br />
* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
<br />
* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
<br />
* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
<br />
* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
<br />
* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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{{Authority control}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21643行为经济学2021-02-07T07:30:38Z<p>Vicky:/* Nudge theory “助推”理论 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
<!--'Economic psychology' redirects here--><br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
<br />
'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
<br />
Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型,补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论,即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman“将心理学研究的见解整合到经济科学中,特别是在不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是身体在面对任务时的非特异性反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>软家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
。<br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
。<br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
。<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
<br />
One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
<br />
反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
<br />
Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
<br />
像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
。<br />
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<br />
<br />
A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
<br />
<br />
<br />
A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
。<br />
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=== Behavioral game theory 行为博弈论===<br />
<br />
{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
<br />
Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
<br />
'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
<br />
<br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
<br />
和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
。<br />
<br />
<br />
<br />
=== Economic reasoning in animals 动物的经济推理===<br />
<br />
A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
<br />
A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
<br />
Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
<br />
除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
<br />
<br />
=== Neuroeconomics 神经经济学===<br />
<br />
{{Main|Neuroeconomics}}<br />
<br />
Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
<br />
Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
<br />
'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
<br />
<br />
It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
<br />
It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
<br />
它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
。<br />
<br />
<br />
<br />
Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
<br />
Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
<br />
行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
<br />
<br />
<br />
<br />
== Notable people 著名人物==<br />
<br />
<br />
<br />
=== Economics 经济学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
<br />
* [[Werner De Bondt]]<br />
<br />
* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
<br />
* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
<br />
* [[Larry Summers]]<br />
<br />
* [[Richard Thaler]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
<br />
* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
<br />
* [[Robert Vishny]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
<br />
{{div col end}}<br />
<br />
<br />
== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
<br />
{{div col|colwidth=30em}}<br />
<br />
* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
<br />
* [[Behavioralism]] 行为主义<br />
<br />
* [[Behavioral analysis of markets]] 市场的行为分析<br />
<br />
* [[Behavioral operations research]] 行为运筹学<br />
<br />
*[[Big Five personality traits]] 大五人格<br />
<br />
* [[Confirmation bias]] 确认偏差<br />
<br />
* [[Cultural economics]] 文化经济学<br />
<br />
* [[Culture change]] 文化变迁<br />
<br />
* [[Economic sociology]] 经济社会学<br />
<br />
* [[Emotional bias]] 情绪偏差<br />
<br />
* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
<br />
* [[Hindsight bias]] 后见之明偏差<br />
<br />
* ''[[Homo reciprocans]]'' “人属”<br />
<br />
* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
<br />
* [[List of cognitive biases]] 认知偏差列表<br />
<br />
* [[Market sentiment]] 市场情绪<br />
<br />
* [[Methodological individualism]] 方法论个人主义<br />
<br />
* [[Nudge theory]] “助推”理论<br />
<br />
* [[Observational techniques]] 可观察的技术<br />
<br />
* [[Praxeology]] 人类行为学<br />
<br />
* [[Priority heuristic]] 齐当别启发式<br />
<br />
* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
<br />
* [[Repugnancy costs]] 厌恶成本<br />
<br />
* [[Socioeconomics]] 社会经济学<br />
<br />
* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
<br />
* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
<br />
* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
<br />
* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
<br />
* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
<br />
* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
<br />
* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
<br />
* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
<br />
* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
<br />
* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
<br />
* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
<br />
* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
<br />
* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
<br />
* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
<br />
* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
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* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
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*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E9%BA%A6%E5%85%8B%E6%96%AF%E9%9F%A6%E5%A6%96&diff=21642麦克斯韦妖2021-02-07T07:10:46Z<p>Vicky:</p>
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[[File:Maxwell's demon.svg|right|340px|thumb|麦克斯韦妖假想实验示意图。]]<br />
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'''Maxwell's demon''' is a [[thought experiment]] created by the physicist [[James Clerk Maxwell]] in 1867 in which he suggested how the [[second law of thermodynamics]] might hypothetically be violated.<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref> In the thought experiment, a [[Demon (thought experiment)|demon]] controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing [[entropy]] and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and [[information theory]] extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated. In the thought experiment, a demon controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and information theory extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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'''<font color="#ff8000"> 麦克斯韦妖 Maxwell's demon</font>'''是英国物理学家詹姆斯·克拉克·麦克斯韦 James Clerk Maxwell于1867年为了说明违反'''<font color="#ff8000"> 热力学第二定律 second law of thermodynamics</font>'''的可能性而设想的假想实验。在这个实验当中,一个妖怪控制着两个气体舱之间的一扇小门。当独立的气体分子接近门时,妖怪迅速的打开和关闭门,快速的分子进入其中的一个腔,慢速的分子进入另外一个腔。因为速度更快的分子温度更高,妖怪的动作导致一个腔室升温,另一个腔室降温,从而减少熵,违反了热力学第二定律。<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref>这个假想实验引起了关于热力学和信息论之间关系的争论和理论工作,并一直延续到今天,一些科学家认为理论上的考虑排除了任何以这种方式违反第二定律的实际装置。<br />
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== 思想的起源和历史 ==<br />
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The [[thought experiment]] first appeared in a letter [[James Clerk Maxwell|Maxwell]] wrote to [[Peter Guthrie Tait]] on 11 December 1867. It appeared again in a letter to [[John William Strutt]] in 1871, before it was presented to the public in Maxwell's 1872 book on [[thermodynamics]] titled ''Theory of Heat''.<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to John William Strutt in 1871, before it was presented to the public in Maxwell's 1872 book on thermodynamics titled Theory of Heat.<br />
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1867年12月11日,Maxwell在写给彼得·格思里·泰特 Peter Guthrie Tait的一封信中首次提出了这个假想实验。Maxwell在1871年写给约翰·威廉·斯特鲁特 John William Strutt 的信中再次提到该试验,后来在Maxwell 1872年出版的热力学书籍《热理论》(Theory of Heat)中公之于众。<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". [[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]] was the first to use the word "demon" for Maxwell's concept, in the journal ''[[Nature (journal)|Nature]]'' in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". William Thomson (Lord Kelvin) was the first to use the word "demon" for Maxwell's concept, in the journal Nature in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<br />
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在Maxwell的信件和书中,他将妖怪打开腔室的门描述为一个“有限的存在”。威廉·汤姆森 William Thomson (开尔文勋爵)在1874年的《自然》杂志上第一次用“妖”这个词来形容Maxwell的这一概念,并且表示他打算扩展这个词的含义,而不是恶意曲解。<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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== 最初的假想实验 ==<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different [[temperature]], when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature.<ref name="Bennett87">{{cite journal<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. The second law is also expressed as the assertion that in an isolated system, entropy never decreases.<br />
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热力学第二定律确保(通过统计概率)当两个不同温度的物体相互接触并与宇宙的其余部分隔离时,它们将演化为热力学平衡,最后两个物体的温度大致相同。第二定律也表示为这样的结论:在一个孤立的系统中,熵永远不会减少。<br />
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Maxwell构想了一个假想实验,作为进一步理解第二定律的方法。他对实验的描述如下:<br />
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....如果我们设想一种妖能力非常发达,以至于他能够跟踪每一个分子的运行轨迹,那么这种本质上和我们一样有限的存在,就能够做到我们不可能做到的事情。因为我们已经看到,在一个充满空气的容器中,在均匀的温度下,分子的运动速度决不是均匀的,尽管任意选择的大量分子的平均速度几乎是均匀的。假设我们有一箱气体被分成A和B两个区域,分割板上面有一个小洞。这个能够观察每一个分子的生灵,可以打开或关闭这个小洞,只允许速度快的分子从A飞向B,而速度慢的分子从B飞向A。如此一来,不需要任何外界做功,我们就可以升高B区的温度而降低A区的温度,从而打破热力学第二定律。<br />
<font color="#32cd32"> 这里多了一段非原文 </font> <br />
In other words, Maxwell imagines one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics. A heat engine operating between the thermal reservoirs A and B could extract useful work from this temperature difference.<br />
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换句话说,Maxwell假设一个容器被分成A和B两部分。两部分在相同的温度下装入相同的气体,并且相邻放置。通过观察两边的分子,一个假想中的妖怪守护着两部分之间的活动门。当一个来自A的比平均速度快的分子飞向活动门的时候,妖怪打开了这个活动门,这个分子就会从A飞向B。相对应的,当一个来自B的比平均速度慢的分子飞向活动门的时候,妖怪会让它从B飞向A。B中的分子的平均速度就会增加,而A中的分子的平均速度会减慢。由于平均分子速度与温度相对应,因此A中的温度降低,B中的温度升高,这与热力学第二定律相反。在热源A和热源B之间运行的热机可以从这种温度差中提取有用的功。<br />
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The demon must allow molecules to pass in both directions in order to produce only a temperature difference; one-way passage only of faster-than-average molecules from A to B will cause higher temperature and pressure to develop on the B side.<br />
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妖必须允许分子在两个方向上通过,以便只产生温度差; 只有比平均速度快的分子从A到B 单向通过才会使B部分产生更高的温度和压力。<br />
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== 批评与发展 ==<br />
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Several physicists have presented calculations that show that the second law of thermodynamics will not actually be violated, if a more complete analysis is made of the whole system including the demon. The essence of the physical argument is to show, by calculation, that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described. That is, it would take more thermodynamic work to gauge the speed of the molecules and selectively allow them to pass through the opening between A and B than the amount of energy gained by the difference of temperature caused by doing so.<br />
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一些物理学家展示的计算结果表明,如果对包括妖在内的整个系统进行更完整的分析,则实际上不会违反热力学第二定律。物理论证的精髓在于,通过计算来证明,任何妖都必须“产生”更多的熵来分离分子,这比描述的方法所消除的熵多。就是说,与通过这种方式引起的温度差所获得的能量相比,需要更多的热力学功来衡量分子的速度并选择性地使它们通过A和B之间的门。<br />
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One of the most famous responses to this question was suggested in 1929 by Leó Szilárd, and later by Léon Brillouin. He realized that some measuring processes need not increase thermodynamic entropy as long as they were thermodynamically reversible. He suggested these "reversible" measurements could be used to sort the molecules, violating the Second Law. However, due to the connection between thermodynamic entropy and information entropy, this also meant that the recorded measurement must not be erased. In other words, to determine whether to let a molecule through, the demon must acquire information about the state of the molecule and either discard it or store it. Discarding it leads to immediate increase in entropy but the demon cannot store it indefinitely. In 1982, Charles Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Although Bennett had reached the same conclusion as Szilard's 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons. Regarding Landauer's principle, the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz et al. in 2012. Furthermore, Lutz et al. confirmed that in order to approach the Landauer's limit, the system must asymptotically approach zero processing speed.<br />
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对这个问题最著名的回答之一是1929年由莱奥·西拉拉德Leó Szilárd和莱昂·布里渊 Léon Brillouin提出的。Szilárd指出,麦克斯韦妖需要一些方法来测量分子的速度,而获取信息的过程需要消耗能量。由于妖和气体是相互作用的,我们必须考虑气体和妖的总熵。妖的能量消耗将导致妖熵值的增加,这将大于气体熵值的降低。1960年,罗尔夫·兰道尔 Rolf Landauer提出了一个例外。他认识到,只要某些测量过程是热力学可逆的,就不需要增加熵。他认为这些“可逆”的测量可以用来分类分子,违反第二定律。但是,由于热力学熵和信息熵之间的联系,这还意味着不得删除已记录的测量。换句话说,为了决定是否让一个分子通过,妖必须获得关于分子状态的信息,要么丢弃它,要么存储它。丢弃它会立即导致熵的增加,但是妖不能无限期地储存它。1982年,查尔斯·本内特 Charles Bennett指出,无论准备得多么充分,妖最终都会耗尽信息存储空间,并且必须开始删除它先前收集的信息。擦除信息是一种热力学不可逆性过程,它增加了系统的熵。虽然Bennett得出了与Szilárd1929年的论文相同的结论,即麦克斯韦妖不能违反第二定律,因为会产生熵,而熵是由于不同的原因而达到的。根据Landauer原理,埃里克·卢兹 Eric Lutz等人在2012年通过实验测量了擦除信息所消耗的最小能量。此外,Lutz 等人证实,为了接近 Landauer 的极限,系统必须渐近接近零处理速度。<br />
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John Earman and John D. Norton have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the second law of thermodynamics cannot be violated by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc. It would therefore be circular to invoke these derived properties to defend the second law from the demonic argument. Bennett later acknowledged the validity of Earman and Norton's argument, while maintaining that Landauer's principle explains the mechanism by which real systems do not violate the second law of thermodynamics.<br />
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约翰·厄曼 John Earman和约翰 诺顿 John d. Norton 认为 Szilárd 和 Landauer 对麦克斯韦妖的解释是从假设热力学第二定律不会被妖侵犯开始的,并且从这个假设中得出妖的进一步属性,包括在擦除信息时消耗能量的必要性等等。因此援引这些派生属性来捍卫第二定律不受妖的影响是循环的。Bennett后来承认 Earman 和 Norton 的论点是正确的,同时坚持 Landauer 原理解释了真实系统不违反热力学第二定律的机制<br />
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== 近来的发展 ==<br />
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Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating systems has provided deeper insight on each information process with each subsystem. From this viewpoint, the measurement process is regarded as a process where the correlation (mutual information) between the engine and the demon increases, and the feedback process is regarded as a process where the correlation decreases. If the correlation changes, thermodynamic relations as the second law of thermodynamics and the fluctuation theorem for each subsystem should be modified, and for the case of external control a second-law like inequality and a generalized fluctuation theorem with mutual information are satisfied. These relations suggest that we need extra thermodynamic cost to increase correlation (measurement case), and in contrast we can apparently violate the second law up to the consumption of correlation (feedback case). For more general information processes including biological information processing, both inequality and equality with mutual information hold.<br />
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虽然 Landauer 和 Bennett 的论证只是回答了热力学第二定律和整个 Szilard 引擎系统的循环过程之间的一致性(引擎和妖的组合系统) ,但是最近一个基于非平衡态热力学的方法为小型波动系统提供了对每个子系统的信息处理的更深入的了解。从这个观点出发,将测量过程看作是引擎与妖之间相关性(互信息)增加的过程,而反馈过程看作是相关性减少的过程。如果相关性发生变化,则应修改作为热力学第二定律的热力学关系和每个子系统的波动定理,对于外部控制,则满足第二定律,如不等式和具有互信息的广义波动定理。这些关系表明,我们需要额外的热力学成本来增加相关性(测量案例) ,相比之下,我们可以明显地违反第二定律,直到消耗相关性(反馈案例)。对于包括生物信息处理在内的更一般的信息处理过程,互信息的不平等和平等都成立。<br />
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== 应用 ==<br />
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Real-life versions of Maxwellian demons occur, but all such "real demons" or molecular demons have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology. Single-atom traps used by particle physicists allow an experimenter to control the state of individual quanta in a way similar to Maxwell's demon.<br />
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现实版本的麦克斯韦妖也会出现,但是所有这些“真正的妖”或者分子妖都有其降低熵值的作用,并且在其他地方熵值的增加中得到适当的平衡。分子大小的机制不再只存在于生物学中; 它们也是纳米技术这一新兴领域的主题。粒子物理学家使用的单原子陷阱使得实验者可以像麦克斯韦妖那样控制单个量子的状态。<br />
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If hypothetical mirror matter exists, Zurab Silagadze proposes that demons can be envisaged, "which can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons."<br />
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如果假想的镜像物质存在,祖拉布·西拉加兹 Zurab Silagadze 提出妖可以被设想,“妖可以像第二类永久移动物一样: 只从一个蓄热池中提取热能,用它来做功,并与其他普通世界隔绝。然而,第二定律并没有被违反,因为妖通过发射镜像光子在世界的隐藏(镜像)区域付出了熵代价。<br />
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== 实验性工作 == <br />
In the February 2007 issue of Nature, David Leigh, a professor at the University of Edinburgh, announced the creation of a nano-device based on the Brownian ratchet popularized by Richard Feynman. Leigh's device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (light in this case) and therefore does not violate thermodynamics.<br />
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在2007年2月的《自然》杂志上,爱丁堡大学的戴维·利 David Leigh 教授宣布制造了一种基于理查德·费曼 Richard Feynman 推广的布朗棘轮的纳米装置。Leigh的设备能够使化学系统失衡,但它必须由外部源(在这种情况下是光)提供动力,因此不违反热力学。<br />
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Previously, researchers including Nobel Prize winner Fraser Stoddart, created ring-shaped molecules called rotaxanes which could be placed on an axle connecting two sites, A and B. Particles from either site would bump into the ring and move it from end to end. If a large collection of these devices were placed in a system, half of the devices had the ring at site A and half at B, at any given moment in time.<br />
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此前,包括诺贝尔奖获得者弗雷泽·斯托达特 Fraser Stoddart在内的研究人员创造了一种环状分子,称为轮烷,可以放置在连接两个位点A和B的轴上,任何一个位点的粒子都会撞到环上,从一端移动到另一端。如果将大量的这类设备放置在系统中,则在任何给定时间,一半的设备的环在站点A处,一半的站点在B处。<br />
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Leigh made a minor change to the axle so that if a light is shone on the device, the center of the axle will thicken, restricting the motion of the ring. It only keeps the ring from moving, however, if it is at A. Over time, therefore, the rings will be bumped from B to A and get stuck there, creating an imbalance in the system. In his experiments, Leigh was able to take a pot of "billions of these devices" from 50:50 equilibrium to a 70:30 imbalance within a few minutes.<br />
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Leigh对轮轴做了很小的改动,因此,如果在设备上照亮了灯,轮轴的中心将会变厚,从而限制了环的运动。但是,如果它位于A处,则只能阻止环移动。随着时间的推移,因此,环将从B碰撞到A并被困在那里,在系统中创建不平衡状态。在他的实验中,利 Leigh在几分钟之内就能从50:50的平衡状态变成70:30的不平衡状态,造就了“数十亿个此类设备”。<br />
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In 2009 Mark G. Raizen developed a laser atomic cooling technique which realizes the process Maxwell envisioned of sorting individual atoms in a gas into different containers based on their energy. The new concept is a one-way wall for atoms or molecules that allows them to move in one direction, but not go back. The operation of the one-way wall relies on an irreversible atomic and molecular process of absorption of a photon at a specific wavelength, followed by spontaneous emission to a different internal state. The irreversible process is coupled to a conservative force created by magnetic fields and/or light. Raizen and collaborators proposed using the one-way wall in order to reduce the entropy of an ensemble of atoms. In parallel, Gonzalo Muga and Andreas Ruschhaupt independently developed a similar concept. Their "atom diode" was not proposed for cooling, but rather for regulating the flow of atoms. The Raizen Group demonstrated significant cooling of atoms with the one-way wall in a series of experiments in 2008. Subsequently, the operation of a one-way wall for atoms was demonstrated by Daniel Steck and collaborators later in 2008. Their experiment was based on the 2005 scheme for the one-way wall, and was not used for cooling. The cooling method realized by the Raizen Group was called "single-photon cooling", because only one photon on average is required in order to bring an atom to near-rest. This is in contrast to other laser cooling techniques which use the momentum of the photon and require a two-level cycling transition.<br />
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2009年,马克 雷岑Mark g. Raizen开发了一种激光原子冷却技术,该技术实现了Maxwell设想的基于能量将气体中的单个原子分类放入不同容器的过程。这个新概念是原子或分子的单向墙,允许它们向一个方向运动,但不能向后移动。单向壁的操作依赖于一个不可逆的原子和分子过程,即吸收一个特定波长的光子,然后自发发射到另一个内部状态。不可逆性与磁场和/或光产生的保守力相耦合。Raizen 和他的合作者提出使用单向壁来减少原子团的熵。与此同时,贡萨洛·穆加 Gonzalo Muga 和安德烈亚斯 Andreas Ruschhaupt 独立地提出了一个类似的概念。他们的“原子二极管”不是用来冷却的,而是用来调节原子流。在2008年的一系列实验中,Raizen 团队证明了单向壁对原子的显著冷却作用。随后,丹尼尔·斯特克 Daniel Steck和合作者在2008年晚些时候演示了单向原子墙的操作。他们的实验是基于2005年的单向墙计划,并没有用于冷却。Raizen团队实现的冷却方法被称为“单光子冷却” ,因为平均只需要一个光子就可以使原子接近静止。这与其他激光冷却技术相反,后者使用光子的动量并需要两级循环过渡。<br />
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In 2006, Raizen, Muga, and Ruschhaupt showed in a theoretical paper that as each atom crosses the one-way wall, it scatters one photon, and information is provided about the turning point and hence the energy of that particle. The entropy increase of the radiation field scattered from a directional laser into a random direction is exactly balanced by the entropy reduction of the atoms as they are trapped by the one-way wall.<br />
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2006年,Raizen,Muga,和 Ruschhaupt 在一篇论文中指出,当每个原子穿过单向墙时,它散射一个光子,并提供了关于转折点的信息,因此也就提供了这个粒子的能量。定向激光向随机方向散射的辐射场的熵增与被单向壁俘获的原子的熵减完全平衡。<br />
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This technique is widely described as a "Maxwell's demon" because it realizes Maxwell's process of creating a temperature difference by sorting high and low energy atoms into different containers. However, scientists have pointed out that it is not a true Maxwell's demon in the sense that it does not violate the second law of thermodynamics; it does not result in a net decrease in entropy Only a year later and based on an earlier theoretical proposal, the same group presented the first experimental realization of an autonomous Maxwell's demon, which extracts microscopic information from a system and reduces its entropy by applying feedback. The demon is based on two capacitively coupled single-electron devices, both integrated on the same electronic circuit. The operation of the demon is directly observed as a temperature drop in the system, with a simultaneous temperature rise in the demon arising from the thermodynamic cost of generating the mutual information. In 2016, Pekola et al. demonstrated a proof-of-principle of an autonomous demon in coupled single-electron circuits, showing a way to cool critical elements in a circuit with information as a fuel. Pekola et al. have also proposed that a simple qubit circuit, e.g., made of a superconducting circuit, could provide a basis to study a quantum Szilard's engine.<br />
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这种技术被广泛地描述为“麦克斯韦妖”,因为它通过将高能和低能原子分类到不同的容器中产生温差实现了Maxwell的过程。然而,科学家已经指出,它不是一个真正的麦克斯韦妖,因为它没有违反热力学第二定律; 它不会导致熵减,也不能用来产生有用的能量。这是因为这个过程需要更多的能量从激光束比可能产生的温差。原子从激光束中吸收低熵的光子,并以随机方向发射它们,从而增加了环境的熵。<br />
<font color="#32cd32"> 可能缺失部分原文</font> <br />
2014年,佩科拉 Pekola 等人展示了 Szilárd 引擎实验的实现。仅仅一年之后,同一个研究小组根据早先的理论提议,第一次实验性地实现了自主的麦克斯韦妖,它从一个系统中提取微观信息,并通过反馈减少系统的熵。这个妖是基于集成在同一电路上的两个电容耦合的单电子器件。妖的运行直接表现为系统中的温度下降,同时由于产生互信息的热力学成本而引起的妖中的温度上升。2016年,Pekola 等人证明了单电子耦合电路中存在自主妖的原理,展示了一种以信息为燃料冷却电路中关键元件的方法。Pekola等人还提出,一个简单的量子比特电路,例如由超导电路构成的电路,可以为研究量子Szilárd引擎提供基础。<br />
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== 作为一种隐喻 ==<br />
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Daemons in computing, generally processes that run on servers to respond to users, are named for Maxwell's demon.<br />
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计算中的妖(通常是在服务器上运行以响应用户的进程)以麦克斯韦妖命名。<br />
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Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as a historical metaphor, though he misunderstood and misapplied the original principle. Adams interpreted history as a process moving towards "equilibrium", but he saw militaristic nations (he felt Germany pre-eminent in this class) as tending to reverse this process, a Maxwell's demon of history. Adams made many attempts to respond to the criticism of his formulation from his scientific colleagues, but the work remained incomplete at Adams' death in 1918. It was only published posthumously.<br />
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亨利·布鲁克斯·亚当斯 Henry Brooks Adams在他的手稿《应用于历史的阶段规则 》中试图用麦克斯韦妖作为历史隐喻,尽管他误解和误用了其原本的含义。Adams将历史解释为一个走向“均衡”的过程,但他认为军国主义国家(他认为德国在这一阶层中处于领先地位)倾向于扭转这一过程,这是历史的麦克斯韦妖。Adams曾多次尝试回应他的科学同事对他的公式的批评,但在1918年Adams去世时,这项工作仍未完成。这本书是死后才出版的。<br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21641行为经济学2021-02-07T06:32:07Z<p>Vicky:/* Responses 回应 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型,补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论,即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman“将心理学研究的见解整合到经济科学中,特别是在不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是身体在面对任务时的非特异性反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
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该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
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Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
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'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
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和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
。<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
<br />
Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
。<br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
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<br />
== Notable people 著名人物==<br />
<br />
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<br />
=== Economics 经济学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
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* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
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* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
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* [[Larry Summers]]<br />
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* [[Richard Thaler]]<br />
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{{div col end}}<br />
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<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
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* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
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* [[Robert Vishny]]<br />
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{{div col end}}<br />
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<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
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{{div col end}}<br />
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== See also 参见==<br />
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{{Wikipedia books|Finance}} <br />
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{{div col|colwidth=30em}}<br />
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* [[Adaptive market hypothesis]] 适应性市场假设<br />
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* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
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* [[Behavioralism]] 行为主义<br />
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* [[Behavioral analysis of markets]] 市场的行为分析<br />
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* [[Behavioral operations research]] 行为运筹学<br />
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*[[Big Five personality traits]] 大五人格<br />
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* [[Confirmation bias]] 确认偏差<br />
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* [[Cultural economics]] 文化经济学<br />
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* [[Culture change]] 文化变迁<br />
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* [[Economic sociology]] 经济社会学<br />
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* [[Emotional bias]] 情绪偏差<br />
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* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
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* [[Hindsight bias]] 后见之明偏差<br />
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* ''[[Homo reciprocans]]'' “人属”<br />
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* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
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* [[List of cognitive biases]] 认知偏差列表<br />
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* [[Market sentiment]] 市场情绪<br />
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* [[Methodological individualism]] 方法论个人主义<br />
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* [[Nudge theory]] “助推”理论<br />
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* [[Observational techniques]] 可观察的技术<br />
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* [[Praxeology]] 人类行为学<br />
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* [[Priority heuristic]] 齐当别启发式<br />
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* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
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* [[Repugnancy costs]] 厌恶成本<br />
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* [[Socioeconomics]] 社会经济学<br />
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* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
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{{div col end}}<br />
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== Citations ==<br />
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{{reflist|30em}}<br />
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== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
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* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
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* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
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* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
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* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
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* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
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* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
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* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
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* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
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* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
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* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
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* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
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* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
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* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
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* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
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* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
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* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
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* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
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* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
<br />
* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
<br />
*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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== External links ==<!-- This section is linked from Behavioral finance --><br />
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外部链接! -- 这一部分链接来自行为金融学 -- <br />
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{{wikiquote}}<br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21605行为经济学2021-02-05T09:57:42Z<p>Vicky:/* Prospect theory 前景理论 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型,补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论,即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman“将心理学研究的见解整合到经济科学中,特别是在不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
。<br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
。<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
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Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
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'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
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和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
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== Notable people 著名人物==<br />
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=== Economics 经济学===<br />
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{{div col|colwidth=20em}}<br />
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* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
<br />
* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
<br />
* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
<br />
* [[Larry Summers]]<br />
<br />
* [[Richard Thaler]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
<br />
* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
<br />
* [[Robert Vishny]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
<br />
{{div col end}}<br />
<br />
<br />
== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
<br />
{{div col|colwidth=30em}}<br />
<br />
* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
<br />
* [[Behavioralism]] 行为主义<br />
<br />
* [[Behavioral analysis of markets]] 市场的行为分析<br />
<br />
* [[Behavioral operations research]] 行为运筹学<br />
<br />
*[[Big Five personality traits]] 大五人格<br />
<br />
* [[Confirmation bias]] 确认偏差<br />
<br />
* [[Cultural economics]] 文化经济学<br />
<br />
* [[Culture change]] 文化变迁<br />
<br />
* [[Economic sociology]] 经济社会学<br />
<br />
* [[Emotional bias]] 情绪偏差<br />
<br />
* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
<br />
* [[Hindsight bias]] 后见之明偏差<br />
<br />
* ''[[Homo reciprocans]]'' “人属”<br />
<br />
* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
<br />
* [[List of cognitive biases]] 认知偏差列表<br />
<br />
* [[Market sentiment]] 市场情绪<br />
<br />
* [[Methodological individualism]] 方法论个人主义<br />
<br />
* [[Nudge theory]] “助推”理论<br />
<br />
* [[Observational techniques]] 可观察的技术<br />
<br />
* [[Praxeology]] 人类行为学<br />
<br />
* [[Priority heuristic]] 齐当别启发式<br />
<br />
* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
<br />
* [[Repugnancy costs]] 厌恶成本<br />
<br />
* [[Socioeconomics]] 社会经济学<br />
<br />
* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
<br />
* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
<br />
* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
<br />
* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
<br />
* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
<br />
* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
<br />
* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
<br />
* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
<br />
* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
<br />
* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
<br />
* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
<br />
* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
<br />
* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
<br />
* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
<br />
* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
<br />
* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
<br />
* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
<br />
*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
<br />
* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
<br />
*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
<br />
<br />
<br />
== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
<br />
== External links ==<!-- This section is linked from Behavioral finance --><br />
<br />
外部链接! -- 这一部分链接来自行为金融学 -- <br />
<br />
{{wikiquote}}<br />
<br />
* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
<br />
* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
<br />
* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
<br />
* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
<br />
* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
<br />
* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
<br />
* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
<br />
* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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{{Authority control}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21597行为经济学2021-02-04T14:28:09Z<p>Vicky:/* Prospect theory 前景理论 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
<!--'Economic psychology' redirects here--><br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
<br />
'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
<br />
Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型,补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论,即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman因为他“将心理学研究的见解整合到经济科学中——关于不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
。<br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
。<br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
。<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
<br />
One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
<br />
反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
<br />
Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
<br />
像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
。<br />
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<br />
<br />
A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
<br />
<br />
<br />
A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
。<br />
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=== Behavioral game theory 行为博弈论===<br />
<br />
{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
<br />
Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
<br />
'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
<br />
<br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
<br />
和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
。<br />
<br />
<br />
<br />
=== Economic reasoning in animals 动物的经济推理===<br />
<br />
A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
<br />
A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
<br />
Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
<br />
除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
<br />
<br />
=== Neuroeconomics 神经经济学===<br />
<br />
{{Main|Neuroeconomics}}<br />
<br />
Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
<br />
Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
<br />
'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
<br />
<br />
It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
<br />
It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
<br />
它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
。<br />
<br />
<br />
<br />
Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
<br />
Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
<br />
行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
<br />
<br />
<br />
<br />
== Notable people 著名人物==<br />
<br />
<br />
<br />
=== Economics 经济学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
<br />
* [[Werner De Bondt]]<br />
<br />
* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
<br />
* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
<br />
* [[Larry Summers]]<br />
<br />
* [[Richard Thaler]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
<br />
* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
<br />
* [[Robert Vishny]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
<br />
{{div col end}}<br />
<br />
<br />
== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
<br />
{{div col|colwidth=30em}}<br />
<br />
* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
<br />
* [[Behavioralism]] 行为主义<br />
<br />
* [[Behavioral analysis of markets]] 市场的行为分析<br />
<br />
* [[Behavioral operations research]] 行为运筹学<br />
<br />
*[[Big Five personality traits]] 大五人格<br />
<br />
* [[Confirmation bias]] 确认偏差<br />
<br />
* [[Cultural economics]] 文化经济学<br />
<br />
* [[Culture change]] 文化变迁<br />
<br />
* [[Economic sociology]] 经济社会学<br />
<br />
* [[Emotional bias]] 情绪偏差<br />
<br />
* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
<br />
* [[Hindsight bias]] 后见之明偏差<br />
<br />
* ''[[Homo reciprocans]]'' “人属”<br />
<br />
* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
<br />
* [[List of cognitive biases]] 认知偏差列表<br />
<br />
* [[Market sentiment]] 市场情绪<br />
<br />
* [[Methodological individualism]] 方法论个人主义<br />
<br />
* [[Nudge theory]] “助推”理论<br />
<br />
* [[Observational techniques]] 可观察的技术<br />
<br />
* [[Praxeology]] 人类行为学<br />
<br />
* [[Priority heuristic]] 齐当别启发式<br />
<br />
* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
<br />
* [[Repugnancy costs]] 厌恶成本<br />
<br />
* [[Socioeconomics]] 社会经济学<br />
<br />
* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
<br />
* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
<br />
* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
<br />
* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
<br />
* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
<br />
* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
<br />
* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
<br />
* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
<br />
* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
<br />
* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
<br />
* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
<br />
* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
<br />
* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
<br />
* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
<br />
* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
<br />
* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
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*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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== External links ==<!-- This section is linked from Behavioral finance --><br />
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外部链接! -- 这一部分链接来自行为金融学 -- <br />
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{{wikiquote}}<br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21596行为经济学2021-02-04T14:21:24Z<p>Vicky:/* Bounded rationality 有限理性 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型,补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论——即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''所能解释的一切。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman因为他“将心理学研究的见解整合到经济科学中——关于不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
<br />
Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
<br />
:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
。<br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
。<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
<br />
Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
<br />
'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
<br />
<br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
<br />
和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
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== Notable people 著名人物==<br />
<br />
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<br />
=== Economics 经济学===<br />
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{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
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* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
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* [[Linda C. Babcock]]<br />
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* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
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* [[David Laibson]]<br />
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* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
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* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
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* [[Larry Summers]]<br />
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* [[Richard Thaler]]<br />
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{{div col end}}<br />
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=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
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* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
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* [[Andrei Shleifer]]<br />
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* [[Robert Vishny]]<br />
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{{div col end}}<br />
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<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
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{{div col end}}<br />
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== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
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{{div col|colwidth=30em}}<br />
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* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
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* [[Behavioralism]] 行为主义<br />
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* [[Behavioral analysis of markets]] 市场的行为分析<br />
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* [[Behavioral operations research]] 行为运筹学<br />
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*[[Big Five personality traits]] 大五人格<br />
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* [[Confirmation bias]] 确认偏差<br />
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* [[Cultural economics]] 文化经济学<br />
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* [[Culture change]] 文化变迁<br />
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* [[Economic sociology]] 经济社会学<br />
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* [[Emotional bias]] 情绪偏差<br />
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* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
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* [[Hindsight bias]] 后见之明偏差<br />
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* ''[[Homo reciprocans]]'' “人属”<br />
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* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
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* [[List of cognitive biases]] 认知偏差列表<br />
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* [[Market sentiment]] 市场情绪<br />
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* [[Methodological individualism]] 方法论个人主义<br />
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* [[Nudge theory]] “助推”理论<br />
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* [[Observational techniques]] 可观察的技术<br />
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* [[Praxeology]] 人类行为学<br />
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* [[Priority heuristic]] 齐当别启发式<br />
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* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
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* [[Repugnancy costs]] 厌恶成本<br />
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* [[Socioeconomics]] 社会经济学<br />
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* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
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{{div col end}}<br />
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<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
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<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
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** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
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** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
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** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
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** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
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* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
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* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
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* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
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* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
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* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
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* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
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* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
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* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
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* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
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* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
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* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
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* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
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* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
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* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
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* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
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* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
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*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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== External links ==<!-- This section is linked from Behavioral finance --><br />
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外部链接! -- 这一部分链接来自行为金融学 -- <br />
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{{wikiquote}}<br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21590行为经济学2021-02-04T13:47:34Z<p>Vicky:/* Bounded rationality 有限理性 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知的局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型。它补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论——即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''所能解释的一切。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman因为他“将心理学研究的见解整合到经济科学中——关于不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
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该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
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Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
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'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
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和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
。<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
<br />
Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
。<br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
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<br />
== Notable people 著名人物==<br />
<br />
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<br />
=== Economics 经济学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
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* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
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* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
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* [[Larry Summers]]<br />
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* [[Richard Thaler]]<br />
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{{div col end}}<br />
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<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
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* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
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* [[Robert Vishny]]<br />
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{{div col end}}<br />
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<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
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{{div col end}}<br />
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== See also 参见==<br />
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{{Wikipedia books|Finance}} <br />
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{{div col|colwidth=30em}}<br />
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* [[Adaptive market hypothesis]] 适应性市场假设<br />
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* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
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* [[Behavioralism]] 行为主义<br />
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* [[Behavioral analysis of markets]] 市场的行为分析<br />
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* [[Behavioral operations research]] 行为运筹学<br />
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*[[Big Five personality traits]] 大五人格<br />
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* [[Confirmation bias]] 确认偏差<br />
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* [[Cultural economics]] 文化经济学<br />
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* [[Culture change]] 文化变迁<br />
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* [[Economic sociology]] 经济社会学<br />
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* [[Emotional bias]] 情绪偏差<br />
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* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
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* [[Hindsight bias]] 后见之明偏差<br />
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* ''[[Homo reciprocans]]'' “人属”<br />
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* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
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* [[List of cognitive biases]] 认知偏差列表<br />
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* [[Market sentiment]] 市场情绪<br />
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* [[Methodological individualism]] 方法论个人主义<br />
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* [[Nudge theory]] “助推”理论<br />
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* [[Observational techniques]] 可观察的技术<br />
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* [[Praxeology]] 人类行为学<br />
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* [[Priority heuristic]] 齐当别启发式<br />
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* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
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* [[Repugnancy costs]] 厌恶成本<br />
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* [[Socioeconomics]] 社会经济学<br />
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* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
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{{div col end}}<br />
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== Citations ==<br />
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{{reflist|30em}}<br />
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== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
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* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
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* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
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* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
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* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
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* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
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* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
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* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
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* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
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* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
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* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
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* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
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* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
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* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
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* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
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* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
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* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
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* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
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* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
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* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
<br />
* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
<br />
*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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== External links ==<!-- This section is linked from Behavioral finance --><br />
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外部链接! -- 这一部分链接来自行为金融学 -- <br />
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{{wikiquote}}<br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=21589行为经济学2021-02-04T13:45:06Z<p>Vicky:/* Bounded rationality 有限理性 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受限于决策问题的可操作性、自身认知局限性和时间。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型。它补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论——即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''所能解释的一切。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman因为他“将心理学研究的见解整合到经济科学中——关于不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
。<br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
。<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
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Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
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'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
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和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
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== Notable people 著名人物==<br />
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=== Economics 经济学===<br />
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{{div col|colwidth=20em}}<br />
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* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
<br />
* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
<br />
* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
<br />
* [[Larry Summers]]<br />
<br />
* [[Richard Thaler]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
<br />
* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
<br />
* [[Robert Vishny]]<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
<br />
{{div col end}}<br />
<br />
<br />
== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
<br />
{{div col|colwidth=30em}}<br />
<br />
* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
<br />
* [[Behavioralism]] 行为主义<br />
<br />
* [[Behavioral analysis of markets]] 市场的行为分析<br />
<br />
* [[Behavioral operations research]] 行为运筹学<br />
<br />
*[[Big Five personality traits]] 大五人格<br />
<br />
* [[Confirmation bias]] 确认偏差<br />
<br />
* [[Cultural economics]] 文化经济学<br />
<br />
* [[Culture change]] 文化变迁<br />
<br />
* [[Economic sociology]] 经济社会学<br />
<br />
* [[Emotional bias]] 情绪偏差<br />
<br />
* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
<br />
* [[Hindsight bias]] 后见之明偏差<br />
<br />
* ''[[Homo reciprocans]]'' “人属”<br />
<br />
* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
<br />
* [[List of cognitive biases]] 认知偏差列表<br />
<br />
* [[Market sentiment]] 市场情绪<br />
<br />
* [[Methodological individualism]] 方法论个人主义<br />
<br />
* [[Nudge theory]] “助推”理论<br />
<br />
* [[Observational techniques]] 可观察的技术<br />
<br />
* [[Praxeology]] 人类行为学<br />
<br />
* [[Priority heuristic]] 齐当别启发式<br />
<br />
* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
<br />
* [[Repugnancy costs]] 厌恶成本<br />
<br />
* [[Socioeconomics]] 社会经济学<br />
<br />
* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
<br />
{{div col end}}<br />
<br />
<br />
<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
<br />
<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
<br />
** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
<br />
** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
<br />
** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
<br />
* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
<br />
* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
<br />
* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
<br />
* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
<br />
* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
<br />
* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
<br />
* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
<br />
* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
<br />
* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
<br />
* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
<br />
* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
<br />
* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
<br />
* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
<br />
* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
<br />
* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
<br />
* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
<br />
* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
<br />
*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
<br />
* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
<br />
*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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<br />
== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
<br />
== External links ==<!-- This section is linked from Behavioral finance --><br />
<br />
外部链接! -- 这一部分链接来自行为金融学 -- <br />
<br />
{{wikiquote}}<br />
<br />
* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
<br />
* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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{{Authority control}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%96%E4%BA%9A%E5%81%87%E8%AF%B4&diff=21584盖亚假说2021-02-04T13:21:29Z<p>Vicky:/* Criticism in the 21st century21世纪的批评 */</p>
<hr />
<div>此词条由Henry第一次翻译。<br />
已由三奇同学完成校对。<br />
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{{short description|Hypothesis that living organisms interact with their surroundings in a self-regulating system}}<br />
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[[File:The Earth seen from Apollo 17.jpg|thumb|The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth]]'s conditions, as the Earth is the only planet currently known to harbour life (''[[The Blue Marble]]'', 1972 [[Apollo 17]] photograph)]]<br />
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The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth's conditions, as the Earth is the only planet currently known to harbour life (The Blue Marble, 1972 Apollo 17 photograph)]]<br />
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对行星可居住性的研究主要基于对[[地球条件]的了解进行推断,因为地球是目前已知的唯一一颗拥有生命的行星 <br />
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The '''Gaia hypothesis''' {{IPAc-en|ˈ|ɡ|aɪ|.|ə}}, also known as the '''Gaia theory''' or the '''Gaia principle''', proposes that living [[organism]]s interact with their [[Inorganic compound|inorganic]] surroundings on [[Earth]] to form a [[Synergy|synergistic]] and [[Homeostasis|self-regulating]], [[complex system]] that helps to maintain and perpetuate the conditions for [[life]] on the planet.<br />
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The Gaia hypothesis , also known as the Gaia theory or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.<br />
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盖亚假说(又称盖亚理论或盖亚原理)认为,生物体与地球上的无机环境相互作用,形成一个协同和自我调节的复杂系统,有助于维持和延续地球上的生命条件。<br />
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The hypothesis was formulated by the chemist [[James Lovelock]]<ref name="J1972" /> and co-developed by the microbiologist [[Lynn Margulis]] in the 1970s.<ref name="lovelock1974">{{cite journal|last1=Lovelock|first1=J.E.|last2=Margulis|first2=L.|title=Atmospheric homeostasis by and for the biosphere: the Gaia hypothesis|journal=Tellus|date=1974|volume=26|series=Series A|issue=1–2|pages=2–10|doi=10.1111/j.2153-3490.1974.tb01946.x|publisher=International Meteorological Institute|location=Stockholm|issn=1600-0870|ref=harv|bibcode=1974Tell...26....2L}}</ref> Lovelock named the idea after [[Gaia]], the primordial goddess who personified the Earth in [[Greek mythology]]. In 2006, the [[Geological Society of London]] awarded Lovelock the [[Wollaston Medal]] in part for his work on the Gaia hypothesis.<ref>{{cite web|title=Wollaston Award Lovelock|url=https://www.geolsoc.org.uk/About/History/Awards-Citations-Replies-2001-Onwards/2006-Awards-Citations-Replies|accessdate=19 October 2015}}</ref><br />
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The hypothesis was formulated by the chemist James Lovelock Lovelock named the idea after Gaia, the primordial goddess who personified the Earth in Greek mythology. In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.<br />
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这个假设是由化学家詹姆斯·洛夫洛克提出的,他以希腊神话中地球的化身盖亚的名字命名了这个想法。2006年,伦敦地质学会授予洛夫洛克沃拉斯顿勋章,以表彰他在<font color="#ff8000"> 盖亚假说Gaia hypothesis</font>方面的工作。 <br />
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Topics related to the hypothesis include how the [[biosphere]] and the [[evolution]] of organisms affect the stability of [[global temperature]], [[salinity]] of [[seawater]], [[atmospheric oxygen]] levels, the maintenance of a [[hydrosphere]] of liquid water and other environmental variables that affect the [[habitability of Earth]].<br />
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Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenance of a hydrosphere of liquid water and other environmental variables that affect the habitability of Earth.<br />
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与该假设有关的主题包括生物圈和生物体的进化如何影响全球温度的稳定性、海水的盐度、大气中的氧含量、液态水水圈的维持以及其他影响地球宜居性的环境变量。<br />
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The Gaia hypothesis was initially criticized for being [[teleological]] and against the principles of [[natural selection]], but later refinements aligned the Gaia hypothesis with ideas from fields such as [[Earth system science]], [[biogeochemistry]] and [[systems ecology]].<ref name="Turney, Jon 2003"/><ref name="Schwartzman2002">{{cite book |author=Schwartzman, David |title=Life, Temperature, and the Earth: The Self-Organizing Biosphere |publisher=Columbia University Press |date=2002 |isbn=978-0-231-10213-1 }}</ref><ref>Gribbin, John (1990), "Hothouse earth: The greenhouse effect and Gaia" (Weidenfeld & Nicolson)</ref> Lovelock also once described the "geophysiology" of the Earth.<ref name="agesofgaia">Lovelock, James, (1995) "The Ages of Gaia: A Biography of Our Living Earth" (W.W.Norton & Co)</ref>{{Explain|date=December 2017}} Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<ref name="kirchner2002">{{Citation |last= Kirchner |first = James W. |title =Toward a future for Gaia theory |journal=[[Climatic Change (journal)|Climatic Change]] |volume = 52 |issue = 4 |pages = 391–408 |date = 2002 | doi = 10.1023/a:1014237331082 }}</ref><ref name="volk2002">{{Citation |last= Volk |first = Tyler |title =The Gaia hypothesis: fact, theory, and wishful thinking |journal = Climatic Change |volume = 52 |issue = 4 |pages = 423–430 |date = 2002 | doi = 10.1023/a:1014218227825 }}</ref><ref name="beerling2007">{{cite book |last=Beerling |first=David |authorlink=David Beerling|date=2007 |title=The Emerald Planet: How plants changed Earth's history |url=http://ukcatalogue.oup.com/product/9780192806024.do |location=Oxford|publisher=Oxford University Press |page= |isbn= 978-0-19-280602-4 |accessdate= }}</ref><br />
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The Gaia hypothesis was initially criticized for being teleological and against the principles of natural selection, but later refinements aligned the Gaia hypothesis with ideas from fields such as Earth system science, biogeochemistry and systems ecology. Lovelock also once described the "geophysiology" of the Earth. Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<br />
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盖亚假说最初被诟病为目的论、反对自然选择的原则,但后来的改进使盖亚假说与来自地球系统科学、生物地球化学和系统生态学等领域的观点相一致。洛夫洛克还曾经描述过地球的“地球物理学”。即便如此,盖亚假说仍然受到一些批评,今天许多科学家认为只有少数证据支持这一理论,或与现有的证据相矛盾。<br />
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==Overview总览==<br />
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Gaian hypotheses suggest that organisms [[Co-evolution|co-evolve]] with their environment: that is, they "influence their [[abiotic]] environment, and that environment in turn influences the [[Biota (ecology)|biota]] by [[Darwinism|Darwinian process]]". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early [[Bacteria|thermo-acido-philic]] and [[methanogenic bacteria]] towards the oxygen-enriched [[atmosphere]] today that supports more [[Phanerozoic|complex life]].<br />
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Gaian hypotheses suggest that organisms co-evolve with their environment: that is, they "influence their abiotic environment, and that environment in turn influences the biota by Darwinian process". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early thermo-acido-philic and methanogenic bacteria towards the oxygen-enriched atmosphere today that supports more complex life.<br />
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盖亚假说认为,生物体与其环境共同进化。也就是说,生物“影响它们的非生物环境,而环境反过来又通过自然选择的过程影响生物群”。Lovelock(1995)在他的第二本书中提供了证据,展示了从早期嗜酸、产甲烷细菌的世界向今天支持更复杂生命的富氧大气的进化。<br />
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A reduced version of the hypothesis has been called "influential Gaia"<ref name=":02">{{Cite journal|last=Lapenis|first=Andrei G.|year=2002|title=Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?|url=|journal=The Professional Geographer|volume=54 |issue=3|pages=379–391|via=[Peer Reviewed Journal]|doi=10.1111/0033-0124.00337}}</ref> in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the [[Biota (ecology)|biota]] influence certain aspects of the abiotic world, e.g. [[temperature]] and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<ref name=":02" /> and biogeochemical processes. An example is how the activity of [[Photosynthesis|photosynthetic]] bacteria during Precambrian times completely modified the [[Earth's atmosphere|Earth atmosphere]] to turn it aerobic, and thus supports the evolution of life (in particular [[eukaryotic]] life).<br />
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A reduced version of the hypothesis has been called "influential Gaia" in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the biota influence certain aspects of the abiotic world, e.g. temperature and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<br />
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在《生物圈的定向进化: 生物地球化学选择还是盖亚? 》一书中,这一假说的简化版被称为“有影响力的盖亚”。安德烈·G·拉佩尼斯在这本书中指出生物影响着非生物世界的温度和大气等多个方面。这本书不是一个人的工作,而是一群俄罗斯科研人员的成果合并成这个通过同行评议的出版物。它通过“微观力量”阐述了生命与环境的共同进化。<br />
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Since barriers existed throughout the twentieth century between Russia and the rest of the world, it is only relatively recently that the early Russian scientists who introduced concepts overlapping the Gaia hypothesis have become better known to the Western scientific community.<ref name=":02" /> These scientists include [[Piotr Kropotkin|Piotr Alekseevich Kropotkin]] (1842–1921) (although he spent much of his professional life outside Russia), Vasil’evich Rizpolozhensky (1847–1918), [[Vladimir Ivanovich Vernadsky]] (1863–1945), and Vladimir Alexandrovich Kostitzin (1886–1963).<br />
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由于二十世纪苏联与西方国家存在隔阂,直到最近,在盖亚假说中引进重叠概念的早期苏联科学家才为西方科学界所熟知。<br />
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The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<br />
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盖亚假说认为,地球是一个自我调节的复杂系统,包括生物圈、大气层、水圈和土壤圈,作为一个进化的系统紧密结合在一起。这个假说认为,这个被称为盖亚的系统作为整体,寻求适合当代生命的物理和化学环境。<br />
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Biologists and Earth scientists usually view the factors that stabilize the characteristics of a period as an undirected [[emergent property]] or [[entelechy]] of the system; as each individual species pursues its own self-interest, for example, their combined actiYons may have counterbalancing effects on environmental change. Opponents of this view sometimes reference examples of events that resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth's atmosphere from a [[reducing environment]] to an [[oxygen]]-rich one at the end of the [[Archean|Archaean]] and the beginning of the [[Proterozoic]] periods.<br />
生物学家和地球科学家通常将平衡一个时期的特征的因素视为系统的无方向[[涌现属性]]或[[有目的行为]];例如,由于每个物种都追求自身利益,它们的联合行动可能对环境变化产生抵消作用。反对这一观点的人有时会举出一些导致了巨大变化而非平衡的事件作为反例,例如在[[太古宙|太古代]]末期和[[元古代]]时期开始时,地球大气从[[还原环境]]转变为富含[[氧气]]。 <br />
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Gaia evolves through a cybernetic feedback system operated unconsciously by the biota, leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially microorganisms, with inorganic elements. These processes establish a global control system that regulates Earth's surface temperature, atmosphere composition and ocean salinity, powered by the global thermodynamic disequilibrium state of the Earth system.<!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
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盖亚通过一个由生物群无意识操作的控制论反馈系统实现进化,在完全的内稳态中广泛获得稳定的可居住条件。地球表面的许多过程对生命的保障条件至关重要,这些过程依赖于生命形式,特别是微生物与无机元素的相互作用。这些过程建立了一个全球控制系统,由地球系统的全球热力学不平衡状态提供动力,调节地球表面温度、大气成分和海洋盐度。<br />
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Less accepted versions of the hypothesis claim that changes in the biosphere are brought about through the [[Superorganism|coordination of living organisms]] and maintain those conditions through [[homeostasis]]. In some versions of [[Gaia philosophy]], all lifeforms are considered part of one single living planetary being called ''Gaia''. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the [[Coevolution|coevolving]] diversity of living organisms.<br />
一种不太被接受的假说声称生物圈的变化是通过[[超级有机体|生物体的协调]]来实现的,并通过[[内稳态]]来维持这些条件。在一些版本的[[盖亚哲学]]中,所有的生命形式都是一个被称为“盖亚”的生命行星的一部分。在这种观点下,大气、海洋和地壳将是盖亚通过生物多样性进行干预的结果。 <br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of biogeochemistry, and it is being investigated also in other fields like Earth system science. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<br />
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以前在生物地球化学领域已经观察到受生命形式影响的行星内稳态的存在,而且地球系统科学等其他领域也在研究这一现象。盖亚假说的原创性依赖于这样一种观点: 即使地球或外部事件威胁到内稳态平衡,盖亚也会为了保持生命的最佳状态而积极追求这种平衡。<br />
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The Gaia hypothesis was an influence on the [[deep ecology]] movement.<ref>David Landis Barnhill, Roger S. Gottlieb (eds.), ''Deep Ecology and World Religions: New Essays on Sacred Ground'', SUNY Press, 2010, p. 32.</ref><br />
盖亚假说对[[深层生态学]]运动产生了影响 <br />
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==Details细节==<br />
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Rob Rohde's palaeotemperature graphs<br />
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罗布·罗德的古温度图<br />
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The Gaia hypothesis posits that the Earth is a self-regulating [[complex system]] involving the [[biosphere]], the [[Earth's atmosphere|atmosphere]], the [[hydrosphere]]s and the [[pedosphere]], tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<ref name="vanishing255">Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 255. {{ISBN|978-0-465-01549-8}}</ref><br />
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盖亚假说假设地球是一个自我调节的[[复杂系统]],包括[[生物圈]]、[[地球大气|大气]]、[[水圈]]和[[土壤圈]],作为一个进化系统紧密耦合。该假说认为,这个系统作为一个整体,称为盖亚,寻求一个最适合当代生活的物理和化学环境 <br />
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Since life started on Earth, the energy provided by the Sun has increased by 25% to 30%; however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on Titan. research has suggested that "oxygen shocks" and reduced methane levels led, during the Huronian, Sturtian and Marinoan/Varanger Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre Phanerozoic biosphere to fully self-regulate.<br />
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自从地球上有生命以来,太阳提供的能量增加了25%到30%;然而,地球表面温度一直保持在适宜居住的水平上,不曾突破上限或是下限。洛夫洛克还假设,产甲烷菌在早期大气中产生了较高水平的甲烷,这与在石化烟雾中发现的成分相似,在某些方面与土卫六上的大气相似。研究表明,在休伦期、斯图尔特期和马里诺/瓦朗格冰期,“氧冲击”和甲烷含量降低导致世界几乎变成了一个坚实的“雪球”。这些时代是前显生宙生物圈完全拥有自我调节能力的证据。<br />
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Gaia evolves through a [[Cybernetic#In biology|cybernetic]] [[feedback]] system operated unconsciously by the [[biota (ecology)|biota]], leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially [[microorganisms]], with inorganic elements. These processes establish a global control system that regulates Earth's [[Sea surface temperature|surface temperature]], [[atmosphere composition]] and [[ocean]] [[salinity]], powered by the global thermodynamic disequilibrium state of the Earth system.<ref>Kleidon, Axel. ''How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?''. Article submitted to the ''Philosophical Transactions of the Royal Society'' on Thu, 10 Mar 2011</ref><!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
盖亚通过一个[[控制论|生物学|控制论]][[反馈]]系统在[[生物群(生态学)|生物群]]的无意识运作中实现进化,导致在完全的内稳态中广泛存在稳定的可居住条件。地球表面对生命条件至关重要的许多过程都依赖于生物,特别是[微生物]与无机元素的相互作用。这些过程建立了一个全球控制系统,调节地球的[[海表温度|表面温度]]、[[大气组成]]和[[海洋]][[盐度]],其动力来自地球系统的全球热力学不平衡状态。<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
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温室气体CO<sub>2</sub>的处理在维持地球温度在可居住范围内起着关键作用(解释详见下文)。<br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of [[biogeochemistry]], and it is being investigated also in other fields like [[Earth system science]]. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 179. {{ISBN|978-0-465-01549-8}}</ref><br />
受生命形式影响的行星内稳态的存在,以前在[[生物地球化学]]领域就已被观察到,而且其他领域,如[[地球系统科学]]也在研究这种稳态。盖亚假说的独创性依赖于这样一种观点,即盖亚积极追求这种内平衡,以保持维护生命的最佳状态,即使是在地球或外部事件威胁它们的时候。<br />
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The CLAW hypothesis, inspired by the Gaia hypothesis, proposes a feedback loop that operates between ocean ecosystems and the Earth's climate. The hypothesis specifically proposes that particular phytoplankton that produce dimethyl sulfide are responsive to variations in climate forcing, and that these responses lead to a negative feedback loop that acts to stabilise the temperature of the Earth's atmosphere.<br />
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受盖亚假说的启发,CLAW 假说提出了一个在海洋生态系统和地球气候之间运行的反馈回路。该假说特别提出,产生二甲硫醚的浮游植物对气候变化有反应,这些反应导致了一个负反馈循环,稳定了地球大气的温度。<br />
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===Regulation of global surface temperature地球表面温度的调控===<br />
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[[File:All palaeotemps.png|thumb|480px|Rob Rohde's palaeotemperature graphs]]<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of greenhouse gases may cause negative feedbacks in the environment to become positive feedback. Lovelock has stated that this could bring an extremely accelerated global warming, but he has since stated the effects will likely occur more slowly.<br />
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目前,人口的增加及其活动对环境的影响,例如温室气体的增加,可能导致环境中的负反馈成为正反馈。洛夫洛克表示,这可能会极大地加速全球变暖,但他后来又表示,这种影响也可能发生得更慢。<br />
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{{See also|Paleoclimatology}}<br />
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Since life started on Earth, the energy provided by the [[Sun]] has increased by 25% to 30%;<ref name="Owen1979">{{cite journal | author = Owen, T. | author2 = Cess, R.D. | author3 = Ramanathan, V. | date = 1979 | title = Earth: An enhanced carbon dioxide greenhouse to compensate for reduced solar luminosity | journal = [[Nature (journal)|Nature]] | volume = 277 | pages = 640–2 | doi = 10.1038/277640a0 | issue=5698 | bibcode = 1979Natur.277..640O | ref = harv }}</ref> however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on [[Titan (moon)|Titan]].<ref name="agesofgaia"/> This, he suggests tended to screen out ultraviolet until the formation of the ozone screen, maintaining a degree of homeostasis. However, the [[Snowball Earth]]<ref>Hoffman, P.F. 2001. [http://www.snowballearth.org ''Snowball Earth theory'']</ref> research has suggested that "oxygen shocks" and reduced methane levels led, during the [[Huronian]], [[Sturtian]] and [[Marinoan]]/[[Cryogenian|Varanger]] Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre [[Phanerozoic]] biosphere to fully self-regulate.<br />
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Plots from a standard black and white [[Daisyworld simulation]]<br />
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从一个标准的黑白图[[雏菊世界模拟]]<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
说明了在温室气体维持低于临界温度的过程中,CO2起着至关重要的作用。 <br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic group selection and cooperation between organisms, James Lovelock and Andrew Watson developed a mathematical model, Daisyworld, in which ecological competition underpinned planetary temperature regulation.<br />
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有人批评盖亚假说似乎需要有机体之间不切实际的群体选择与合作,为了回应这种批评,James Lovelock 和 Andrew Watson建立了一个数学模型---- 雏菊世界,其中生态竞争支撑着地。<br />
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The [[CLAW hypothesis]], inspired by the Gaia hypothesis, proposes a [[feedback|feedback loop]] that operates between [[ocean]] [[ecosystem]]s and the [[Earth]]'s [[climate]].<ref name="CLAW87">{{cite journal |doi=10.1038/326655a0 |author=[[Robert Jay Charlson|Charlson, R. J.]], [[James Lovelock|Lovelock, J. E]], Andreae, M. O. and Warren, S. G. |title=Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate |journal=Nature |volume=326 |issue=6114 |pages=655–661 |date=1987 |bibcode=1987Natur.326..655C |ref=harv }}</ref> The [[hypothesis]] specifically proposes that particular [[phytoplankton]] that produce [[dimethyl sulfide]] are responsive to variations in [[climate forcing]], and that these responses lead to a [[negative feedback|negative feedback loop]] that acts to stabilise the [[temperature]] of the [[Earth's atmosphere]].<br />
受到盖亚假说启发的[[爪假说]]提出了一个在[[海洋]][[生态系统]]和[[地球]]的[[气候]]之间运行的[[反馈|反馈回路]]。<br />
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Daisyworld examines the energy budget of a planet populated by two different types of plants, black daisies and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the albedo of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
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《雏菊世界》调查了一个星球的能量预算,这个星球上生长着两种不同的植物,黑色雏菊和白色雏菊,这两种植物占据了星球表面的很大一部分。雏菊的颜色影响了地球的反照率,黑色的雏菊吸收更多的光线,使地球变暖,而白色的雏菊则反射更多的光线,使地球变冷。人们认为黑色雏菊在较低的温度下生长和繁殖最好,而白色雏菊则被认为在较高的温度下生长最好。当温度上升到接近白色雏菊所喜欢的温度时,白色雏菊繁殖率高于黑色雏菊,导致更大比例的白色表面,更多的阳光被反射,减少热量输入,最终使地球降温。相反,随着气温的下降,黑色雏菊繁殖率高于白色雏菊,吸收了更多的阳光,使地球变暖。因此,温度会收敛于两种植物繁殖率相等时对应温度的值。<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of [[greenhouse gases]] may cause [[negative feedback]]s in the environment to become [[positive feedback]]. Lovelock has stated that this could bring an [[James Lovelock#The revenge of Gaia|extremely accelerated global warming]],<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, {{ISBN|978-0-465-01549-8}}</ref> but he has since stated the effects will likely occur more slowly.<ref>Lovelock J., NBC News. [http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite Link] Published 23 April 2012, accessed 22 August 2012. {{Webarchive|url=https://web.archive.org/web/20120913163635/http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite |date=13 September 2012 }}</ref><br />
目前,人口的增加及其活动对环境的影响,如[[温室气体]]的倍增,可能导致环境中的[[负反馈]]变成[[正反馈]]。洛夫洛克曾表示,这可能会带来一场【【James Loveloc【《盖亚的复仇』极度加速的全球变暖】】 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this negative feedback due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
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洛夫洛克和沃森指出,在有限的条件下,如果太阳的能量输出发生变化,由于竞争产生的负反馈可以将地球温度稳定在支持生命存在的范围内,而没有生命的地球则会表现出巨大的温度波动。白色和黑色雏菊的百分比会不断变化,以保持植物繁殖率相等的温度值,使两种生命形式都能茁壮成长。<br />
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====Daisyworld simulations雏菊世界模拟====<br />
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[[File:StandardDaisyWorldRun2color.gif|thumb|280px|Plots from a standard black and white [[Daisyworld]] simulation]]<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<br />
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有人认为,这些结果是可以预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的答案。<br />
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{{Main|Daisyworld}}<br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic [[group selection]] and [[Cooperation (evolution)|cooperation]] between organisms, James Lovelock and [[Andrew Watson (scientist)|Andrew Watson]] developed a mathematical model, [[Daisyworld]], in which [[Competition (biology)|ecological competition]] underpinned planetary temperature regulation.<ref name="daisyworld">{{cite journal<br />
有人批评盖亚假说似乎需要有机体之间不切实际的[[群体选择]]和[[合作(进化)|合作]],詹姆斯·洛夫洛克和[[安德鲁·沃森(科学家)|安德鲁·沃森]]开发了一个数学模型,[[雏菊世界]],其中[[竞争(生物学)|生态竞争]]为基础行星温度调节。 <br />
|date = 1983<br />
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Ocean salinity has been constant at about 3.5% for a very long time. Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested that salinity may also be strongly influenced by seawater circulation through hot basaltic rocks, and emerging as hot water vents on mid-ocean ridges. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<br />
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长期以来,海洋盐度一直保持在3.5% 左右。海洋环境中盐度的稳定性很重要,因为大多数细胞需要相当恒定的盐度,一般不能耐受超过5% 的盐度值。海洋盐度为何恒定是一个长期的奥秘,因为没有任何方法可以抵消来自河流的流入盐。最近有人提出,盐分也会洋中脊的热水喷口排出,因此盐度可能受到穿过炽热玄武岩的海水循环的强烈影响。然而,海水的组成离平衡还很远,如果没有有机过程的影响,很难解释这一事实。有一种解释认为,地球历史上盐滩的形成是盐度平衡的原因之一。据推测,这些盐滩是由细菌菌落产生的,它们在生命过程中固定离子和重金属。<br />
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|title = Biological homeostasis of the global environment: the parable of Daisyworld<br />
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|journal = Tellus<br />
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|volume = 35B<br />
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Vostok, Antarctica research station. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
沃斯托克,南极洲研究站。当前期间在左边。<!--基于此图表的GIMP-FX版本的非源材料。现在的版本是正确的,原版的。必须删除这句话:请注意,当前CO2水平超过390ppm,远高于过去40万年来的任何时候-->] <br />
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|pages = 286–9<br />
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|bibcode = 1983TellB..35..284W<br />
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|doi = 10.1111/j.1600-0889.1983.tb00031.x<br />
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The Gaia hypothesis states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organisms or processed by them.<br />
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盖亚假说认为,地球的大气组成是由于生命的存在而保持在动态稳定的状态。大气成分提供了支持现代生命的条件。大气中除惰性气体以外的所有大气气体,要么是由生物体产生的,要么是由生物体加工的。<br />
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|last1 = Watson | first1= A.J. | last2= Lovelock | first2= J.E<br />
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|issue = 4<br />
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The stability of the atmosphere in Earth is not a consequence of chemical equilibrium. Oxygen is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the Great Oxygenation Event. Since the start of the Cambrian period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume. Traces of methane (at an amount of 100,000 tonnes produced per year) should not exist, as methane is combustible in an oxygen atmosphere.<br />
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地球大气层的稳定性不是化学平衡的结果。氧是一种活性化合物,最终会与地球大气层和地壳中的气体和矿物质结合。在大氧化事件开始之前,大约5000万年前,氧气才开始在大气中持续少量存在。自寒武纪以来,大气中氧浓度一直在大气体积的15% 至35% 之间波动。微量的甲烷(每年产生100,000吨)不适合存在,因为甲烷在氧气氛中是可燃的。<br />
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|ref = harv<br />
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}}</ref><br />
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Dry air in the atmosphere of Earth contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases including methane. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. <br />
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地球大气层中的干燥空气大致(按体积计算)含有78.09% 的氮气、20.95% 的氧气、0.93% 的氩气、0.039% 的二氧化碳以及少量的其他气体,包括甲烷。洛夫洛克最初推测,高于25% 的氧气浓度会增加森林大火和森林大火的发生频率。石炭纪和白垩纪煤系地质时期O2浓度确实超过了25%时,正是这一时期形成了火成木炭。这一结果支持了 Lovelock 的论点。<br />
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Daisyworld examines the [[Earth's energy budget|energy budget]] of a [[planet]] populated by two different types of plants, black [[Asteraceae|daisies]] and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the [[albedo]] of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
Daisyworld研究了居住着两种不同类型的植物的[[地球的能源预算|能源预算]],这两种植物是黑色的[[菊科的雏菊]]和白色的雏菊,这两种植物被认为占据了地表的很大一部分。雏菊的颜色影响着这个星球的[反照率],因此黑色雏菊吸收更多的光并温暖地球,而白色雏菊则反射更多的光并使地球降温。黑雏菊在较低温度下生长繁殖最好,而白雏菊在较高温度下生长繁殖最好。当温度上升到接近白色雏菊的最适生长温度时,白色雏菊的繁殖能力超过了黑色雏菊,导致白色表面的比例增大,更多的阳光被反射,减少了热量输入,最终使地球变冷。相反,随着温度的下降,黑雏菊的繁殖能力超过了白雏菊,吸收了更多的阳光,使地球变暖。因此,温度将收敛到两种植物繁殖率相等对应的温度值。 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this [[negative feedback]] due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
Lovelock和Watson表明,在有限的条件范围内,如果太阳的能量输出发生变化,由于竞争而产生的[[负反馈]]可以将地球的温度稳定在支持生命的值上,而没有生命的行星则会出现大范围的温度波动。白雏菊和黑雏菊的比例会不断变化,以使温度保持在植物繁殖率相等的值,从而使两种生命形式都能茁壮成长。 <br />
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Gaia scientists see the participation of living organisms in the carbon cycle as one of the complex processes that maintain conditions suitable for life. The only significant natural source of atmospheric carbon dioxide (CO<sub>2</sub>) is volcanic activity, while the only significant removal is through the precipitation of carbonate rocks. Carbon precipitation, solution and fixation are influenced by the bacteria and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
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盖亚假说的科学家们把生物体参与碳循环看作是维持适合生命条件的复杂过程之一。火山活动是大气中二氧化碳的最重要的自然来源,而碳酸盐岩的沉淀是大气中二氧化碳最重要的去除途径。碳沉淀、溶解和固定受到土壤中细菌和植物根系的影响,这些细菌和植物根系可以改善气体循环,或者在珊瑚礁中,碳酸钙以固体的形式沉积在海底。碳酸钙被活的有机体用来制造含碳的结构和外壳。一旦死亡,生物体的外壳就会沉到海底,在那里它们产生白垩和石灰石的沉淀物。<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<ref>{{cite journal | doi = 10.1023/A:1023494111532 | date = 2003 | last1 = Kirchner | first1 = James W. | journal = Climatic Change | volume = 58 |issue=1–2| pages = 21–45 |title=The Gaia Hypothesis: Conjectures and Refutations | ref = harv}}</ref><br />
有人认为,结果是可预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的反应。 <br />
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One of these organisms is Emiliania huxleyi, an abundant coccolithophore algae which also has a role in the formation of clouds. CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants. Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean algal blooms are also increasing.<br />
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其中一种是赫氏圆石藻,这是一种数量丰富的颗石藻类,也参与了云的形成。通过增加球石氟化物的寿命来补偿过量的CO < sub > 2 </sub > ,增加了锁定在海底的 CO < sub > 2 </sub > 的数量。球石粉会增加云量,从而控制地表温度,有助于降低整个地球的温度,有利于地球上植物所必需的降水。近年来,大气中 CO < < sub > 2 </sub > 浓度有所增加,有证据表明,海洋藻华的浓度也在增加。<br />
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===Regulation of oceanic salinity海洋盐度调节 ===<br />
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Lichen and other organisms accelerate the weathering of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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地衣和其他生物加速了岩石表面的风化,而岩石在土壤中的分解也加快了,这要归功于根、真菌、细菌和地下动物的活动。因此,二氧化碳从大气层流向土壤的过程是在生物的帮助下调节的。当大气中 CO2水平升高时,温度升高,植物生长。这种生长会增加植物对二氧化碳的消耗,植物会将二氧化碳处理到土壤中,从大气中排出。<br />
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Ocean [[salinity]] has been constant at about 3.5% for a very long time.<ref name=":0">{{Cite book|title=The Introduction to Ocean Sciences|last=Segar|first=Douglas|publisher=Library of Congress|year=2012|isbn=978-0-9857859-0-1|location=http://www.reefimages.com/oceans/SegarOcean3Chap05.pdf|pages=Chapter 5 3rd Edition|quote=|via=}}</ref> Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested<ref name="Gorham19912">{{cite journal|last=Gorham|first=Eville|date=1 January 1991|title=Biogeochemistry: its origins and development|journal=Biogeochemistry|publisher=Kluwer Academic|volume=13|issue=3|pages=199–239|doi=10.1007/BF00002942|issn=1573-515X|ref=harv}}</ref> that salinity may also be strongly influenced by [[seawater]] circulation through hot [[basalt]]ic rocks, and emerging as hot water vents on [[mid-ocean ridge]]s. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<ref name=":0" /><br />
在很长一段时间内,海洋盐度一直保持在3.5%左右。[23]海洋环境中的盐度稳定性非常重要,因为大多数细胞需要相当恒定的盐度,并且通常不能耐受超过5%的盐度值。恒定的海洋盐度是一个长期存在的谜团,因为没有任何过程可以抵消河流中的盐流入。大洋中脊上的热水喷口会排出盐分,有人认为[24]这说明盐分也会受到海水循环的强烈影响。然而,海水的组成远未达到平衡,如果没有有机过程的影响,很难解释这一事实。地球历史中盐滩的形成是一个常用的证据。据推测,这些盐滩是由在生命过程中固定离子和重金属的菌落产生的<br />
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In the biogeochemical processes of Earth, sources and sinks are the movement of elements. The composition of salt ions within our oceans and seas is: sodium (Na<sup>+</sup>), chlorine (Cl<sup>−</sup>), sulfate (SO<sub>4</sub><sup>2−</sup>), magnesium (Mg<sup>2+</sup>), calcium (Ca<sup>2+</sup>) and potassium (K<sup>+</sup>). The elements that comprise salinity do not readily change and are a conservative property of seawater.<ref name=":0" /> There are many mechanisms that change salinity from a particulate form to a dissolved form and back. The known sources of sodium i.e. salts are when weathering, erosion, and dissolution of rocks are transported into rivers and deposited into the oceans.<br />
在地球的生物地球化学过程中,源和汇是元素的运动。我们海洋中盐离子的组成是:钠(Na+)、氯(Cl-)、硫酸盐(SO42-)、镁(Mg2+)、钙(Ca2+)和钾(K+)。构成盐度的元素不易变化,是海水的一种保守属性。[23]有许多机制可以将盐度从颗粒形态改变为溶解形态,然后再返回。已知的钠(即盐)因为岩石的风化、侵蚀和溶解作用被输送到河流中并沉积到海洋中。 <br />
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The [[Mediterranean Sea]] as being Gaia's kidney is found ([http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/ here]) by Kenneth J. Hsue, a correspondence author in 2001. The "[[desiccation]]" of the Mediterranean is the evidence of a functioning kidney. Earlier "kidney functions" were performed during the "[[Deposition (geology)|deposition]] of the [[Cretaceous]] ([[Atlantic Ocean|South Atlantic]]), [[Jurassic]] ([[Gulf of Mexico]]), [[Permian–Triassic extinction event|Permo-Triassic]] ([[Europe]]), [[Devonian]] ([[Canada]]), [[Cambrian]]/[[Precambrian]] ([[Gondwana]]) saline giants."<ref>{{Cite web|url=http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/|title=Scientia Marina: List of Issues|last=http://www.webviva.com|first=Justino Martinez. Web Viva 2007|website=scimar.icm.csic.es|language=English|access-date=2017-02-04}}</ref><br />
地中海是盖亚的肾脏,由肯尼斯·J·休伊(KennethJ.Hsue)在2001年发现的。地中海的“干涸”是肾功能正常的证据。早期的“肾功能”是在“白垩纪(南大西洋)、侏罗纪(墨西哥湾)、二叠纪-三叠纪(欧洲)、泥盆纪(加拿大)、寒武纪/前寒武纪(冈瓦纳)盐沼沉积时期进行的。” <br />
[[Earthrise taken from Apollo 8 on December 24, 1968]]<br />
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[1968年12月24日阿波罗8号拍摄的地出]<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = <br />
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地球是一个完整的整体,一个有生命的存在,这个观念有着悠久的传统。神话中的盖亚是拟人化地球的原始希腊女神,是希腊版本的“自然母亲”(来自 Ge = 地球,和 Aia = <br />
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===Regulation of oxygen in the atmosphere大气层的氧气调节===<br />
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PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a suggestion from the novelist William Golding, who was living in the same village as Lovelock at the time (Bowerchalke, Wiltshire, UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of living organisms, climate, and Earth's crust. His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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派祖母,或地球母亲。詹姆斯·洛夫洛克根据小说家威廉·戈尔丁的建议给他的假设起了这个名字,他当时和洛夫洛克住在同一个村子里(英国威尔特郡鲍尔查尔克)。戈尔丁的建议是以Gea为基础的,Gea是希腊女神名字的另一种拼写,在地质学、地球物理和地球化学中,Gea是前缀。后来,博物学家和探险家亚历山大·冯·洪堡认识到生物、气候和地壳的共同进化。他的远见卓识的声明在西方没有被广泛接受,几十年后,盖亚假说刚提出时同样受到了科学界的抵制。<br />
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[[File:Vostok 420ky 4curves insolation.jpg|thumb|280px|Levels of gases in the atmosphere in 420,000 years of ice core data from [[Vostok Station|Vostok, Antarctica research station]]. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
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{{See also|Geological history of oxygen}}<br />
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Also in the turn to the 20th century Aldo Leopold, pioneer in the development of modern environmental ethics and in the movement for wilderness conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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同样在20世纪之交,现代环境伦理学发展的先驱、荒野保护运动的先驱奥尔多 · 利奥波德在他的生物中心或整体的土地伦理学中提出了一个有生命的地球。<br />
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The Gaia hypothesis states that the Earth's [[Atmospheric chemistry#Atmospheric composition|atmospheric composition]] is kept at a dynamically steady state by the presence of life.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 163. {{ISBN|978-0-465-01549-8}}</ref> The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than [[noble gas]]es present in the atmosphere are either made by organisms or processed by them.<br />
盖亚假说指出,地球的大气成分由于生命的存在而保持在动态稳定的状态。大气中除惰性气体以外的所有大气气体都是由生物体制造或加工而成。<br />
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The stability of the atmosphere in Earth is not a consequence of [[chemical equilibrium]]. [[Oxygen]] is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the [[Great Oxygenation Event]].<ref name=Anabar2007>{{Cite journal| last4 = Arnold| last6 = Creaser| last3 = Lyons| first1 = A. | first2 = Y.| last9 = Scott| last2 = Duan | first3 = T. | first4 = G.| last8 = Gordon | first5 = B. | first10 = J. | first6 = R.| last10 = Garvin | first7 = A.| last11 = Buick | first8 = G. | first11 = R. | first9 = C.| title = A whiff of oxygen before the great oxidation event?| journal = Science| volume = 317| issue = 5846| year = 2007| last7 = Kaufman| pages = 1903–1906| last5 = Kendall| pmid = 17901330| last1 = Anbar | doi = 10.1126/science.1140325|bibcode = 2007Sci...317.1903A }}</ref> Since the start of the [[Cambrian]] period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume.<br />
地球大气的稳定性不是化学平衡造成的。氧气是一种活性化合物,最终会与地球大气层和地壳上的气体和矿物质结合。在大氧化事件开始前的5000万年,氧气才在大气中少量存在。自寒武纪开始以来,大气氧浓度值一直在大气体积的15%到35%之间波动。甲烷的痕迹(每年产生10万吨)是不存在的,因为甲烷在氧气环境中是可燃的。<br />
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Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut William Anders in 1968 during the Apollo 8 mission became, through the Overview Effect an early symbol for the global ecology movement.<br />
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盖亚假说和环境运动的另一个影响来自于苏联和美利坚合众国之间太空竞赛。在20世纪60年代,第一批进入太空的人类可以看到地球作为一个整体的样子。1968年,宇航员威廉 · 安德斯在阿波罗8号任务期间拍摄的地出照片,通过总体效应成为全球生态运动的早期象征。<br />
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| pmid = 10500106<br />
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| date=Sep 1999 | last1 = Berner | first1 = R. A.<br />
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| title = Atmospheric oxygen over Phanerozoic time<br />
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[[James Lovelock, 2005]]<br />
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[ James Lovelock,2005]<br />
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| volume = 96<br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the Jet Propulsion Laboratory in California on methods of detecting life on Mars. The first paper to mention it was Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life, co-authored with C.E. Giffin. A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the Pic du Midi observatory, planets like Mars or Venus had atmospheres in chemical equilibrium. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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65年9月,洛夫洛克在加利福尼亚喷气推进实验室研究探测火星生命的方法时,开始定义由生物群落控制的自我调节地球的概念。第一篇提到它的论文是行星大气:与C.E.Giffin合著的与生命存在有关的成分和其他变化。一个主要的概念是,通过大气的化学成分可以在行星尺度上探测到生命。根据picdumidi天文台收集的数据,像火星或金星这样的行星,其大气层处于化学平衡状态。这种与地球大气的差异被认为是这些行星上没有生命的证据。 <br />
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| issue = 20<br />
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Lovelock formulated the Gaia Hypothesis in journal articles in 1972 and 1974, and a popular book length version of the hypothesis, published in 1979 as The Quest for Gaia, began to attract scientific and critical attention.<br />
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洛夫洛克在1972年和1974年的期刊文章中提出了盖亚假说,并在1979年出版了一本畅销书,名为《寻找盖亚》 ,开始引起科学界和批判界的关注。<br />
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| journal = Proceedings of the National Academy of Sciences of the United States of America<br />
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Lovelock called it first the Earth feedback hypothesis, and it was a way to explain the fact that combinations of chemicals including oxygen and methane persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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洛夫洛克首先将其称为地球反馈假说,解释氧气和甲烷等化学物质在地球大气中如何保持稳定浓度。洛夫洛克认为,在其他行星的大气层中探测这种组合,是一种相对便宜可靠的探测生命的方法。<br />
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| doi = 10.1073/pnas.96.20.10955<br />
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[[Lynn Margulis]]<br />
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[琳 · 玛格丽丝]<br />
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|bibcode = 1999PNAS...9610955B }}</ref> Traces of [[Atmospheric methane|methane]] (at an amount of 100,000 tonnes produced per year)<ref name="Cicerone1988">{{cite journal |last1=Cicerone |first1=R.J. |last2=Oremland |first2=R.S. |date=1988 |title=Biogeochemical aspects of atmospheric methane |journal=Global Biogeochemical Cycles |volume=2 |issue=4 |pages=299–327 |url=//webfiles.uci.edu/setrumbo/public/Methane_papers/Cicerone_Global%20Biogeochem%20Cy_1988.pdf |doi=10.1029/GB002i004p00299 |bibcode=1988GBioC...2..299C}}</ref> should not exist, as methane is combustible in an oxygen atmosphere.<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<br />
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后来出现了其他关系,例如海洋生物产生的硫和碘的数量与陆地生物所需的数量大致相同,这些都支持了这一假说。<br />
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Dry air in the [[atmosphere of Earth]] contains roughly (by volume) 78.09% [[nitrogen]], 20.95% oxygen, 0.93% [[argon]], 0.039% [[Carbon dioxide in the Earth's atmosphere|carbon dioxide]], and small amounts of other gases including [[methane]]. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. {{citation needed|date=June 2012}}<br />
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[[地球大气]]中的干空气大约(按体积)包含78.09%[[氮]],20.95%的氧,0.93%[[氩]],0.039%[地球大气中的二氧化碳|二氧化碳]],以及少量其他气体,包括[[甲烷]]。洛夫洛克最初推测,氧气浓度超过25%会增加森林火灾和火灾的发生率。最近在石炭纪和白垩纪煤系中火成木炭的研究(这两个地质时期O<sub>2</sub>浓度超过25%)支持了Lovelock的观点 <br />
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In 1971 microbiologist Dr. Lynn Margulis joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet. The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of eukaryotic organelles and her contributions to the endosymbiotic theory, nowadays accepted. Margulis dedicated the last of eight chapters in her book, The Symbiotic Planet, to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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1971年,微生物学家 Lynn Margulis 博士加入了 Lovelock 的行列,努力将最初的假设充实为科学证明的概念。Margulis 贡献了她关于微生物如何影响大气层和地球表面不同层次的知识。这位美国生物学家也唤受到科学界的批评,因为她倡导真核细胞器起源的理论,以及她对美国共生发源学会的贡献——现在被接受了。玛格丽丝在她的书《共生星球》中将最后八章用于描述盖亚。然而,她反对对盖亚的广泛拟人化,并强调盖亚“不是一个有机体” ,而是“有机体之间相互作用的一个新兴属性”。她将盖亚定义为“组成地球表面一个巨大生态系统的一系列相互作用的生态系统”。句号”。这本书最令人难忘的“口号”实际上是由马古利斯的一个学生打趣说的: “从太空看,盖亚只是共生而已。”。<br />
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===Processing of CO<sub>2</sub>二氧化碳处理===<br />
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{{See also|Carbon cycle}}<br />
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James Lovelock called his first proposal the Gaia hypothesis but has also used the term Gaia theory. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments and provided a number of useful predictions. In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating. The principal sponsor was the National Audubon Society. Speakers included James Lovelock, George Wald, Mary Catherine Bateson, Lewis Thomas, John Todd, Donald Michael, Christopher Bird, Thomas Berry, David Abram, Michael Cohen, and William Fields. Some 500 people attended.<br />
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詹姆斯 · 洛夫洛克称他的第一个提议为盖亚假说,但也使用了盖亚理论这个术语。洛夫洛克说,最初的提法是基于观察,但仍然缺乏科学的解释。盖亚假说从那以后得到了一些科学实验的支持,并提供了一些有用的预测。事实上,更广泛的研究证明了最初的假设是错误的,在这个意义上,不是生命本身,而是整个地球系统在调节。主要赞助者是奥杜邦学会。讲者包括 James Lovelock、 George Wald、 Mary Catherine Bateson、 Lewis Thomas、 John Todd、 Donald Michael、 Christopher Bird、 Thomas Berry、 David Abram、 Michael Cohen 和 William Fields。大约有500人参加。<br />
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Gaia scientists see the participation of living organisms in the [[carbon cycle]] as one of the complex processes that maintain conditions suitable for life. The only significant natural source of [[Carbon dioxide in Earth's atmosphere|atmospheric carbon dioxide]] ([[Carbon dioxide|CO<sub>2</sub>]]) is [[volcanic activity]], while the only significant removal is through the precipitation of [[carbonate rocks]].<ref name="Karhu1996">{{cite journal | author = Karhu, J.A. | author2 = Holland, H.D. | date = 1 October 1996 | title = Carbon isotopes and the rise of atmospheric oxygen | journal = [[Geology (journal)|Geology]] | volume = 24 | issue = 10 | pages = 867–870 | doi = 10.1130/0091-7613(1996)024<0867:CIATRO>2.3.CO;2|bibcode = 1996Geo....24..867K | ref = harv}}</ref> Carbon precipitation, solution and [[Carbon fixation|fixation]] are influenced by the [[bacteria]] and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
盖亚的科学家认为,生物参与[[碳循环]是维持适宜生命条件的复杂过程之一。[[地球大气中的二氧化碳|大气二氧化碳]]([[二氧化碳| CO2]])最重要的自然来源是[[火山活动]],而最重要的去除过程是[[碳酸盐岩]]的沉淀,溶液和[[固碳|固碳]]受土壤中的[[细菌]]和植物根系的影响,它们改善了气体循环,珊瑚礁中碳酸钙以固体形式沉积在海底。碳酸钙被生物用来制造含碳结构和贝壳。一旦死亡,这些生物的壳就会落到海底,在那里它们会产生白垩和石灰岩的沉积物。 <br />
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One of these organisms is ''[[Emiliania huxleyi]]'', an abundant [[coccolithophore]] [[algae]] which also has a role in the formation of [[cloud]]s.<ref name="Harding2006">{{cite book |author=Harding, Stephan |title=Animate Earth |publisher=Chelsea Green Publishing |date=2006 |pages=65 |isbn=978-1-933392-29-5 }}</ref> CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants.{{citation needed|date=July 2015}} Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean [[algal bloom]]s are also increasing.<ref>{{Cite web | date = 12 September 2007 | title = Interagency Report Says Harmful Algal Blooms Increasing | url = http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | url-status = dead | archiveurl = https://web.archive.org/web/20080209234239/http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | archivedate = 9 February 2008 }}</ref><br />
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In 1988, climatologist Stephen Schneider organised a conference of the American Geophysical Union. The first Chapman Conference on Gaia,<br />
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在1988年,气候学家史蒂芬·史奈德组织了一次美国美国地球物理联盟协会的会议。关于盖亚假说的第一次查普曼会议,<br />
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[[Lichen]] and other organisms accelerate the [[weathering]] of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the Daisyworld Model (and its modifications, above) as evidence against most of these criticisms.<br />
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然而,洛夫洛克和其他支持盖亚理论的科学家确实试图反驳这样一种说法,即这种假设不科学,因为不可能通过控制实验来检验它。例如,针对盖亚假说是目的论的指责,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修正,上文)反驳这些批评。<br />
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==History历史==<br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of teleologism ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,这一版本中盖亚并不是有意地在她的环境中维持生命赖以生存的复杂平衡。看起来,盖亚假说“故意”行为的说法只是他那本广受欢迎的书中的一个比喻性陈述,并不是字面意义上的理解。这种对盖亚假说的新陈述更能为科学界所接受。在这次会议之后,大多数关于目的论的指责都停止了。<br />
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===Precedents先例===<br />
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[[File:NASA-Apollo8-Dec24-Earthrise.jpg|thumb|''[[Earthrise]]'' taken from [[Apollo 8]] on December 24, 1968]]<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000, the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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到2000年6月23日在西班牙巴伦西亚举行关于盖亚假说的第二次查普曼会议时,情况发生了重大变化。与其讨论盖亚假说的目的论观点,或盖亚假说的“类型” ,不如将重点放在具体的机制上,通过这些机制,短期内基本稳态在重要的进化长期结构变化的框架内得以维持。<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The [[Gaia (mythology)|mythical Gaia]] was the primal Greek goddess personifying the [[Earth]], the Greek version of "[[Mother Nature]]" (from Ge = Earth, and Aia = <br />
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[[PIE]] grandmother), or the [[Earth Mother]]. James Lovelock gave this name to his hypothesis after a suggestion from the novelist [[William Golding]], who was living in the same village as Lovelock at the time ([[Bowerchalke]], [[Wiltshire]], UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry.<ref name=vanish09 /> Golding later made reference to Gaia in his [[Nobel prize]] acceptance speech.<br />
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The major questions were:<br />
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主要的问题是:<br />
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In the eighteenth century, as [[geology]] consolidated as a modern science, [[James Hutton]] maintained that geological and biological processes are interlinked.<ref name=CapraWeb>{{cite book |author=Capra, Fritjof |title=The web of life: a new scientific understanding of living systems |publisher=Anchor Books |location=Garden City, N.Y |date=1996 |page=[https://archive.org/details/weboflifenewscie00capr/page/23 23] |isbn=978-0-385-47675-1 |url=https://archive.org/details/weboflifenewscie00capr/page/23 }}</ref> Later, the [[naturalist]] and explorer [[Alexander von Humboldt]] recognized the coevolution of living organisms, climate, and Earth's crust.<ref name=CapraWeb /> In the twentieth century, [[Vladimir Vernadsky]] formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian [[geochemist]] and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological processes. During the 1920s he published works arguing that living organisms could reshape the planet as surely as any physical force. Vernadsky was a pioneer of the scientific bases for the environmental sciences.<ref>S.R. Weart, 2003, ''The Discovery of Global Warming'', Cambridge, Harvard Press</ref> His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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"How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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“被称为盖亚的全球生物地球化学/气候系统是如何及时发生变化的?它的历史是什么?盖亚假说能够在一个时间尺度上保持系统的稳定性,但是在更长的时间尺度上仍然经历矢量变化吗?如何利用地质记录来检验这些问题? ”<br />
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"What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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“盖亚假说的结构是什么?这些反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由在任何特定时间进行的学科研究务实地决定的,还是有一些部分应该被认为是最真实的,以了解盖亚假说随着时间的推移包含进化中的生物体?盖亚系统这些不同部分之间的反馈是什么? 对盖亚假说作为全球生态系统的结构和生命的生产力来说,物质的近乎封闭意味着什么? ”<br />
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Also in the turn to the 20th century [[Aldo Leopold]], pioneer in the development of modern [[environmental ethics]] and in the movement for [[wilderness]] conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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"How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
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“盖亚假说过程和现象的模型如何与现实相关,它们如何帮助解决和理解盖亚?雏菊世界的成果如何转移到现实世界?什么是“雏菊”的主要候选人?我们发现雏菊与否对盖亚理论重要吗?我们应该怎样寻找雏菊,我们应该加紧寻找吗?如何利用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制? ”<br />
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{{quotation|It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated functions, but possibly also that process of consumption as replacement which in biology we call metabolism, or growth. In such case we would have all the visible attributes of a living thing, which we do not realize to be such because it is too big, and its life processes too slow.| Stephan Harding | ''Animate Earth''.<ref>Harding, Stephan. ''Animate Earth Science, Intuition and Gaia''. Chelsea Green Publishing, 2006, p. 44. {{ISBN|1-933392-29-0}}</ref>}}<br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise entropy production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
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1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是一种向远离平衡的稳态演化的结果,这种平衡状态使熵产生最大化,克莱顿(2004)同意这样的说法:“自稳态行为可以从与行星反照率相关的MEP状态中产生”;“……一个如盖亚假说所述,处于MEP状态的生物地球很可能导致地球系统在长时间尺度上的近稳态行为。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。<br />
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Another influence for the Gaia hypothesis and the [[environmental movement]] in general came as a side effect of the [[Space Race]] between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph ''[[Earthrise]]'' taken by astronaut [[William Anders]] in 1968 during the [[Apollo 8]] mission became, through the [[Overview Effect]] an early symbol for the global ecology movement.<ref>[http://digitaljournalist.org/issue0309/lm11.html 100 Photographs that Changed the World by Life - The Digital Journalist]</ref><br />
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盖亚假说和[[环境运动]]的另一个总体影响来自苏联和美利坚合众国之间[[太空竞赛]]的副作用。在20世纪60年代,第一批进入太空的人类可以看到地球的整体面貌。1968年宇航员[[William Anders]]在[[Apollo 8]]任务期间拍摄的照片“[[地球升起]”,通过[[概述效果]]成为全球生态运动的早期标志<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<br />
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第四次关于盖亚假说的国际会议,由北弗吉尼亚地区公园管理局和其他机构主办,于2006年10月在弗吉尼亚州乔治梅森大学的阿灵顿校区举行。<br />
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===Formulation of the hypothesis假说形成===<br />
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[[File:James Lovelock in 2005.jpg|thumb|[[James Lovelock]], 2005]]<br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
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马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。Lynn Margulis是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the [[Jet Propulsion Laboratory]] in California on methods of detecting [[life on Mars (planet)|life on Mars]].<ref name="Lovelock1965">{{cite journal | author = Lovelock, J.E. | date = 1965 | title = A physical basis for life detection experiments | journal = [[Nature (journal)|Nature]] | volume = 207 | issue = 7 | pages = 568–570 | doi = 10.1038/207568a0 | pmid=5883628|bibcode = 1965Natur.207..568L | ref = harv}}</ref><ref>{{Cite web |url=http://www.jameslovelock.org/page4.html |title=Geophysiology |access-date=2007-05-05 |archive-url=https://web.archive.org/web/20070506073502/http://www.jameslovelock.org/page4.html |archive-date=2007-05-06 |url-status=dead }}</ref> The first paper to mention it was ''Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life'', co-authored with C.E. Giffin.<ref>{{cite journal | author1 = Lovelock, J.E. | author2 = Giffin, C.E. | date = 1969 | title = Planetary Atmospheres: Compositional and other changes associated with the presence of Life | journal = Advances in the Astronautical Sciences | volume = 25 | pages = 179–193 | isbn = 978-0-87703-028-7 | ref = harv}}</ref> A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the [[Pic du Midi de Bigorre|Pic du Midi observatory]], planets like Mars or Venus had atmospheres in [[chemical equilibrium]]. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
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这次会议将盖亚假说作为一种科学和隐喻的手段,来理解我们如何开始解决21世纪的问题,如气候变化和持续的环境破坏。<br />
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Lovelock formulated the ''Gaia Hypothesis'' in journal articles in 1972<ref name="J1972">{{cite journal | author = J. E. Lovelock | title = Gaia as seen through the atmosphere | date = 1972 | journal = [[Atmospheric Environment]] | volume = 6 | issue = 8 | pages = 579–580 | doi = 10.1016/0004-6981(72)90076-5 | ref = harv|bibcode = 1972AtmEn...6..579L }}</ref> and 1974,<ref name="lovelock1974" /> followed by a popularizing 1979 book ''Gaia: A new look at life on Earth''. An article in the ''[[New Scientist]]'' of February 6, 1975,<ref>Lovelock, John and Sidney Epton, (February 8, 1975). "The quest for Gaia". [https://books.google.com/books?id=pnV6UYEkU4YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false New Scientist], p. 304.</ref> and a popular book length version of the hypothesis, published in 1979 as ''The Quest for Gaia'', began to attract scientific and critical attention.<br />
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Lovelock called it first the Earth feedback hypothesis,<ref name="Lovelock01">{{harvnb|Lovelock, James|2001}}</ref> and it was a way to explain the fact that combinations of chemicals including [[oxygen]] and [[methane]] persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as Ford Doolittle, Richard Dawkins and Stephen Jay Gould. Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists, He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoietic or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole. With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<br />
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在最初几乎没有引起科学家的注意之后(从1969年到1977年) ,有一段时间,最初的盖亚假说受到了一些科学家的批评,如福特杜利特,理查德道金斯和史蒂芬·古尔德。洛夫洛克说,因为他的假说是以一位希腊女神的名字命名的,并得到许多非科学家的拥护,他想知道实现自我调节体内平衡的实际机制。在为盖亚辩护时,戴维•阿布拉姆认为,古尔德忽视了一个事实,即“机制”本身就是一个隐喻——尽管这个隐喻极其常见,而且往往不为人所知——这个隐喻让我们把自然和生命系统看作是由外部组织和建造的机器(而不是自动生成或自组织现象)。根据阿布拉姆的说法,机械隐喻使我们忽略了生命实体的活跃性或代表性,而盖亚假说的有机隐喻强调了生物群和整个生物圈的活跃性。关于盖亚的因果关系,洛夫洛克认为没有单一的机制是负责任的,各种已知机制之间的联系可能永远不会被人知道,这在生物学和生态学的其他领域是理所当然地被接受的,并且由于其他原因,特定的敌意是保留给他自己的假设的。<br />
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[[File:Lynn Margulis.jpg|thumb|left|[[Lynn Margulis]]]]<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of greedy reductionism in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<br />
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除了澄清他的语言和理解什么是生命形式,洛夫洛克自己把大部分的批评归因于他的批评者缺乏对非线性数学的理解,以及贪婪还原主义的线性化形式,在这种形式中,所有事件都必须立即归因于事件发生之前的特定原因。他还表示,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,以及一些自我调节现象可能无法在数学上解释。<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<ref>{{cite journal | first1=W.D. | last1=Hamilton | first2=T.M. | last2=Lenton | title=Spora and Gaia: how microbes fly with their clouds | journal=Ethology Ecology & Evolution | volume=10 | pages=1–16 | date=1998 | issue=1 | url=http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | format=PDF | doi=10.1080/08927014.1998.9522867 | ref=harv | url-status=dead | archiveurl=https://web.archive.org/web/20110723055017/http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | archivedate=2011-07-23 }}</ref><br />
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Evolutionary biologist W. D. Hamilton called the concept of Gaia Copernican, adding that it would take another Newton to explain how Gaian self-regulation takes place through Darwinian natural selection. More recently Ford Doolittle building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis. <br />
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进化生物学家W.D.Hamilton称盖亚假说为哥白尼式的概念,并补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。最近,Ford Doolittle在他和Inkpen的ITSNTS(这是歌手而不是歌曲)的建议中提出,差异持续性可以在自然选择进化中起到与差异生殖相似的作用,从而为自然选择理论和盖亚假说之间提供了一种可能的调和。 <br />
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In 1971 [[microbiologist]] Dr. [[Lynn Margulis]] joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet.<ref name="Turney, Jon 2003">{{cite book |author=Turney, Jon |title=Lovelock and Gaia: Signs of Life |publisher=Icon Books |location=UK |date=2003 |isbn=978-1-84046-458-0 |url-access=registration |url=https://archive.org/details/lovelockgaiasign0000turn }}</ref> The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of [[eukaryote|eukaryotic]] [[organelle]]s and her contributions to the [[endosymbiotic theory]], nowadays accepted. Margulis dedicated the last of eight chapters in her book, ''The Symbiotic Planet'', to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal Climatic Change in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it. to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background" The CLAW hypothesis, In 2009 the Medea hypothesis was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<br />
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盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论据是,生命对环境产生了有害或不稳定的影响,而不是采取行动加以调节。为了“令人不安地徘徊在污点隐喻、事实和虚假科学之间,我宁愿把盖亚假说牢牢地放在背景下。”爪假说,2009年提出的美狄亚假说:生命对行星条件有高度有害的(生物杀灭)影响,与盖亚假说直接相反。 <br />
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James Lovelock called his first proposal the ''Gaia hypothesis'' but has also used the term ''Gaia theory''. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments<ref name="J1990">{{cite journal | author = J. E. Lovelock | title = Hands up for the Gaia hypothesis | date = 1990 | journal = [[Nature (journal)|Nature]] | volume = 344 | issue = 6262 | pages = 100–2 | doi = 10.1038/344100a0|bibcode = 1990Natur.344..100L | ref = harv}}</ref> and provided a number of useful predictions.<ref name="Volk2003">{{cite book |author=Volk, Tyler |title=Gaia's Body: Toward a Physiology of Earth |publisher=[[MIT Press]] |location=Cambridge, Massachusetts |date=2003 |isbn=978-0-262-72042-7 }}</ref> In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating.<ref name="vanishing255"/><br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it". Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works". This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<br />
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2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新想法,并倡导一种整体的方法来研究地球”。在其他地方,他提出了自己的结论:“盖亚假说并不是我们这个世界如何运转的精确图像”。这种说法需要被理解为是指盖亚假说的“强”和“中”形式,生物群遵循的原则是使地球成为最佳(强度5)或有利于生命(强度4),或是作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化的盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释。<br />
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===First Gaia conference第一次盖亚会议===<br />
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In 1985, the first public symposium on the Gaia hypothesis, ''Is The Earth A Living Organism?'' was held at [[University of Massachusetts Amherst]], August 1–6.<ref>{{cite news |last=Joseph |first=Lawrence E. |title=Britain's Whole Earth Guru |work=The New York Times Magazine |date=November 23, 1986 |url=https://www.nytimes.com/1986/11/23/magazine/britain-s-whole-earth-guru.html |accessdate=1 December 2013}}</ref> The principal sponsor was the [[National Audubon Society]]. Speakers included James Lovelock, [[George Wald]], [[Mary Catherine Bateson]], [[Lewis Thomas]], [[John Todd (Canadian biologist)|John Todd]], Donald Michael, [[Christopher Bird]], [[Thomas Berry]], [[David Abram]], [[Michael A. Cohen|Michael Cohen]], and William Fields. Some 500 people attended.<ref>Bunyard, Peter (1996), "Gaia in Action: Science of the Living Earth" (Floris Books)</ref><br />
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1985年,关于盖亚假说的第一次公开研讨会,“地球是一个活的有机体吗?”在马萨诸塞大学阿默斯特举行 <br />
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===Second Gaia conference第二次盖亚会议===<br />
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In 1988, [[climatology|climatologist]] [[Stephen Schneider]] organised a conference of the [[American Geophysical Union]]. The first Chapman Conference on Gaia,<ref name="ReferenceB"/> was held in San Diego, California on March 7, 1988.<br />
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1988年,climatology和Stephen Schneider组织了一次美国地球物理联合会会议。关于盖亚假说的第一次查普曼会议 <br />
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During the "philosophical foundations" session of the conference, [[David Abram]] spoke on the influence of metaphor in science, and of the Gaia hypothesis as offering a new and potentially game-changing metaphorics, while [[James Kirchner]] criticised the Gaia hypothesis for its imprecision. Kirchner claimed that Lovelock and Margulis had not presented one Gaia hypothesis, but four -<br />
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在会议的“哲学基础”会议上,David Abram谈到了隐喻在科学中的影响,盖亚假说提供了一种新的、可能改变游戏规则的隐喻,而James Kirchner则批评盖亚假说的不精确性。基什纳声称,洛夫洛克和马古利斯提出的盖亚假说不是一个,而是四个- <br />
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* [[Coevolution|CoEvolutionary]] Gaia: that life and the environment had evolved in a coupled way. Kirchner claimed that this was already accepted scientifically and was not new.<br />
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* [[Homeostatic]] Gaia: that life maintained the stability of the natural environment, and that this stability enabled life to continue to exist.<br />
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* [[Geophysics|Geophysical]] Gaia: that the Gaia hypothesis generated interest in geophysical cycles and therefore led to interesting new research in terrestrial geophysical dynamics.<br />
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* Optimising Gaia: that Gaia shaped the planet in a way that made it an optimal environment for life as a whole. Kirchner claimed that this was not testable and therefore was not scientific.<br />
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盖亚:生命和环境是以耦合的方式进化的。基什内尔声称,这已经被科学界接受,并不是什么新鲜事。 <br />
盖亚:生命维持着自然环境的稳定,这种稳定性使生命得以继续存在。 <br />
盖亚:盖亚假说引起了人们对地球物理周期的兴趣,因此导致了地球物理动力学中有趣的新研究。 <br />
优化盖亚:盖亚塑造了地球,使之成为整个生命的最佳环境。基什内尔声称,这是不可测试的,因此是不科学的。 <br />
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Of Homeostatic Gaia, Kirchner recognised two alternatives. "Weak Gaia" asserted that life tends to make the environment stable for the flourishing of all life. "Strong Gaia" according to Kirchner, asserted that life tends to make the environment stable, ''to enable'' the flourishing of all life. Strong Gaia, Kirchner claimed, was untestable and therefore not scientific.<ref>{{cite journal | bibcode=1989RvGeo..27..223K | doi = 10.1029/RG027i002p00223 | title=The Gaia hypothesis: Can it be tested? | date=1989 | last1=Kirchner | first1=James W. | journal=Reviews of Geophysics | volume=27 | issue=2 | pages=223 | ref=harv}}</ref><br />
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基什内尔发现了两种选择“软弱的盖亚”断言,为了所有生命的繁衍,生命往往会使环境变得稳定根据基什内尔的说法,“强大的盖亚”断言,生命趋向于使环境稳定,“使”所有生命繁荣昌盛。基什内尔声称,强大的盖亚是不稳定的,因此不科学。 <br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the [[Daisyworld]] Model (and its modifications, above) as evidence against most of these criticisms.<ref name="daisyworld"/> Lovelock said that the Daisyworld model "demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways".<ref>{{cite journal | pmid=10968941 | date=2000 | last1=Lenton | first1=TM | last2=Lovelock | first2=JE | s2cid=5486128 | title=Daisyworld is Darwinian: Constraints on adaptation are important for planetary self-regulation | volume=206 | issue=1 | pages=109–14 | doi=10.1006/jtbi.2000.2105 | journal=Journal of Theoretical Biology | ref=harv}}</ref><br />
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然而,洛夫洛克和其他支持盖亚假说的科学家,确实试图反驳这种说法,即这个假设是不科学的,因为不可能通过受控实验来检验它。例如,针对盖亚假说是目的论的指控,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修改,洛夫洛克说,雏菊世界模型“证明了全球环境的自我调节可以通过不同方式改变当地环境的生活类型之间的竞争产生”。 <br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of [[teleology|teleologism]] ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,没有声称盖亚有意或有意识地维持着生命生存所需的复杂平衡。看来盖亚假说“故意”的行为是他最受欢迎的第一本书中的隐喻性陈述,并不是字面意思。盖亚假说的这一新说法更为科学界所接受。在这次会议之后,[[目的论|目的论]]的大多数指控都停止了。<br />
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===Third Gaia conference第三次盖亚会议===<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000,<ref>{{cite news|last=Simón|first=Federico|title=GEOLOGÍA Enfoque multidisciplinar La hipótesis Gaia madura en Valencia con los últimos avances científicos|journal=El País|date=21 June 2000|url=http://elpais.com/diario/2000/06/21/futuro/961538404_850215.html|accessdate=1 December 2013|language=spanish}}</ref> the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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The major questions were:<ref>{{cite web|title=General Information Chapman Conference on the Gaia Hypothesis University of Valencia Valencia, Spain June 19-23, 2000 (Monday through Friday) |url=http://www.agu.org/meetings/chapman/chapman_archive/cc00bcall.html |work=AGU Meetings |accessdate=7 January 2017 |author=American Geophysical Union }}</ref><br />
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# "How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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# "What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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# "How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
“被称为盖亚的全球生物地球化学/气候系统是如何随时间变化的?它的历史是什么?盖亚能在一个时间尺度上保持系统的稳定性,但在较长的时间尺度上仍能经历向量变化吗?如何利用地质记录来检验这些问题?” <br />
“盖亚假说的结构是什么?反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由任何给定时间正在进行的任何学科研究实际确定的,还是有一组应该被视为最真实的部分来理解盖亚假说,即随着时间的推移包含进化中的有机体?盖亚系统的这些不同部分之间的反馈是什么?物质的接近封闭对盖亚作为全球生态系统的结构和生命的生产力意味着什么?” <br />
“盖亚假说过程和现象的模型如何与现实联系起来,它们如何帮助解决和理解盖亚假说?雏菊世界的结果如何传递到真实世界?“雏菊”的主要候选对象是什么?我们是否找到雏菊对盖亚理论有意义吗?我们应该如何寻找雏菊,我们应该加强搜索?如何使用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制?” <br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise [[entropy]] production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是朝着使熵产量最大化的远非平衡的状态演化的结果,克莱顿(2004)同意这样的说法:“自稳行为可以从与行星反照率相关的MEP状态中产生”;“……生物地球在MEP状态下的行为很可能导致地球系统在长时间尺度上的近稳态行为,正如盖亚假说所述”。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。 <br />
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===Fourth Gaia conference第四次盖亚会议===<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<ref>{{cite web|title=Gaia Theory Conference at George Mason University Law School|url=http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|accessdate=1 December 2013|author=Official Site of Arlington County Virginia|archive-url=https://web.archive.org/web/20131203043657/http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|archive-date=2013-12-03|url-status=dead}}</ref><br />
第四届盖亚假说国际会议于2006年10月在乔治梅森大学阿灵顿分校举行,会议由北弗吉尼亚州公园管理局和其他机构赞助。 <br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。林恩 马古拉斯是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
这次会议将盖亚假说作为一种科学和隐喻来探讨,以此来理解我们如何着手解决21世纪的问题,如气候变化和持续的环境破坏<br />
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==Criticism批评==<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as [[Ford Doolittle]],<ref name=":1">{{Cite journal|last=Doolittle|first=W. F.|year=1981|title=Is Nature Really Motherly|url=|journal=The Coevolution Quarterly|volume=Spring|pages=58–63|via=}}</ref> [[Richard Dawkins]]<ref name=":2">{{Cite book|title=The Extended Phenotype: the Long Reach of the Gene|last=Dawkins|first=Richard|publisher=Oxford University Press|year=1982|isbn=978-0-19-286088-0|location=|pages=}}</ref> and [[Stephen Jay Gould]].<ref name="ReferenceB">Turney, Jon. "Lovelock and Gaia: Signs of Life" (Revolutions in Science)</ref> Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists,<ref name="Lovelock01"/> the Gaia hypothesis was interpreted as a [[neo-Pagan]] [[religion]]. Many scientists in particular also criticised the approach taken in his popular book ''Gaia, a New Look at Life on Earth'' for being [[teleology|teleological]]—a belief that things are purposeful and aimed towards a goal. Responding to this critique in 1990, Lovelock stated, "Nowhere in our writings do we express the idea that planetary self-regulation is purposeful, or involves foresight or planning by the [[biota (ecology)|biota]]".<br />
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最初很少受到科学家的关注(从1969年到1977年),此后的一段时间里,最初的盖亚假说受到了许多科学家的批评,比如福特·杜利特,理查德·道金斯和斯蒂芬·杰伊·古尔德洛夫洛克曾说过,因为他的假设是以希腊女神的名字命名的,新盖亚假说被许多非教派的科学家解释为。特别是许多科学家还批评了他的畅销书《盖亚》中采用的方法,认为地球上的生命是目的论的,认为事物是有目的的,是有目的的。洛夫洛克在1990年回应这一批评时说:“在我们的著作中我们没有任何地方表达行星自我调节是有目的的,或涉及生物群的远见或计划。”<br />
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[[Stephen Jay Gould]] criticised Gaia as being "a metaphor, not a mechanism."<ref name="Gould 1997">{{cite journal |author=Gould S.J. |title=Kropotkin was no crackpot |journal=Natural History |volume=106 |pages=12–21 |date=June 1997 |url=http://libcom.org/library/kropotkin-was-no-crackpot |ref=harv}}</ref> He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as [[autopoiesis|autopoietic]] or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole.<ref>Abram, D. (1988) "The Mechanical and the Organic: On the Impact of Metaphor in Science" in Scientists on Gaia, edited by Stephen Schneider and Penelope Boston, Cambridge, Massachusetts: MIT Press, 1991</ref><ref>{{cite web|url=http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |title=The Mechanical and the Organic |accessdate=August 27, 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120223165936/http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |archivedate=February 23, 2012 }}</ref> With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<ref name="Lovelock, James 2001">Lovelock, James (2001), ''Homage to Gaia: The Life of an Independent Scientist'' (Oxford University Press)</ref><br />
史蒂芬·杰伊·古尔德批评盖亚假说是“一种隐喻,而不是一种机制。”他想知道实现自我调节内稳态的实际机制。在为盖亚假说辩护时,大卫·艾布拉姆认为古尔德忽略了一个事实,即“机制”本身就是一个隐喻——尽管这是一个非常常见且常常未被人认识的隐喻——它使我们把自然和生命系统看作是从外部组织和建造的机器(而不是自动或自组织的)现象)。艾布拉姆认为,机械隐喻使我们忽视了生命实体的活动性或能动性,而盖亚假说的有机体隐喻强调了生物群和生物圈作为一个整体的能动性。关于盖亚假说的因果关系,洛夫洛克认为没有单一的机制负责各种已知机制之间的联系可能永远不为人所知,这一点在其他生物学和生态学领域都是理所当然的,而具体的敌意是出于其他原因留给他自己的假设的<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of [[greedy reductionism]] in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<ref name="Lovelock, James 2001"/><br />
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除了澄清自己的语言和对生命形式的理解之外,洛夫洛克自己将大部分批评归咎于批评家对非线性数学缺乏理解,以及贪婪还原论的线性化形式,在这种形式中,所有事件都必须在事实发生之前立即归因于特定的原因。他还指出,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,有些自我调节的现象可能无法用数学解释 <br />
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===Natural selection and evolution自然选择和进化===<br />
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Lovelock has suggested that global biological feedback mechanisms could evolve by [[natural selection]], stating that organisms that improve their environment for their survival do better than those that damage their environment. However, in the early 1980s, [[Ford Doolittle|W. Ford Doolittle]] and [[Richard Dawkins]] separately argued against this aspect of Gaia. Doolittle argued that nothing in the [[genome]] of individual organisms could provide the feedback mechanisms proposed by Lovelock, and therefore the Gaia hypothesis proposed no plausible mechanism and was unscientific.<ref name=":1" /> Dawkins meanwhile stated that for organisms to act in concert would require foresight and planning, which is contrary to the current scientific understanding of evolution.<ref name=":2" /> Like Doolittle, he also rejected the possibility that feedback loops could stabilize the system.<br />
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洛夫洛克提出,全球生物反馈机制可以通过自然选择而进化,他指出,为生存而改善环境的生物比那些破坏环境的生物做得更好。然而,在20世纪80年代早期,W·福特·杜立德和理查德·道金斯分别反对盖亚假说的这一方面。杜立德认为,单个生物体的基因组中没有任何东西能够提供洛夫洛克提出的反馈机制,因此盖亚假说没有提出任何合理的机制,是不科学的。道金斯同时指出,要使有机体协同行动,就需要有远见和计划,这与当前科学界对进化论的理解相悖和杜立德一样,他也拒绝了反馈回路可以稳定系统的可能性。<br />
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[[Lynn Margulis]], a microbiologist who collaborated with Lovelock in supporting the Gaia hypothesis, argued in 1999, that "[[Charles Darwin|Darwin]]'s grand vision was not wrong, only incomplete. In accentuating the direct competition between individuals for resources as the primary selection mechanism, Darwin (and especially his followers) created the impression that the environment was simply a static arena". She wrote that the composition of the Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in [[homeostasis]], but those set points change with time.<ref name="ReferenceA">Margulis, Lynn. Symbiotic Planet: A New Look At Evolution. Houston: Basic Book 1999</ref><br />
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Lynn Margulis,一位与Lovelock合作支持盖亚假说的微生物学家,在1999年指出,“达尔文的宏伟愿景没有错,只是不完整。达尔文(特别是他的追随者)强调个人之间对资源的直接竞争是主要的选择机制,他给人的印象是环境只是一个静态的竞技场”。她写道,地球大气、水圈和岩石圈的组成都是围绕着“设定点”来调节的,就像在体内平衡中一样,但是这些设定点会随着时间的推移而变化 <br />
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Evolutionary biologist [[W. D. Hamilton]] called the concept of Gaia [[Nicolaus Copernicus|Copernican]], adding that it would take another [[Isaac Newton|Newton]] to explain how Gaian self-regulation takes place through Darwinian [[natural selection]].<ref name=vanish09>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, pp. 195-197. {{ISBN|978-0-465-01549-8}}</ref>{{better source|date=September 2012|reason=it should be possible to find the original place where Hamilton said this}} More recently [[Ford Doolittle]] building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal<ref name="ITSNTS">Doolittle WF, Inkpen SA. Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking. [https://www.pnas.org/content/115/16/4006 PNAS April 17, 2018 115 (16)] 4006-4014 </ref> proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis<ref name="Darwinizing Gaia">Doolittle WF. Darwinizing Gaia. [https://doi.org/10.1016/j.jtbi.2017.02.015 Journal of Theoretical BiologyVolume 434], 7 December 2017, Pages 11-19 </ref>. <br />
进化生物学家汉密尔顿称盖亚哥白尼为盖亚的概念,他补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。通过自然选择在进化过程中的繁殖,从而为自然选择理论和盖亚假说提供了可能的调和。 <br />
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===Criticism in the 21st century21世纪的批评===<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal ''Climatic Change'' in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it.<ref name="kirchner2002"/><ref name="volk2002"/> Several recent books have criticised the Gaia hypothesis, expressing views ranging from "... the Gaia hypothesis lacks unambiguous observational support and has significant theoretical difficulties"<ref>{{cite book |last=Waltham |first=David |authorlink=David Waltham |date=2014 |title=Lucky Planet: Why Earth is Exceptional – and What that Means for Life in the Universe |url=https://archive.org/details/luckyplanetwhyea0000walt |location= |publisher=Icon Books |page= |isbn=9781848316560 |accessdate= |url-access=registration }}</ref> to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background"<ref name="beerling2007"/> to "The Gaia hypothesis is supported neither by evolutionary theory nor by the empirical evidence of the geological record".<ref>{{cite book |last1=Cockell |first1=Charles |authorlink1=Charles Cockell |last2=Corfield |first2=Richard |last3=Dise |first3= Nancy |last4=Edwards |first4=Neil |last5=Harris |first5=Nigel |date=2008 |title= An Introduction to the Earth-Life System |url= http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/palaeontology-and-life-history/introduction-earth-life-system |location=Cambridge (UK) |publisher= Cambridge University Press |page= |isbn= 9780521729536 |accessdate= }}</ref> The [[CLAW hypothesis]],<ref name="CLAW87" /> initially suggested as a potential example of direct Gaian feedback, has subsequently been found to be less credible as understanding of [[cloud condensation nuclei]] has improved.<ref>{{Citation |last1= Quinn |first1=P.K. |last2= Bates |first2=T.S. |title =The case against climate regulation via oceanic phytoplankton sulphur emissions |journal =Nature |volume=480 |issue=7375 |pages =51–56 |date = 2011 |doi=10.1038/nature10580|bibcode = 2011Natur.480...51Q |pmid=22129724|url=https://zenodo.org/record/1233319 }}</ref> In 2009 the [[Medea hypothesis]] was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<ref>Peter Ward (2009), ''The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?'', {{ISBN|0-691-13075-2}}</ref><br />
盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论点是在许多例子中,生命对环境产生了有害或不稳定的影响,而不是采取行动来调节它。最近几本书批评了盖亚假说,譬如“盖亚假说缺乏明确的观察支持,并且有重大的理论困难”“(盖亚假说)令人不安地徘徊在污点、隐喻、事实和虚假科学之间,我宁愿把盖亚牢牢地放在原有的背景中”“盖亚假说既没有进化论的支持,也没有地质记录的经验证据的支持。爪假说最初被认为是盖亚直接反馈的一个潜在例子,后来被发现对云的理解不那么可信凝聚核已经得到了改善。2009年,美狄亚假说提出:生命对行星的状况非常有害,这与盖亚假说直接相反。 <br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it".<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=209 |isbn=9780691121581 |accessdate= }}</ref> Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works".<ref>{{Citation |last= Tyrrell |first = Toby |title =Gaia: the verdict is… |journal = New Scientist |volume = 220 |issue = 2940 |pages = 30–31 |date= 26 October 2013 |doi=10.1016/s0262-4079(13)62532-4}}</ref> This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=208 |isbn=9780691121581 |accessdate= }}</ref><br />
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2013年,托比·泰瑞尔在一本书中对盖亚假说总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,认识到他大胆的概念有助于激发许多关于地球的新思想,并倡导一种研究地球的整体方法。”在其他地方,他提出了自己的结论:“盖亚假说并不能精确地描述我们世界的运转机制。”这种说法需要被理解为是指盖亚假说的“强大”和“温和”形式,生物群遵循的原则是使地球处于最佳状态(强度5)或有利于生命(强度4),或者它作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化德盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释 <br />
Category:Cybernetics<br />
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类别: 控制论<br />
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Category:Ecological theories<br />
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范畴: 生态学理论<br />
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==See also==<br />
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Category:Superorganisms<br />
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类别: 超级有机体<br />
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{{Portal|Environment|Earth sciences|Geography}}<br />
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Category:Climate change feedbacks<br />
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类别: 气候变化反馈<br />
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Category:1965 introductions<br />
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类别: 1965年引言<br />
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* {{annotated link|Biocoenosis}}<br />
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Category:Biogeochemistry<br />
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类别: 生物地球化学<br />
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* {{annotated link|Earth science}}<br />
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Category:Earth<br />
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类别: 地球<br />
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* {{annotated link|Environmentalism}}<br />
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Category:Biological hypotheses<br />
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类别: 生物学假说<br />
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* {{annotated link|Gaianism}}<br />
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Category:Astronomical hypotheses<br />
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Category:Meteorological hypotheses<br />
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类别: 气象假说<br />
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<small>This page was moved from [[wikipedia:en:Gaia hypothesis]]. Its edit history can be viewed at [[盖亚假说/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%96%E4%BA%9A%E5%81%87%E8%AF%B4&diff=21582盖亚假说2021-02-04T13:19:36Z<p>Vicky:/* Criticism in the 21st century21世纪的批评 */</p>
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<div>此词条由Henry第一次翻译。<br />
已由三奇同学完成校对。<br />
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{{short description|Hypothesis that living organisms interact with their surroundings in a self-regulating system}}<br />
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[[File:The Earth seen from Apollo 17.jpg|thumb|The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth]]'s conditions, as the Earth is the only planet currently known to harbour life (''[[The Blue Marble]]'', 1972 [[Apollo 17]] photograph)]]<br />
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The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth's conditions, as the Earth is the only planet currently known to harbour life (The Blue Marble, 1972 Apollo 17 photograph)]]<br />
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对行星可居住性的研究主要基于对[[地球条件]的了解进行推断,因为地球是目前已知的唯一一颗拥有生命的行星 <br />
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The '''Gaia hypothesis''' {{IPAc-en|ˈ|ɡ|aɪ|.|ə}}, also known as the '''Gaia theory''' or the '''Gaia principle''', proposes that living [[organism]]s interact with their [[Inorganic compound|inorganic]] surroundings on [[Earth]] to form a [[Synergy|synergistic]] and [[Homeostasis|self-regulating]], [[complex system]] that helps to maintain and perpetuate the conditions for [[life]] on the planet.<br />
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The Gaia hypothesis , also known as the Gaia theory or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.<br />
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盖亚假说(又称盖亚理论或盖亚原理)认为,生物体与地球上的无机环境相互作用,形成一个协同和自我调节的复杂系统,有助于维持和延续地球上的生命条件。<br />
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The hypothesis was formulated by the chemist [[James Lovelock]]<ref name="J1972" /> and co-developed by the microbiologist [[Lynn Margulis]] in the 1970s.<ref name="lovelock1974">{{cite journal|last1=Lovelock|first1=J.E.|last2=Margulis|first2=L.|title=Atmospheric homeostasis by and for the biosphere: the Gaia hypothesis|journal=Tellus|date=1974|volume=26|series=Series A|issue=1–2|pages=2–10|doi=10.1111/j.2153-3490.1974.tb01946.x|publisher=International Meteorological Institute|location=Stockholm|issn=1600-0870|ref=harv|bibcode=1974Tell...26....2L}}</ref> Lovelock named the idea after [[Gaia]], the primordial goddess who personified the Earth in [[Greek mythology]]. In 2006, the [[Geological Society of London]] awarded Lovelock the [[Wollaston Medal]] in part for his work on the Gaia hypothesis.<ref>{{cite web|title=Wollaston Award Lovelock|url=https://www.geolsoc.org.uk/About/History/Awards-Citations-Replies-2001-Onwards/2006-Awards-Citations-Replies|accessdate=19 October 2015}}</ref><br />
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The hypothesis was formulated by the chemist James Lovelock Lovelock named the idea after Gaia, the primordial goddess who personified the Earth in Greek mythology. In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.<br />
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这个假设是由化学家詹姆斯·洛夫洛克提出的,他以希腊神话中地球的化身盖亚的名字命名了这个想法。2006年,伦敦地质学会授予洛夫洛克沃拉斯顿勋章,以表彰他在<font color="#ff8000"> 盖亚假说Gaia hypothesis</font>方面的工作。 <br />
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Topics related to the hypothesis include how the [[biosphere]] and the [[evolution]] of organisms affect the stability of [[global temperature]], [[salinity]] of [[seawater]], [[atmospheric oxygen]] levels, the maintenance of a [[hydrosphere]] of liquid water and other environmental variables that affect the [[habitability of Earth]].<br />
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Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenance of a hydrosphere of liquid water and other environmental variables that affect the habitability of Earth.<br />
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与该假设有关的主题包括生物圈和生物体的进化如何影响全球温度的稳定性、海水的盐度、大气中的氧含量、液态水水圈的维持以及其他影响地球宜居性的环境变量。<br />
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The Gaia hypothesis was initially criticized for being [[teleological]] and against the principles of [[natural selection]], but later refinements aligned the Gaia hypothesis with ideas from fields such as [[Earth system science]], [[biogeochemistry]] and [[systems ecology]].<ref name="Turney, Jon 2003"/><ref name="Schwartzman2002">{{cite book |author=Schwartzman, David |title=Life, Temperature, and the Earth: The Self-Organizing Biosphere |publisher=Columbia University Press |date=2002 |isbn=978-0-231-10213-1 }}</ref><ref>Gribbin, John (1990), "Hothouse earth: The greenhouse effect and Gaia" (Weidenfeld & Nicolson)</ref> Lovelock also once described the "geophysiology" of the Earth.<ref name="agesofgaia">Lovelock, James, (1995) "The Ages of Gaia: A Biography of Our Living Earth" (W.W.Norton & Co)</ref>{{Explain|date=December 2017}} Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<ref name="kirchner2002">{{Citation |last= Kirchner |first = James W. |title =Toward a future for Gaia theory |journal=[[Climatic Change (journal)|Climatic Change]] |volume = 52 |issue = 4 |pages = 391–408 |date = 2002 | doi = 10.1023/a:1014237331082 }}</ref><ref name="volk2002">{{Citation |last= Volk |first = Tyler |title =The Gaia hypothesis: fact, theory, and wishful thinking |journal = Climatic Change |volume = 52 |issue = 4 |pages = 423–430 |date = 2002 | doi = 10.1023/a:1014218227825 }}</ref><ref name="beerling2007">{{cite book |last=Beerling |first=David |authorlink=David Beerling|date=2007 |title=The Emerald Planet: How plants changed Earth's history |url=http://ukcatalogue.oup.com/product/9780192806024.do |location=Oxford|publisher=Oxford University Press |page= |isbn= 978-0-19-280602-4 |accessdate= }}</ref><br />
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The Gaia hypothesis was initially criticized for being teleological and against the principles of natural selection, but later refinements aligned the Gaia hypothesis with ideas from fields such as Earth system science, biogeochemistry and systems ecology. Lovelock also once described the "geophysiology" of the Earth. Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<br />
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盖亚假说最初被诟病为目的论、反对自然选择的原则,但后来的改进使盖亚假说与来自地球系统科学、生物地球化学和系统生态学等领域的观点相一致。洛夫洛克还曾经描述过地球的“地球物理学”。即便如此,盖亚假说仍然受到一些批评,今天许多科学家认为只有少数证据支持这一理论,或与现有的证据相矛盾。<br />
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==Overview总览==<br />
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Gaian hypotheses suggest that organisms [[Co-evolution|co-evolve]] with their environment: that is, they "influence their [[abiotic]] environment, and that environment in turn influences the [[Biota (ecology)|biota]] by [[Darwinism|Darwinian process]]". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early [[Bacteria|thermo-acido-philic]] and [[methanogenic bacteria]] towards the oxygen-enriched [[atmosphere]] today that supports more [[Phanerozoic|complex life]].<br />
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Gaian hypotheses suggest that organisms co-evolve with their environment: that is, they "influence their abiotic environment, and that environment in turn influences the biota by Darwinian process". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early thermo-acido-philic and methanogenic bacteria towards the oxygen-enriched atmosphere today that supports more complex life.<br />
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盖亚假说认为,生物体与其环境共同进化。也就是说,生物“影响它们的非生物环境,而环境反过来又通过自然选择的过程影响生物群”。Lovelock(1995)在他的第二本书中提供了证据,展示了从早期嗜酸、产甲烷细菌的世界向今天支持更复杂生命的富氧大气的进化。<br />
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A reduced version of the hypothesis has been called "influential Gaia"<ref name=":02">{{Cite journal|last=Lapenis|first=Andrei G.|year=2002|title=Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?|url=|journal=The Professional Geographer|volume=54 |issue=3|pages=379–391|via=[Peer Reviewed Journal]|doi=10.1111/0033-0124.00337}}</ref> in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the [[Biota (ecology)|biota]] influence certain aspects of the abiotic world, e.g. [[temperature]] and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<ref name=":02" /> and biogeochemical processes. An example is how the activity of [[Photosynthesis|photosynthetic]] bacteria during Precambrian times completely modified the [[Earth's atmosphere|Earth atmosphere]] to turn it aerobic, and thus supports the evolution of life (in particular [[eukaryotic]] life).<br />
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A reduced version of the hypothesis has been called "influential Gaia" in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the biota influence certain aspects of the abiotic world, e.g. temperature and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<br />
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在《生物圈的定向进化: 生物地球化学选择还是盖亚? 》一书中,这一假说的简化版被称为“有影响力的盖亚”。安德烈·G·拉佩尼斯在这本书中指出生物影响着非生物世界的温度和大气等多个方面。这本书不是一个人的工作,而是一群俄罗斯科研人员的成果合并成这个通过同行评议的出版物。它通过“微观力量”阐述了生命与环境的共同进化。<br />
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Since barriers existed throughout the twentieth century between Russia and the rest of the world, it is only relatively recently that the early Russian scientists who introduced concepts overlapping the Gaia hypothesis have become better known to the Western scientific community.<ref name=":02" /> These scientists include [[Piotr Kropotkin|Piotr Alekseevich Kropotkin]] (1842–1921) (although he spent much of his professional life outside Russia), Vasil’evich Rizpolozhensky (1847–1918), [[Vladimir Ivanovich Vernadsky]] (1863–1945), and Vladimir Alexandrovich Kostitzin (1886–1963).<br />
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由于二十世纪苏联与西方国家存在隔阂,直到最近,在盖亚假说中引进重叠概念的早期苏联科学家才为西方科学界所熟知。<br />
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The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<br />
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盖亚假说认为,地球是一个自我调节的复杂系统,包括生物圈、大气层、水圈和土壤圈,作为一个进化的系统紧密结合在一起。这个假说认为,这个被称为盖亚的系统作为整体,寻求适合当代生命的物理和化学环境。<br />
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Biologists and Earth scientists usually view the factors that stabilize the characteristics of a period as an undirected [[emergent property]] or [[entelechy]] of the system; as each individual species pursues its own self-interest, for example, their combined actiYons may have counterbalancing effects on environmental change. Opponents of this view sometimes reference examples of events that resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth's atmosphere from a [[reducing environment]] to an [[oxygen]]-rich one at the end of the [[Archean|Archaean]] and the beginning of the [[Proterozoic]] periods.<br />
生物学家和地球科学家通常将平衡一个时期的特征的因素视为系统的无方向[[涌现属性]]或[[有目的行为]];例如,由于每个物种都追求自身利益,它们的联合行动可能对环境变化产生抵消作用。反对这一观点的人有时会举出一些导致了巨大变化而非平衡的事件作为反例,例如在[[太古宙|太古代]]末期和[[元古代]]时期开始时,地球大气从[[还原环境]]转变为富含[[氧气]]。 <br />
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Gaia evolves through a cybernetic feedback system operated unconsciously by the biota, leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially microorganisms, with inorganic elements. These processes establish a global control system that regulates Earth's surface temperature, atmosphere composition and ocean salinity, powered by the global thermodynamic disequilibrium state of the Earth system.<!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
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盖亚通过一个由生物群无意识操作的控制论反馈系统实现进化,在完全的内稳态中广泛获得稳定的可居住条件。地球表面的许多过程对生命的保障条件至关重要,这些过程依赖于生命形式,特别是微生物与无机元素的相互作用。这些过程建立了一个全球控制系统,由地球系统的全球热力学不平衡状态提供动力,调节地球表面温度、大气成分和海洋盐度。<br />
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Less accepted versions of the hypothesis claim that changes in the biosphere are brought about through the [[Superorganism|coordination of living organisms]] and maintain those conditions through [[homeostasis]]. In some versions of [[Gaia philosophy]], all lifeforms are considered part of one single living planetary being called ''Gaia''. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the [[Coevolution|coevolving]] diversity of living organisms.<br />
一种不太被接受的假说声称生物圈的变化是通过[[超级有机体|生物体的协调]]来实现的,并通过[[内稳态]]来维持这些条件。在一些版本的[[盖亚哲学]]中,所有的生命形式都是一个被称为“盖亚”的生命行星的一部分。在这种观点下,大气、海洋和地壳将是盖亚通过生物多样性进行干预的结果。 <br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of biogeochemistry, and it is being investigated also in other fields like Earth system science. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<br />
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以前在生物地球化学领域已经观察到受生命形式影响的行星内稳态的存在,而且地球系统科学等其他领域也在研究这一现象。盖亚假说的原创性依赖于这样一种观点: 即使地球或外部事件威胁到内稳态平衡,盖亚也会为了保持生命的最佳状态而积极追求这种平衡。<br />
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The Gaia hypothesis was an influence on the [[deep ecology]] movement.<ref>David Landis Barnhill, Roger S. Gottlieb (eds.), ''Deep Ecology and World Religions: New Essays on Sacred Ground'', SUNY Press, 2010, p. 32.</ref><br />
盖亚假说对[[深层生态学]]运动产生了影响 <br />
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==Details细节==<br />
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Rob Rohde's palaeotemperature graphs<br />
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罗布·罗德的古温度图<br />
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The Gaia hypothesis posits that the Earth is a self-regulating [[complex system]] involving the [[biosphere]], the [[Earth's atmosphere|atmosphere]], the [[hydrosphere]]s and the [[pedosphere]], tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<ref name="vanishing255">Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 255. {{ISBN|978-0-465-01549-8}}</ref><br />
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盖亚假说假设地球是一个自我调节的[[复杂系统]],包括[[生物圈]]、[[地球大气|大气]]、[[水圈]]和[[土壤圈]],作为一个进化系统紧密耦合。该假说认为,这个系统作为一个整体,称为盖亚,寻求一个最适合当代生活的物理和化学环境 <br />
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Since life started on Earth, the energy provided by the Sun has increased by 25% to 30%; however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on Titan. research has suggested that "oxygen shocks" and reduced methane levels led, during the Huronian, Sturtian and Marinoan/Varanger Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre Phanerozoic biosphere to fully self-regulate.<br />
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自从地球上有生命以来,太阳提供的能量增加了25%到30%;然而,地球表面温度一直保持在适宜居住的水平上,不曾突破上限或是下限。洛夫洛克还假设,产甲烷菌在早期大气中产生了较高水平的甲烷,这与在石化烟雾中发现的成分相似,在某些方面与土卫六上的大气相似。研究表明,在休伦期、斯图尔特期和马里诺/瓦朗格冰期,“氧冲击”和甲烷含量降低导致世界几乎变成了一个坚实的“雪球”。这些时代是前显生宙生物圈完全拥有自我调节能力的证据。<br />
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Gaia evolves through a [[Cybernetic#In biology|cybernetic]] [[feedback]] system operated unconsciously by the [[biota (ecology)|biota]], leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially [[microorganisms]], with inorganic elements. These processes establish a global control system that regulates Earth's [[Sea surface temperature|surface temperature]], [[atmosphere composition]] and [[ocean]] [[salinity]], powered by the global thermodynamic disequilibrium state of the Earth system.<ref>Kleidon, Axel. ''How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?''. Article submitted to the ''Philosophical Transactions of the Royal Society'' on Thu, 10 Mar 2011</ref><!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
盖亚通过一个[[控制论|生物学|控制论]][[反馈]]系统在[[生物群(生态学)|生物群]]的无意识运作中实现进化,导致在完全的内稳态中广泛存在稳定的可居住条件。地球表面对生命条件至关重要的许多过程都依赖于生物,特别是[微生物]与无机元素的相互作用。这些过程建立了一个全球控制系统,调节地球的[[海表温度|表面温度]]、[[大气组成]]和[[海洋]][[盐度]],其动力来自地球系统的全球热力学不平衡状态。<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
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温室气体CO<sub>2</sub>的处理在维持地球温度在可居住范围内起着关键作用(解释详见下文)。<br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of [[biogeochemistry]], and it is being investigated also in other fields like [[Earth system science]]. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 179. {{ISBN|978-0-465-01549-8}}</ref><br />
受生命形式影响的行星内稳态的存在,以前在[[生物地球化学]]领域就已被观察到,而且其他领域,如[[地球系统科学]]也在研究这种稳态。盖亚假说的独创性依赖于这样一种观点,即盖亚积极追求这种内平衡,以保持维护生命的最佳状态,即使是在地球或外部事件威胁它们的时候。<br />
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The CLAW hypothesis, inspired by the Gaia hypothesis, proposes a feedback loop that operates between ocean ecosystems and the Earth's climate. The hypothesis specifically proposes that particular phytoplankton that produce dimethyl sulfide are responsive to variations in climate forcing, and that these responses lead to a negative feedback loop that acts to stabilise the temperature of the Earth's atmosphere.<br />
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受盖亚假说的启发,CLAW 假说提出了一个在海洋生态系统和地球气候之间运行的反馈回路。该假说特别提出,产生二甲硫醚的浮游植物对气候变化有反应,这些反应导致了一个负反馈循环,稳定了地球大气的温度。<br />
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===Regulation of global surface temperature地球表面温度的调控===<br />
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[[File:All palaeotemps.png|thumb|480px|Rob Rohde's palaeotemperature graphs]]<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of greenhouse gases may cause negative feedbacks in the environment to become positive feedback. Lovelock has stated that this could bring an extremely accelerated global warming, but he has since stated the effects will likely occur more slowly.<br />
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目前,人口的增加及其活动对环境的影响,例如温室气体的增加,可能导致环境中的负反馈成为正反馈。洛夫洛克表示,这可能会极大地加速全球变暖,但他后来又表示,这种影响也可能发生得更慢。<br />
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{{See also|Paleoclimatology}}<br />
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Since life started on Earth, the energy provided by the [[Sun]] has increased by 25% to 30%;<ref name="Owen1979">{{cite journal | author = Owen, T. | author2 = Cess, R.D. | author3 = Ramanathan, V. | date = 1979 | title = Earth: An enhanced carbon dioxide greenhouse to compensate for reduced solar luminosity | journal = [[Nature (journal)|Nature]] | volume = 277 | pages = 640–2 | doi = 10.1038/277640a0 | issue=5698 | bibcode = 1979Natur.277..640O | ref = harv }}</ref> however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on [[Titan (moon)|Titan]].<ref name="agesofgaia"/> This, he suggests tended to screen out ultraviolet until the formation of the ozone screen, maintaining a degree of homeostasis. However, the [[Snowball Earth]]<ref>Hoffman, P.F. 2001. [http://www.snowballearth.org ''Snowball Earth theory'']</ref> research has suggested that "oxygen shocks" and reduced methane levels led, during the [[Huronian]], [[Sturtian]] and [[Marinoan]]/[[Cryogenian|Varanger]] Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre [[Phanerozoic]] biosphere to fully self-regulate.<br />
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Plots from a standard black and white [[Daisyworld simulation]]<br />
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从一个标准的黑白图[[雏菊世界模拟]]<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
说明了在温室气体维持低于临界温度的过程中,CO2起着至关重要的作用。 <br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic group selection and cooperation between organisms, James Lovelock and Andrew Watson developed a mathematical model, Daisyworld, in which ecological competition underpinned planetary temperature regulation.<br />
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有人批评盖亚假说似乎需要有机体之间不切实际的群体选择与合作,为了回应这种批评,James Lovelock 和 Andrew Watson建立了一个数学模型---- 雏菊世界,其中生态竞争支撑着地。<br />
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The [[CLAW hypothesis]], inspired by the Gaia hypothesis, proposes a [[feedback|feedback loop]] that operates between [[ocean]] [[ecosystem]]s and the [[Earth]]'s [[climate]].<ref name="CLAW87">{{cite journal |doi=10.1038/326655a0 |author=[[Robert Jay Charlson|Charlson, R. J.]], [[James Lovelock|Lovelock, J. E]], Andreae, M. O. and Warren, S. G. |title=Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate |journal=Nature |volume=326 |issue=6114 |pages=655–661 |date=1987 |bibcode=1987Natur.326..655C |ref=harv }}</ref> The [[hypothesis]] specifically proposes that particular [[phytoplankton]] that produce [[dimethyl sulfide]] are responsive to variations in [[climate forcing]], and that these responses lead to a [[negative feedback|negative feedback loop]] that acts to stabilise the [[temperature]] of the [[Earth's atmosphere]].<br />
受到盖亚假说启发的[[爪假说]]提出了一个在[[海洋]][[生态系统]]和[[地球]]的[[气候]]之间运行的[[反馈|反馈回路]]。<br />
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Daisyworld examines the energy budget of a planet populated by two different types of plants, black daisies and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the albedo of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
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《雏菊世界》调查了一个星球的能量预算,这个星球上生长着两种不同的植物,黑色雏菊和白色雏菊,这两种植物占据了星球表面的很大一部分。雏菊的颜色影响了地球的反照率,黑色的雏菊吸收更多的光线,使地球变暖,而白色的雏菊则反射更多的光线,使地球变冷。人们认为黑色雏菊在较低的温度下生长和繁殖最好,而白色雏菊则被认为在较高的温度下生长最好。当温度上升到接近白色雏菊所喜欢的温度时,白色雏菊繁殖率高于黑色雏菊,导致更大比例的白色表面,更多的阳光被反射,减少热量输入,最终使地球降温。相反,随着气温的下降,黑色雏菊繁殖率高于白色雏菊,吸收了更多的阳光,使地球变暖。因此,温度会收敛于两种植物繁殖率相等时对应温度的值。<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of [[greenhouse gases]] may cause [[negative feedback]]s in the environment to become [[positive feedback]]. Lovelock has stated that this could bring an [[James Lovelock#The revenge of Gaia|extremely accelerated global warming]],<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, {{ISBN|978-0-465-01549-8}}</ref> but he has since stated the effects will likely occur more slowly.<ref>Lovelock J., NBC News. [http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite Link] Published 23 April 2012, accessed 22 August 2012. {{Webarchive|url=https://web.archive.org/web/20120913163635/http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite |date=13 September 2012 }}</ref><br />
目前,人口的增加及其活动对环境的影响,如[[温室气体]]的倍增,可能导致环境中的[[负反馈]]变成[[正反馈]]。洛夫洛克曾表示,这可能会带来一场【【James Loveloc【《盖亚的复仇』极度加速的全球变暖】】 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this negative feedback due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
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洛夫洛克和沃森指出,在有限的条件下,如果太阳的能量输出发生变化,由于竞争产生的负反馈可以将地球温度稳定在支持生命存在的范围内,而没有生命的地球则会表现出巨大的温度波动。白色和黑色雏菊的百分比会不断变化,以保持植物繁殖率相等的温度值,使两种生命形式都能茁壮成长。<br />
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====Daisyworld simulations雏菊世界模拟====<br />
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[[File:StandardDaisyWorldRun2color.gif|thumb|280px|Plots from a standard black and white [[Daisyworld]] simulation]]<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<br />
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有人认为,这些结果是可以预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的答案。<br />
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{{Main|Daisyworld}}<br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic [[group selection]] and [[Cooperation (evolution)|cooperation]] between organisms, James Lovelock and [[Andrew Watson (scientist)|Andrew Watson]] developed a mathematical model, [[Daisyworld]], in which [[Competition (biology)|ecological competition]] underpinned planetary temperature regulation.<ref name="daisyworld">{{cite journal<br />
有人批评盖亚假说似乎需要有机体之间不切实际的[[群体选择]]和[[合作(进化)|合作]],詹姆斯·洛夫洛克和[[安德鲁·沃森(科学家)|安德鲁·沃森]]开发了一个数学模型,[[雏菊世界]],其中[[竞争(生物学)|生态竞争]]为基础行星温度调节。 <br />
|date = 1983<br />
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Ocean salinity has been constant at about 3.5% for a very long time. Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested that salinity may also be strongly influenced by seawater circulation through hot basaltic rocks, and emerging as hot water vents on mid-ocean ridges. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<br />
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长期以来,海洋盐度一直保持在3.5% 左右。海洋环境中盐度的稳定性很重要,因为大多数细胞需要相当恒定的盐度,一般不能耐受超过5% 的盐度值。海洋盐度为何恒定是一个长期的奥秘,因为没有任何方法可以抵消来自河流的流入盐。最近有人提出,盐分也会洋中脊的热水喷口排出,因此盐度可能受到穿过炽热玄武岩的海水循环的强烈影响。然而,海水的组成离平衡还很远,如果没有有机过程的影响,很难解释这一事实。有一种解释认为,地球历史上盐滩的形成是盐度平衡的原因之一。据推测,这些盐滩是由细菌菌落产生的,它们在生命过程中固定离子和重金属。<br />
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|title = Biological homeostasis of the global environment: the parable of Daisyworld<br />
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|journal = Tellus<br />
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|volume = 35B<br />
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Vostok, Antarctica research station. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
沃斯托克,南极洲研究站。当前期间在左边。<!--基于此图表的GIMP-FX版本的非源材料。现在的版本是正确的,原版的。必须删除这句话:请注意,当前CO2水平超过390ppm,远高于过去40万年来的任何时候-->] <br />
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|pages = 286–9<br />
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|bibcode = 1983TellB..35..284W<br />
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|doi = 10.1111/j.1600-0889.1983.tb00031.x<br />
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The Gaia hypothesis states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organisms or processed by them.<br />
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盖亚假说认为,地球的大气组成是由于生命的存在而保持在动态稳定的状态。大气成分提供了支持现代生命的条件。大气中除惰性气体以外的所有大气气体,要么是由生物体产生的,要么是由生物体加工的。<br />
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|last1 = Watson | first1= A.J. | last2= Lovelock | first2= J.E<br />
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|issue = 4<br />
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The stability of the atmosphere in Earth is not a consequence of chemical equilibrium. Oxygen is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the Great Oxygenation Event. Since the start of the Cambrian period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume. Traces of methane (at an amount of 100,000 tonnes produced per year) should not exist, as methane is combustible in an oxygen atmosphere.<br />
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地球大气层的稳定性不是化学平衡的结果。氧是一种活性化合物,最终会与地球大气层和地壳中的气体和矿物质结合。在大氧化事件开始之前,大约5000万年前,氧气才开始在大气中持续少量存在。自寒武纪以来,大气中氧浓度一直在大气体积的15% 至35% 之间波动。微量的甲烷(每年产生100,000吨)不适合存在,因为甲烷在氧气氛中是可燃的。<br />
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|ref = harv<br />
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}}</ref><br />
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Dry air in the atmosphere of Earth contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases including methane. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. <br />
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地球大气层中的干燥空气大致(按体积计算)含有78.09% 的氮气、20.95% 的氧气、0.93% 的氩气、0.039% 的二氧化碳以及少量的其他气体,包括甲烷。洛夫洛克最初推测,高于25% 的氧气浓度会增加森林大火和森林大火的发生频率。石炭纪和白垩纪煤系地质时期O2浓度确实超过了25%时,正是这一时期形成了火成木炭。这一结果支持了 Lovelock 的论点。<br />
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Daisyworld examines the [[Earth's energy budget|energy budget]] of a [[planet]] populated by two different types of plants, black [[Asteraceae|daisies]] and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the [[albedo]] of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
Daisyworld研究了居住着两种不同类型的植物的[[地球的能源预算|能源预算]],这两种植物是黑色的[[菊科的雏菊]]和白色的雏菊,这两种植物被认为占据了地表的很大一部分。雏菊的颜色影响着这个星球的[反照率],因此黑色雏菊吸收更多的光并温暖地球,而白色雏菊则反射更多的光并使地球降温。黑雏菊在较低温度下生长繁殖最好,而白雏菊在较高温度下生长繁殖最好。当温度上升到接近白色雏菊的最适生长温度时,白色雏菊的繁殖能力超过了黑色雏菊,导致白色表面的比例增大,更多的阳光被反射,减少了热量输入,最终使地球变冷。相反,随着温度的下降,黑雏菊的繁殖能力超过了白雏菊,吸收了更多的阳光,使地球变暖。因此,温度将收敛到两种植物繁殖率相等对应的温度值。 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this [[negative feedback]] due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
Lovelock和Watson表明,在有限的条件范围内,如果太阳的能量输出发生变化,由于竞争而产生的[[负反馈]]可以将地球的温度稳定在支持生命的值上,而没有生命的行星则会出现大范围的温度波动。白雏菊和黑雏菊的比例会不断变化,以使温度保持在植物繁殖率相等的值,从而使两种生命形式都能茁壮成长。 <br />
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Gaia scientists see the participation of living organisms in the carbon cycle as one of the complex processes that maintain conditions suitable for life. The only significant natural source of atmospheric carbon dioxide (CO<sub>2</sub>) is volcanic activity, while the only significant removal is through the precipitation of carbonate rocks. Carbon precipitation, solution and fixation are influenced by the bacteria and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
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盖亚假说的科学家们把生物体参与碳循环看作是维持适合生命条件的复杂过程之一。火山活动是大气中二氧化碳的最重要的自然来源,而碳酸盐岩的沉淀是大气中二氧化碳最重要的去除途径。碳沉淀、溶解和固定受到土壤中细菌和植物根系的影响,这些细菌和植物根系可以改善气体循环,或者在珊瑚礁中,碳酸钙以固体的形式沉积在海底。碳酸钙被活的有机体用来制造含碳的结构和外壳。一旦死亡,生物体的外壳就会沉到海底,在那里它们产生白垩和石灰石的沉淀物。<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<ref>{{cite journal | doi = 10.1023/A:1023494111532 | date = 2003 | last1 = Kirchner | first1 = James W. | journal = Climatic Change | volume = 58 |issue=1–2| pages = 21–45 |title=The Gaia Hypothesis: Conjectures and Refutations | ref = harv}}</ref><br />
有人认为,结果是可预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的反应。 <br />
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One of these organisms is Emiliania huxleyi, an abundant coccolithophore algae which also has a role in the formation of clouds. CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants. Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean algal blooms are also increasing.<br />
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其中一种是赫氏圆石藻,这是一种数量丰富的颗石藻类,也参与了云的形成。通过增加球石氟化物的寿命来补偿过量的CO < sub > 2 </sub > ,增加了锁定在海底的 CO < sub > 2 </sub > 的数量。球石粉会增加云量,从而控制地表温度,有助于降低整个地球的温度,有利于地球上植物所必需的降水。近年来,大气中 CO < < sub > 2 </sub > 浓度有所增加,有证据表明,海洋藻华的浓度也在增加。<br />
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===Regulation of oceanic salinity海洋盐度调节 ===<br />
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Lichen and other organisms accelerate the weathering of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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地衣和其他生物加速了岩石表面的风化,而岩石在土壤中的分解也加快了,这要归功于根、真菌、细菌和地下动物的活动。因此,二氧化碳从大气层流向土壤的过程是在生物的帮助下调节的。当大气中 CO2水平升高时,温度升高,植物生长。这种生长会增加植物对二氧化碳的消耗,植物会将二氧化碳处理到土壤中,从大气中排出。<br />
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Ocean [[salinity]] has been constant at about 3.5% for a very long time.<ref name=":0">{{Cite book|title=The Introduction to Ocean Sciences|last=Segar|first=Douglas|publisher=Library of Congress|year=2012|isbn=978-0-9857859-0-1|location=http://www.reefimages.com/oceans/SegarOcean3Chap05.pdf|pages=Chapter 5 3rd Edition|quote=|via=}}</ref> Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested<ref name="Gorham19912">{{cite journal|last=Gorham|first=Eville|date=1 January 1991|title=Biogeochemistry: its origins and development|journal=Biogeochemistry|publisher=Kluwer Academic|volume=13|issue=3|pages=199–239|doi=10.1007/BF00002942|issn=1573-515X|ref=harv}}</ref> that salinity may also be strongly influenced by [[seawater]] circulation through hot [[basalt]]ic rocks, and emerging as hot water vents on [[mid-ocean ridge]]s. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<ref name=":0" /><br />
在很长一段时间内,海洋盐度一直保持在3.5%左右。[23]海洋环境中的盐度稳定性非常重要,因为大多数细胞需要相当恒定的盐度,并且通常不能耐受超过5%的盐度值。恒定的海洋盐度是一个长期存在的谜团,因为没有任何过程可以抵消河流中的盐流入。大洋中脊上的热水喷口会排出盐分,有人认为[24]这说明盐分也会受到海水循环的强烈影响。然而,海水的组成远未达到平衡,如果没有有机过程的影响,很难解释这一事实。地球历史中盐滩的形成是一个常用的证据。据推测,这些盐滩是由在生命过程中固定离子和重金属的菌落产生的<br />
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In the biogeochemical processes of Earth, sources and sinks are the movement of elements. The composition of salt ions within our oceans and seas is: sodium (Na<sup>+</sup>), chlorine (Cl<sup>−</sup>), sulfate (SO<sub>4</sub><sup>2−</sup>), magnesium (Mg<sup>2+</sup>), calcium (Ca<sup>2+</sup>) and potassium (K<sup>+</sup>). The elements that comprise salinity do not readily change and are a conservative property of seawater.<ref name=":0" /> There are many mechanisms that change salinity from a particulate form to a dissolved form and back. The known sources of sodium i.e. salts are when weathering, erosion, and dissolution of rocks are transported into rivers and deposited into the oceans.<br />
在地球的生物地球化学过程中,源和汇是元素的运动。我们海洋中盐离子的组成是:钠(Na+)、氯(Cl-)、硫酸盐(SO42-)、镁(Mg2+)、钙(Ca2+)和钾(K+)。构成盐度的元素不易变化,是海水的一种保守属性。[23]有许多机制可以将盐度从颗粒形态改变为溶解形态,然后再返回。已知的钠(即盐)因为岩石的风化、侵蚀和溶解作用被输送到河流中并沉积到海洋中。 <br />
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The [[Mediterranean Sea]] as being Gaia's kidney is found ([http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/ here]) by Kenneth J. Hsue, a correspondence author in 2001. The "[[desiccation]]" of the Mediterranean is the evidence of a functioning kidney. Earlier "kidney functions" were performed during the "[[Deposition (geology)|deposition]] of the [[Cretaceous]] ([[Atlantic Ocean|South Atlantic]]), [[Jurassic]] ([[Gulf of Mexico]]), [[Permian–Triassic extinction event|Permo-Triassic]] ([[Europe]]), [[Devonian]] ([[Canada]]), [[Cambrian]]/[[Precambrian]] ([[Gondwana]]) saline giants."<ref>{{Cite web|url=http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/|title=Scientia Marina: List of Issues|last=http://www.webviva.com|first=Justino Martinez. Web Viva 2007|website=scimar.icm.csic.es|language=English|access-date=2017-02-04}}</ref><br />
地中海是盖亚的肾脏,由肯尼斯·J·休伊(KennethJ.Hsue)在2001年发现的。地中海的“干涸”是肾功能正常的证据。早期的“肾功能”是在“白垩纪(南大西洋)、侏罗纪(墨西哥湾)、二叠纪-三叠纪(欧洲)、泥盆纪(加拿大)、寒武纪/前寒武纪(冈瓦纳)盐沼沉积时期进行的。” <br />
[[Earthrise taken from Apollo 8 on December 24, 1968]]<br />
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[1968年12月24日阿波罗8号拍摄的地出]<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = <br />
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地球是一个完整的整体,一个有生命的存在,这个观念有着悠久的传统。神话中的盖亚是拟人化地球的原始希腊女神,是希腊版本的“自然母亲”(来自 Ge = 地球,和 Aia = <br />
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===Regulation of oxygen in the atmosphere大气层的氧气调节===<br />
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PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a suggestion from the novelist William Golding, who was living in the same village as Lovelock at the time (Bowerchalke, Wiltshire, UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of living organisms, climate, and Earth's crust. His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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派祖母,或地球母亲。詹姆斯·洛夫洛克根据小说家威廉·戈尔丁的建议给他的假设起了这个名字,他当时和洛夫洛克住在同一个村子里(英国威尔特郡鲍尔查尔克)。戈尔丁的建议是以Gea为基础的,Gea是希腊女神名字的另一种拼写,在地质学、地球物理和地球化学中,Gea是前缀。后来,博物学家和探险家亚历山大·冯·洪堡认识到生物、气候和地壳的共同进化。他的远见卓识的声明在西方没有被广泛接受,几十年后,盖亚假说刚提出时同样受到了科学界的抵制。<br />
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[[File:Vostok 420ky 4curves insolation.jpg|thumb|280px|Levels of gases in the atmosphere in 420,000 years of ice core data from [[Vostok Station|Vostok, Antarctica research station]]. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
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{{See also|Geological history of oxygen}}<br />
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Also in the turn to the 20th century Aldo Leopold, pioneer in the development of modern environmental ethics and in the movement for wilderness conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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同样在20世纪之交,现代环境伦理学发展的先驱、荒野保护运动的先驱奥尔多 · 利奥波德在他的生物中心或整体的土地伦理学中提出了一个有生命的地球。<br />
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The Gaia hypothesis states that the Earth's [[Atmospheric chemistry#Atmospheric composition|atmospheric composition]] is kept at a dynamically steady state by the presence of life.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 163. {{ISBN|978-0-465-01549-8}}</ref> The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than [[noble gas]]es present in the atmosphere are either made by organisms or processed by them.<br />
盖亚假说指出,地球的大气成分由于生命的存在而保持在动态稳定的状态。大气中除惰性气体以外的所有大气气体都是由生物体制造或加工而成。<br />
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The stability of the atmosphere in Earth is not a consequence of [[chemical equilibrium]]. [[Oxygen]] is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the [[Great Oxygenation Event]].<ref name=Anabar2007>{{Cite journal| last4 = Arnold| last6 = Creaser| last3 = Lyons| first1 = A. | first2 = Y.| last9 = Scott| last2 = Duan | first3 = T. | first4 = G.| last8 = Gordon | first5 = B. | first10 = J. | first6 = R.| last10 = Garvin | first7 = A.| last11 = Buick | first8 = G. | first11 = R. | first9 = C.| title = A whiff of oxygen before the great oxidation event?| journal = Science| volume = 317| issue = 5846| year = 2007| last7 = Kaufman| pages = 1903–1906| last5 = Kendall| pmid = 17901330| last1 = Anbar | doi = 10.1126/science.1140325|bibcode = 2007Sci...317.1903A }}</ref> Since the start of the [[Cambrian]] period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume.<br />
地球大气的稳定性不是化学平衡造成的。氧气是一种活性化合物,最终会与地球大气层和地壳上的气体和矿物质结合。在大氧化事件开始前的5000万年,氧气才在大气中少量存在。自寒武纪开始以来,大气氧浓度值一直在大气体积的15%到35%之间波动。甲烷的痕迹(每年产生10万吨)是不存在的,因为甲烷在氧气环境中是可燃的。<br />
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Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut William Anders in 1968 during the Apollo 8 mission became, through the Overview Effect an early symbol for the global ecology movement.<br />
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盖亚假说和环境运动的另一个影响来自于苏联和美利坚合众国之间太空竞赛。在20世纪60年代,第一批进入太空的人类可以看到地球作为一个整体的样子。1968年,宇航员威廉 · 安德斯在阿波罗8号任务期间拍摄的地出照片,通过总体效应成为全球生态运动的早期象征。<br />
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| pmid = 10500106<br />
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| date=Sep 1999 | last1 = Berner | first1 = R. A.<br />
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| title = Atmospheric oxygen over Phanerozoic time<br />
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[[James Lovelock, 2005]]<br />
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[ James Lovelock,2005]<br />
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| volume = 96<br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the Jet Propulsion Laboratory in California on methods of detecting life on Mars. The first paper to mention it was Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life, co-authored with C.E. Giffin. A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the Pic du Midi observatory, planets like Mars or Venus had atmospheres in chemical equilibrium. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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65年9月,洛夫洛克在加利福尼亚喷气推进实验室研究探测火星生命的方法时,开始定义由生物群落控制的自我调节地球的概念。第一篇提到它的论文是行星大气:与C.E.Giffin合著的与生命存在有关的成分和其他变化。一个主要的概念是,通过大气的化学成分可以在行星尺度上探测到生命。根据picdumidi天文台收集的数据,像火星或金星这样的行星,其大气层处于化学平衡状态。这种与地球大气的差异被认为是这些行星上没有生命的证据。 <br />
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| issue = 20<br />
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| pages = 10955–10957<br />
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Lovelock formulated the Gaia Hypothesis in journal articles in 1972 and 1974, and a popular book length version of the hypothesis, published in 1979 as The Quest for Gaia, began to attract scientific and critical attention.<br />
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洛夫洛克在1972年和1974年的期刊文章中提出了盖亚假说,并在1979年出版了一本畅销书,名为《寻找盖亚》 ,开始引起科学界和批判界的关注。<br />
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| issn = 0027-8424<br />
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| journal = Proceedings of the National Academy of Sciences of the United States of America<br />
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Lovelock called it first the Earth feedback hypothesis, and it was a way to explain the fact that combinations of chemicals including oxygen and methane persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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洛夫洛克首先将其称为地球反馈假说,解释氧气和甲烷等化学物质在地球大气中如何保持稳定浓度。洛夫洛克认为,在其他行星的大气层中探测这种组合,是一种相对便宜可靠的探测生命的方法。<br />
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| doi = 10.1073/pnas.96.20.10955<br />
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[[Lynn Margulis]]<br />
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[琳 · 玛格丽丝]<br />
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|bibcode = 1999PNAS...9610955B }}</ref> Traces of [[Atmospheric methane|methane]] (at an amount of 100,000 tonnes produced per year)<ref name="Cicerone1988">{{cite journal |last1=Cicerone |first1=R.J. |last2=Oremland |first2=R.S. |date=1988 |title=Biogeochemical aspects of atmospheric methane |journal=Global Biogeochemical Cycles |volume=2 |issue=4 |pages=299–327 |url=//webfiles.uci.edu/setrumbo/public/Methane_papers/Cicerone_Global%20Biogeochem%20Cy_1988.pdf |doi=10.1029/GB002i004p00299 |bibcode=1988GBioC...2..299C}}</ref> should not exist, as methane is combustible in an oxygen atmosphere.<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<br />
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后来出现了其他关系,例如海洋生物产生的硫和碘的数量与陆地生物所需的数量大致相同,这些都支持了这一假说。<br />
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Dry air in the [[atmosphere of Earth]] contains roughly (by volume) 78.09% [[nitrogen]], 20.95% oxygen, 0.93% [[argon]], 0.039% [[Carbon dioxide in the Earth's atmosphere|carbon dioxide]], and small amounts of other gases including [[methane]]. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. {{citation needed|date=June 2012}}<br />
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[[地球大气]]中的干空气大约(按体积)包含78.09%[[氮]],20.95%的氧,0.93%[[氩]],0.039%[地球大气中的二氧化碳|二氧化碳]],以及少量其他气体,包括[[甲烷]]。洛夫洛克最初推测,氧气浓度超过25%会增加森林火灾和火灾的发生率。最近在石炭纪和白垩纪煤系中火成木炭的研究(这两个地质时期O<sub>2</sub>浓度超过25%)支持了Lovelock的观点 <br />
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In 1971 microbiologist Dr. Lynn Margulis joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet. The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of eukaryotic organelles and her contributions to the endosymbiotic theory, nowadays accepted. Margulis dedicated the last of eight chapters in her book, The Symbiotic Planet, to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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1971年,微生物学家 Lynn Margulis 博士加入了 Lovelock 的行列,努力将最初的假设充实为科学证明的概念。Margulis 贡献了她关于微生物如何影响大气层和地球表面不同层次的知识。这位美国生物学家也唤受到科学界的批评,因为她倡导真核细胞器起源的理论,以及她对美国共生发源学会的贡献——现在被接受了。玛格丽丝在她的书《共生星球》中将最后八章用于描述盖亚。然而,她反对对盖亚的广泛拟人化,并强调盖亚“不是一个有机体” ,而是“有机体之间相互作用的一个新兴属性”。她将盖亚定义为“组成地球表面一个巨大生态系统的一系列相互作用的生态系统”。句号”。这本书最令人难忘的“口号”实际上是由马古利斯的一个学生打趣说的: “从太空看,盖亚只是共生而已。”。<br />
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===Processing of CO<sub>2</sub>二氧化碳处理===<br />
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{{See also|Carbon cycle}}<br />
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James Lovelock called his first proposal the Gaia hypothesis but has also used the term Gaia theory. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments and provided a number of useful predictions. In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating. The principal sponsor was the National Audubon Society. Speakers included James Lovelock, George Wald, Mary Catherine Bateson, Lewis Thomas, John Todd, Donald Michael, Christopher Bird, Thomas Berry, David Abram, Michael Cohen, and William Fields. Some 500 people attended.<br />
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詹姆斯 · 洛夫洛克称他的第一个提议为盖亚假说,但也使用了盖亚理论这个术语。洛夫洛克说,最初的提法是基于观察,但仍然缺乏科学的解释。盖亚假说从那以后得到了一些科学实验的支持,并提供了一些有用的预测。事实上,更广泛的研究证明了最初的假设是错误的,在这个意义上,不是生命本身,而是整个地球系统在调节。主要赞助者是奥杜邦学会。讲者包括 James Lovelock、 George Wald、 Mary Catherine Bateson、 Lewis Thomas、 John Todd、 Donald Michael、 Christopher Bird、 Thomas Berry、 David Abram、 Michael Cohen 和 William Fields。大约有500人参加。<br />
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Gaia scientists see the participation of living organisms in the [[carbon cycle]] as one of the complex processes that maintain conditions suitable for life. The only significant natural source of [[Carbon dioxide in Earth's atmosphere|atmospheric carbon dioxide]] ([[Carbon dioxide|CO<sub>2</sub>]]) is [[volcanic activity]], while the only significant removal is through the precipitation of [[carbonate rocks]].<ref name="Karhu1996">{{cite journal | author = Karhu, J.A. | author2 = Holland, H.D. | date = 1 October 1996 | title = Carbon isotopes and the rise of atmospheric oxygen | journal = [[Geology (journal)|Geology]] | volume = 24 | issue = 10 | pages = 867–870 | doi = 10.1130/0091-7613(1996)024<0867:CIATRO>2.3.CO;2|bibcode = 1996Geo....24..867K | ref = harv}}</ref> Carbon precipitation, solution and [[Carbon fixation|fixation]] are influenced by the [[bacteria]] and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
盖亚的科学家认为,生物参与[[碳循环]是维持适宜生命条件的复杂过程之一。[[地球大气中的二氧化碳|大气二氧化碳]]([[二氧化碳| CO2]])最重要的自然来源是[[火山活动]],而最重要的去除过程是[[碳酸盐岩]]的沉淀,溶液和[[固碳|固碳]]受土壤中的[[细菌]]和植物根系的影响,它们改善了气体循环,珊瑚礁中碳酸钙以固体形式沉积在海底。碳酸钙被生物用来制造含碳结构和贝壳。一旦死亡,这些生物的壳就会落到海底,在那里它们会产生白垩和石灰岩的沉积物。 <br />
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One of these organisms is ''[[Emiliania huxleyi]]'', an abundant [[coccolithophore]] [[algae]] which also has a role in the formation of [[cloud]]s.<ref name="Harding2006">{{cite book |author=Harding, Stephan |title=Animate Earth |publisher=Chelsea Green Publishing |date=2006 |pages=65 |isbn=978-1-933392-29-5 }}</ref> CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants.{{citation needed|date=July 2015}} Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean [[algal bloom]]s are also increasing.<ref>{{Cite web | date = 12 September 2007 | title = Interagency Report Says Harmful Algal Blooms Increasing | url = http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | url-status = dead | archiveurl = https://web.archive.org/web/20080209234239/http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | archivedate = 9 February 2008 }}</ref><br />
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In 1988, climatologist Stephen Schneider organised a conference of the American Geophysical Union. The first Chapman Conference on Gaia,<br />
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在1988年,气候学家史蒂芬·史奈德组织了一次美国美国地球物理联盟协会的会议。关于盖亚假说的第一次查普曼会议,<br />
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[[Lichen]] and other organisms accelerate the [[weathering]] of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the Daisyworld Model (and its modifications, above) as evidence against most of these criticisms.<br />
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然而,洛夫洛克和其他支持盖亚理论的科学家确实试图反驳这样一种说法,即这种假设不科学,因为不可能通过控制实验来检验它。例如,针对盖亚假说是目的论的指责,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修正,上文)反驳这些批评。<br />
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==History历史==<br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of teleologism ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,这一版本中盖亚并不是有意地在她的环境中维持生命赖以生存的复杂平衡。看起来,盖亚假说“故意”行为的说法只是他那本广受欢迎的书中的一个比喻性陈述,并不是字面意义上的理解。这种对盖亚假说的新陈述更能为科学界所接受。在这次会议之后,大多数关于目的论的指责都停止了。<br />
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===Precedents先例===<br />
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[[File:NASA-Apollo8-Dec24-Earthrise.jpg|thumb|''[[Earthrise]]'' taken from [[Apollo 8]] on December 24, 1968]]<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000, the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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到2000年6月23日在西班牙巴伦西亚举行关于盖亚假说的第二次查普曼会议时,情况发生了重大变化。与其讨论盖亚假说的目的论观点,或盖亚假说的“类型” ,不如将重点放在具体的机制上,通过这些机制,短期内基本稳态在重要的进化长期结构变化的框架内得以维持。<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The [[Gaia (mythology)|mythical Gaia]] was the primal Greek goddess personifying the [[Earth]], the Greek version of "[[Mother Nature]]" (from Ge = Earth, and Aia = <br />
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[[PIE]] grandmother), or the [[Earth Mother]]. James Lovelock gave this name to his hypothesis after a suggestion from the novelist [[William Golding]], who was living in the same village as Lovelock at the time ([[Bowerchalke]], [[Wiltshire]], UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry.<ref name=vanish09 /> Golding later made reference to Gaia in his [[Nobel prize]] acceptance speech.<br />
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The major questions were:<br />
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主要的问题是:<br />
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In the eighteenth century, as [[geology]] consolidated as a modern science, [[James Hutton]] maintained that geological and biological processes are interlinked.<ref name=CapraWeb>{{cite book |author=Capra, Fritjof |title=The web of life: a new scientific understanding of living systems |publisher=Anchor Books |location=Garden City, N.Y |date=1996 |page=[https://archive.org/details/weboflifenewscie00capr/page/23 23] |isbn=978-0-385-47675-1 |url=https://archive.org/details/weboflifenewscie00capr/page/23 }}</ref> Later, the [[naturalist]] and explorer [[Alexander von Humboldt]] recognized the coevolution of living organisms, climate, and Earth's crust.<ref name=CapraWeb /> In the twentieth century, [[Vladimir Vernadsky]] formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian [[geochemist]] and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological processes. During the 1920s he published works arguing that living organisms could reshape the planet as surely as any physical force. Vernadsky was a pioneer of the scientific bases for the environmental sciences.<ref>S.R. Weart, 2003, ''The Discovery of Global Warming'', Cambridge, Harvard Press</ref> His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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"How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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“被称为盖亚的全球生物地球化学/气候系统是如何及时发生变化的?它的历史是什么?盖亚假说能够在一个时间尺度上保持系统的稳定性,但是在更长的时间尺度上仍然经历矢量变化吗?如何利用地质记录来检验这些问题? ”<br />
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"What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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“盖亚假说的结构是什么?这些反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由在任何特定时间进行的学科研究务实地决定的,还是有一些部分应该被认为是最真实的,以了解盖亚假说随着时间的推移包含进化中的生物体?盖亚系统这些不同部分之间的反馈是什么? 对盖亚假说作为全球生态系统的结构和生命的生产力来说,物质的近乎封闭意味着什么? ”<br />
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Also in the turn to the 20th century [[Aldo Leopold]], pioneer in the development of modern [[environmental ethics]] and in the movement for [[wilderness]] conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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"How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
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“盖亚假说过程和现象的模型如何与现实相关,它们如何帮助解决和理解盖亚?雏菊世界的成果如何转移到现实世界?什么是“雏菊”的主要候选人?我们发现雏菊与否对盖亚理论重要吗?我们应该怎样寻找雏菊,我们应该加紧寻找吗?如何利用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制? ”<br />
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{{quotation|It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated functions, but possibly also that process of consumption as replacement which in biology we call metabolism, or growth. In such case we would have all the visible attributes of a living thing, which we do not realize to be such because it is too big, and its life processes too slow.| Stephan Harding | ''Animate Earth''.<ref>Harding, Stephan. ''Animate Earth Science, Intuition and Gaia''. Chelsea Green Publishing, 2006, p. 44. {{ISBN|1-933392-29-0}}</ref>}}<br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise entropy production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
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1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是一种向远离平衡的稳态演化的结果,这种平衡状态使熵产生最大化,克莱顿(2004)同意这样的说法:“自稳态行为可以从与行星反照率相关的MEP状态中产生”;“……一个如盖亚假说所述,处于MEP状态的生物地球很可能导致地球系统在长时间尺度上的近稳态行为。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。<br />
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Another influence for the Gaia hypothesis and the [[environmental movement]] in general came as a side effect of the [[Space Race]] between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph ''[[Earthrise]]'' taken by astronaut [[William Anders]] in 1968 during the [[Apollo 8]] mission became, through the [[Overview Effect]] an early symbol for the global ecology movement.<ref>[http://digitaljournalist.org/issue0309/lm11.html 100 Photographs that Changed the World by Life - The Digital Journalist]</ref><br />
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盖亚假说和[[环境运动]]的另一个总体影响来自苏联和美利坚合众国之间[[太空竞赛]]的副作用。在20世纪60年代,第一批进入太空的人类可以看到地球的整体面貌。1968年宇航员[[William Anders]]在[[Apollo 8]]任务期间拍摄的照片“[[地球升起]”,通过[[概述效果]]成为全球生态运动的早期标志<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<br />
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第四次关于盖亚假说的国际会议,由北弗吉尼亚地区公园管理局和其他机构主办,于2006年10月在弗吉尼亚州乔治梅森大学的阿灵顿校区举行。<br />
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===Formulation of the hypothesis假说形成===<br />
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[[File:James Lovelock in 2005.jpg|thumb|[[James Lovelock]], 2005]]<br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
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马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。Lynn Margulis是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the [[Jet Propulsion Laboratory]] in California on methods of detecting [[life on Mars (planet)|life on Mars]].<ref name="Lovelock1965">{{cite journal | author = Lovelock, J.E. | date = 1965 | title = A physical basis for life detection experiments | journal = [[Nature (journal)|Nature]] | volume = 207 | issue = 7 | pages = 568–570 | doi = 10.1038/207568a0 | pmid=5883628|bibcode = 1965Natur.207..568L | ref = harv}}</ref><ref>{{Cite web |url=http://www.jameslovelock.org/page4.html |title=Geophysiology |access-date=2007-05-05 |archive-url=https://web.archive.org/web/20070506073502/http://www.jameslovelock.org/page4.html |archive-date=2007-05-06 |url-status=dead }}</ref> The first paper to mention it was ''Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life'', co-authored with C.E. Giffin.<ref>{{cite journal | author1 = Lovelock, J.E. | author2 = Giffin, C.E. | date = 1969 | title = Planetary Atmospheres: Compositional and other changes associated with the presence of Life | journal = Advances in the Astronautical Sciences | volume = 25 | pages = 179–193 | isbn = 978-0-87703-028-7 | ref = harv}}</ref> A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the [[Pic du Midi de Bigorre|Pic du Midi observatory]], planets like Mars or Venus had atmospheres in [[chemical equilibrium]]. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
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这次会议将盖亚假说作为一种科学和隐喻的手段,来理解我们如何开始解决21世纪的问题,如气候变化和持续的环境破坏。<br />
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Lovelock formulated the ''Gaia Hypothesis'' in journal articles in 1972<ref name="J1972">{{cite journal | author = J. E. Lovelock | title = Gaia as seen through the atmosphere | date = 1972 | journal = [[Atmospheric Environment]] | volume = 6 | issue = 8 | pages = 579–580 | doi = 10.1016/0004-6981(72)90076-5 | ref = harv|bibcode = 1972AtmEn...6..579L }}</ref> and 1974,<ref name="lovelock1974" /> followed by a popularizing 1979 book ''Gaia: A new look at life on Earth''. An article in the ''[[New Scientist]]'' of February 6, 1975,<ref>Lovelock, John and Sidney Epton, (February 8, 1975). "The quest for Gaia". [https://books.google.com/books?id=pnV6UYEkU4YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false New Scientist], p. 304.</ref> and a popular book length version of the hypothesis, published in 1979 as ''The Quest for Gaia'', began to attract scientific and critical attention.<br />
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Lovelock called it first the Earth feedback hypothesis,<ref name="Lovelock01">{{harvnb|Lovelock, James|2001}}</ref> and it was a way to explain the fact that combinations of chemicals including [[oxygen]] and [[methane]] persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as Ford Doolittle, Richard Dawkins and Stephen Jay Gould. Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists, He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoietic or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole. With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<br />
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在最初几乎没有引起科学家的注意之后(从1969年到1977年) ,有一段时间,最初的盖亚假说受到了一些科学家的批评,如福特杜利特,理查德道金斯和史蒂芬·古尔德。洛夫洛克说,因为他的假说是以一位希腊女神的名字命名的,并得到许多非科学家的拥护,他想知道实现自我调节体内平衡的实际机制。在为盖亚辩护时,戴维•阿布拉姆认为,古尔德忽视了一个事实,即“机制”本身就是一个隐喻——尽管这个隐喻极其常见,而且往往不为人所知——这个隐喻让我们把自然和生命系统看作是由外部组织和建造的机器(而不是自动生成或自组织现象)。根据阿布拉姆的说法,机械隐喻使我们忽略了生命实体的活跃性或代表性,而盖亚假说的有机隐喻强调了生物群和整个生物圈的活跃性。关于盖亚的因果关系,洛夫洛克认为没有单一的机制是负责任的,各种已知机制之间的联系可能永远不会被人知道,这在生物学和生态学的其他领域是理所当然地被接受的,并且由于其他原因,特定的敌意是保留给他自己的假设的。<br />
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[[File:Lynn Margulis.jpg|thumb|left|[[Lynn Margulis]]]]<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of greedy reductionism in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<br />
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除了澄清他的语言和理解什么是生命形式,洛夫洛克自己把大部分的批评归因于他的批评者缺乏对非线性数学的理解,以及贪婪还原主义的线性化形式,在这种形式中,所有事件都必须立即归因于事件发生之前的特定原因。他还表示,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,以及一些自我调节现象可能无法在数学上解释。<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<ref>{{cite journal | first1=W.D. | last1=Hamilton | first2=T.M. | last2=Lenton | title=Spora and Gaia: how microbes fly with their clouds | journal=Ethology Ecology & Evolution | volume=10 | pages=1–16 | date=1998 | issue=1 | url=http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | format=PDF | doi=10.1080/08927014.1998.9522867 | ref=harv | url-status=dead | archiveurl=https://web.archive.org/web/20110723055017/http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | archivedate=2011-07-23 }}</ref><br />
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Evolutionary biologist W. D. Hamilton called the concept of Gaia Copernican, adding that it would take another Newton to explain how Gaian self-regulation takes place through Darwinian natural selection. More recently Ford Doolittle building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis. <br />
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进化生物学家W.D.Hamilton称盖亚假说为哥白尼式的概念,并补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。最近,Ford Doolittle在他和Inkpen的ITSNTS(这是歌手而不是歌曲)的建议中提出,差异持续性可以在自然选择进化中起到与差异生殖相似的作用,从而为自然选择理论和盖亚假说之间提供了一种可能的调和。 <br />
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In 1971 [[microbiologist]] Dr. [[Lynn Margulis]] joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet.<ref name="Turney, Jon 2003">{{cite book |author=Turney, Jon |title=Lovelock and Gaia: Signs of Life |publisher=Icon Books |location=UK |date=2003 |isbn=978-1-84046-458-0 |url-access=registration |url=https://archive.org/details/lovelockgaiasign0000turn }}</ref> The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of [[eukaryote|eukaryotic]] [[organelle]]s and her contributions to the [[endosymbiotic theory]], nowadays accepted. Margulis dedicated the last of eight chapters in her book, ''The Symbiotic Planet'', to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal Climatic Change in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it. to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background" The CLAW hypothesis, In 2009 the Medea hypothesis was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<br />
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盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论据是,生命对环境产生了有害或不稳定的影响,而不是采取行动加以调节。为了“令人不安地徘徊在污点隐喻、事实和虚假科学之间,我宁愿把盖亚假说牢牢地放在背景下。”爪假说,2009年提出的美狄亚假说:生命对行星条件有高度有害的(生物杀灭)影响,与盖亚假说直接相反。 <br />
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James Lovelock called his first proposal the ''Gaia hypothesis'' but has also used the term ''Gaia theory''. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments<ref name="J1990">{{cite journal | author = J. E. Lovelock | title = Hands up for the Gaia hypothesis | date = 1990 | journal = [[Nature (journal)|Nature]] | volume = 344 | issue = 6262 | pages = 100–2 | doi = 10.1038/344100a0|bibcode = 1990Natur.344..100L | ref = harv}}</ref> and provided a number of useful predictions.<ref name="Volk2003">{{cite book |author=Volk, Tyler |title=Gaia's Body: Toward a Physiology of Earth |publisher=[[MIT Press]] |location=Cambridge, Massachusetts |date=2003 |isbn=978-0-262-72042-7 }}</ref> In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating.<ref name="vanishing255"/><br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it". Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works". This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<br />
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2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新想法,并倡导一种整体的方法来研究地球”。在其他地方,他提出了自己的结论:“盖亚假说并不是我们这个世界如何运转的精确图像”。这种说法需要被理解为是指盖亚假说的“强”和“中”形式,生物群遵循的原则是使地球成为最佳(强度5)或有利于生命(强度4),或是作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化的盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释。<br />
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===First Gaia conference第一次盖亚会议===<br />
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In 1985, the first public symposium on the Gaia hypothesis, ''Is The Earth A Living Organism?'' was held at [[University of Massachusetts Amherst]], August 1–6.<ref>{{cite news |last=Joseph |first=Lawrence E. |title=Britain's Whole Earth Guru |work=The New York Times Magazine |date=November 23, 1986 |url=https://www.nytimes.com/1986/11/23/magazine/britain-s-whole-earth-guru.html |accessdate=1 December 2013}}</ref> The principal sponsor was the [[National Audubon Society]]. Speakers included James Lovelock, [[George Wald]], [[Mary Catherine Bateson]], [[Lewis Thomas]], [[John Todd (Canadian biologist)|John Todd]], Donald Michael, [[Christopher Bird]], [[Thomas Berry]], [[David Abram]], [[Michael A. Cohen|Michael Cohen]], and William Fields. Some 500 people attended.<ref>Bunyard, Peter (1996), "Gaia in Action: Science of the Living Earth" (Floris Books)</ref><br />
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1985年,关于盖亚假说的第一次公开研讨会,“地球是一个活的有机体吗?”在马萨诸塞大学阿默斯特举行 <br />
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===Second Gaia conference第二次盖亚会议===<br />
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In 1988, [[climatology|climatologist]] [[Stephen Schneider]] organised a conference of the [[American Geophysical Union]]. The first Chapman Conference on Gaia,<ref name="ReferenceB"/> was held in San Diego, California on March 7, 1988.<br />
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1988年,climatology和Stephen Schneider组织了一次美国地球物理联合会会议。关于盖亚假说的第一次查普曼会议 <br />
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During the "philosophical foundations" session of the conference, [[David Abram]] spoke on the influence of metaphor in science, and of the Gaia hypothesis as offering a new and potentially game-changing metaphorics, while [[James Kirchner]] criticised the Gaia hypothesis for its imprecision. Kirchner claimed that Lovelock and Margulis had not presented one Gaia hypothesis, but four -<br />
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在会议的“哲学基础”会议上,David Abram谈到了隐喻在科学中的影响,盖亚假说提供了一种新的、可能改变游戏规则的隐喻,而James Kirchner则批评盖亚假说的不精确性。基什纳声称,洛夫洛克和马古利斯提出的盖亚假说不是一个,而是四个- <br />
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* [[Coevolution|CoEvolutionary]] Gaia: that life and the environment had evolved in a coupled way. Kirchner claimed that this was already accepted scientifically and was not new.<br />
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* [[Homeostatic]] Gaia: that life maintained the stability of the natural environment, and that this stability enabled life to continue to exist.<br />
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* [[Geophysics|Geophysical]] Gaia: that the Gaia hypothesis generated interest in geophysical cycles and therefore led to interesting new research in terrestrial geophysical dynamics.<br />
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* Optimising Gaia: that Gaia shaped the planet in a way that made it an optimal environment for life as a whole. Kirchner claimed that this was not testable and therefore was not scientific.<br />
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盖亚:生命和环境是以耦合的方式进化的。基什内尔声称,这已经被科学界接受,并不是什么新鲜事。 <br />
盖亚:生命维持着自然环境的稳定,这种稳定性使生命得以继续存在。 <br />
盖亚:盖亚假说引起了人们对地球物理周期的兴趣,因此导致了地球物理动力学中有趣的新研究。 <br />
优化盖亚:盖亚塑造了地球,使之成为整个生命的最佳环境。基什内尔声称,这是不可测试的,因此是不科学的。 <br />
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Of Homeostatic Gaia, Kirchner recognised two alternatives. "Weak Gaia" asserted that life tends to make the environment stable for the flourishing of all life. "Strong Gaia" according to Kirchner, asserted that life tends to make the environment stable, ''to enable'' the flourishing of all life. Strong Gaia, Kirchner claimed, was untestable and therefore not scientific.<ref>{{cite journal | bibcode=1989RvGeo..27..223K | doi = 10.1029/RG027i002p00223 | title=The Gaia hypothesis: Can it be tested? | date=1989 | last1=Kirchner | first1=James W. | journal=Reviews of Geophysics | volume=27 | issue=2 | pages=223 | ref=harv}}</ref><br />
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基什内尔发现了两种选择“软弱的盖亚”断言,为了所有生命的繁衍,生命往往会使环境变得稳定根据基什内尔的说法,“强大的盖亚”断言,生命趋向于使环境稳定,“使”所有生命繁荣昌盛。基什内尔声称,强大的盖亚是不稳定的,因此不科学。 <br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the [[Daisyworld]] Model (and its modifications, above) as evidence against most of these criticisms.<ref name="daisyworld"/> Lovelock said that the Daisyworld model "demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways".<ref>{{cite journal | pmid=10968941 | date=2000 | last1=Lenton | first1=TM | last2=Lovelock | first2=JE | s2cid=5486128 | title=Daisyworld is Darwinian: Constraints on adaptation are important for planetary self-regulation | volume=206 | issue=1 | pages=109–14 | doi=10.1006/jtbi.2000.2105 | journal=Journal of Theoretical Biology | ref=harv}}</ref><br />
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然而,洛夫洛克和其他支持盖亚假说的科学家,确实试图反驳这种说法,即这个假设是不科学的,因为不可能通过受控实验来检验它。例如,针对盖亚假说是目的论的指控,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修改,洛夫洛克说,雏菊世界模型“证明了全球环境的自我调节可以通过不同方式改变当地环境的生活类型之间的竞争产生”。 <br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of [[teleology|teleologism]] ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,没有声称盖亚有意或有意识地维持着生命生存所需的复杂平衡。看来盖亚假说“故意”的行为是他最受欢迎的第一本书中的隐喻性陈述,并不是字面意思。盖亚假说的这一新说法更为科学界所接受。在这次会议之后,[[目的论|目的论]]的大多数指控都停止了。<br />
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===Third Gaia conference第三次盖亚会议===<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000,<ref>{{cite news|last=Simón|first=Federico|title=GEOLOGÍA Enfoque multidisciplinar La hipótesis Gaia madura en Valencia con los últimos avances científicos|journal=El País|date=21 June 2000|url=http://elpais.com/diario/2000/06/21/futuro/961538404_850215.html|accessdate=1 December 2013|language=spanish}}</ref> the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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The major questions were:<ref>{{cite web|title=General Information Chapman Conference on the Gaia Hypothesis University of Valencia Valencia, Spain June 19-23, 2000 (Monday through Friday) |url=http://www.agu.org/meetings/chapman/chapman_archive/cc00bcall.html |work=AGU Meetings |accessdate=7 January 2017 |author=American Geophysical Union }}</ref><br />
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# "How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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# "What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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# "How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
“被称为盖亚的全球生物地球化学/气候系统是如何随时间变化的?它的历史是什么?盖亚能在一个时间尺度上保持系统的稳定性,但在较长的时间尺度上仍能经历向量变化吗?如何利用地质记录来检验这些问题?” <br />
“盖亚假说的结构是什么?反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由任何给定时间正在进行的任何学科研究实际确定的,还是有一组应该被视为最真实的部分来理解盖亚假说,即随着时间的推移包含进化中的有机体?盖亚系统的这些不同部分之间的反馈是什么?物质的接近封闭对盖亚作为全球生态系统的结构和生命的生产力意味着什么?” <br />
“盖亚假说过程和现象的模型如何与现实联系起来,它们如何帮助解决和理解盖亚假说?雏菊世界的结果如何传递到真实世界?“雏菊”的主要候选对象是什么?我们是否找到雏菊对盖亚理论有意义吗?我们应该如何寻找雏菊,我们应该加强搜索?如何使用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制?” <br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise [[entropy]] production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是朝着使熵产量最大化的远非平衡的状态演化的结果,克莱顿(2004)同意这样的说法:“自稳行为可以从与行星反照率相关的MEP状态中产生”;“……生物地球在MEP状态下的行为很可能导致地球系统在长时间尺度上的近稳态行为,正如盖亚假说所述”。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。 <br />
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===Fourth Gaia conference第四次盖亚会议===<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<ref>{{cite web|title=Gaia Theory Conference at George Mason University Law School|url=http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|accessdate=1 December 2013|author=Official Site of Arlington County Virginia|archive-url=https://web.archive.org/web/20131203043657/http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|archive-date=2013-12-03|url-status=dead}}</ref><br />
第四届盖亚假说国际会议于2006年10月在乔治梅森大学阿灵顿分校举行,会议由北弗吉尼亚州公园管理局和其他机构赞助。 <br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。林恩 马古拉斯是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
这次会议将盖亚假说作为一种科学和隐喻来探讨,以此来理解我们如何着手解决21世纪的问题,如气候变化和持续的环境破坏<br />
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==Criticism批评==<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as [[Ford Doolittle]],<ref name=":1">{{Cite journal|last=Doolittle|first=W. F.|year=1981|title=Is Nature Really Motherly|url=|journal=The Coevolution Quarterly|volume=Spring|pages=58–63|via=}}</ref> [[Richard Dawkins]]<ref name=":2">{{Cite book|title=The Extended Phenotype: the Long Reach of the Gene|last=Dawkins|first=Richard|publisher=Oxford University Press|year=1982|isbn=978-0-19-286088-0|location=|pages=}}</ref> and [[Stephen Jay Gould]].<ref name="ReferenceB">Turney, Jon. "Lovelock and Gaia: Signs of Life" (Revolutions in Science)</ref> Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists,<ref name="Lovelock01"/> the Gaia hypothesis was interpreted as a [[neo-Pagan]] [[religion]]. Many scientists in particular also criticised the approach taken in his popular book ''Gaia, a New Look at Life on Earth'' for being [[teleology|teleological]]—a belief that things are purposeful and aimed towards a goal. Responding to this critique in 1990, Lovelock stated, "Nowhere in our writings do we express the idea that planetary self-regulation is purposeful, or involves foresight or planning by the [[biota (ecology)|biota]]".<br />
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最初很少受到科学家的关注(从1969年到1977年),此后的一段时间里,最初的盖亚假说受到了许多科学家的批评,比如福特·杜利特,理查德·道金斯和斯蒂芬·杰伊·古尔德洛夫洛克曾说过,因为他的假设是以希腊女神的名字命名的,新盖亚假说被许多非教派的科学家解释为。特别是许多科学家还批评了他的畅销书《盖亚》中采用的方法,认为地球上的生命是目的论的,认为事物是有目的的,是有目的的。洛夫洛克在1990年回应这一批评时说:“在我们的著作中我们没有任何地方表达行星自我调节是有目的的,或涉及生物群的远见或计划。”<br />
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[[Stephen Jay Gould]] criticised Gaia as being "a metaphor, not a mechanism."<ref name="Gould 1997">{{cite journal |author=Gould S.J. |title=Kropotkin was no crackpot |journal=Natural History |volume=106 |pages=12–21 |date=June 1997 |url=http://libcom.org/library/kropotkin-was-no-crackpot |ref=harv}}</ref> He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as [[autopoiesis|autopoietic]] or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole.<ref>Abram, D. (1988) "The Mechanical and the Organic: On the Impact of Metaphor in Science" in Scientists on Gaia, edited by Stephen Schneider and Penelope Boston, Cambridge, Massachusetts: MIT Press, 1991</ref><ref>{{cite web|url=http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |title=The Mechanical and the Organic |accessdate=August 27, 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120223165936/http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |archivedate=February 23, 2012 }}</ref> With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<ref name="Lovelock, James 2001">Lovelock, James (2001), ''Homage to Gaia: The Life of an Independent Scientist'' (Oxford University Press)</ref><br />
史蒂芬·杰伊·古尔德批评盖亚假说是“一种隐喻,而不是一种机制。”他想知道实现自我调节内稳态的实际机制。在为盖亚假说辩护时,大卫·艾布拉姆认为古尔德忽略了一个事实,即“机制”本身就是一个隐喻——尽管这是一个非常常见且常常未被人认识的隐喻——它使我们把自然和生命系统看作是从外部组织和建造的机器(而不是自动或自组织的)现象)。艾布拉姆认为,机械隐喻使我们忽视了生命实体的活动性或能动性,而盖亚假说的有机体隐喻强调了生物群和生物圈作为一个整体的能动性。关于盖亚假说的因果关系,洛夫洛克认为没有单一的机制负责各种已知机制之间的联系可能永远不为人所知,这一点在其他生物学和生态学领域都是理所当然的,而具体的敌意是出于其他原因留给他自己的假设的<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of [[greedy reductionism]] in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<ref name="Lovelock, James 2001"/><br />
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除了澄清自己的语言和对生命形式的理解之外,洛夫洛克自己将大部分批评归咎于批评家对非线性数学缺乏理解,以及贪婪还原论的线性化形式,在这种形式中,所有事件都必须在事实发生之前立即归因于特定的原因。他还指出,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,有些自我调节的现象可能无法用数学解释 <br />
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===Natural selection and evolution自然选择和进化===<br />
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Lovelock has suggested that global biological feedback mechanisms could evolve by [[natural selection]], stating that organisms that improve their environment for their survival do better than those that damage their environment. However, in the early 1980s, [[Ford Doolittle|W. Ford Doolittle]] and [[Richard Dawkins]] separately argued against this aspect of Gaia. Doolittle argued that nothing in the [[genome]] of individual organisms could provide the feedback mechanisms proposed by Lovelock, and therefore the Gaia hypothesis proposed no plausible mechanism and was unscientific.<ref name=":1" /> Dawkins meanwhile stated that for organisms to act in concert would require foresight and planning, which is contrary to the current scientific understanding of evolution.<ref name=":2" /> Like Doolittle, he also rejected the possibility that feedback loops could stabilize the system.<br />
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洛夫洛克提出,全球生物反馈机制可以通过自然选择而进化,他指出,为生存而改善环境的生物比那些破坏环境的生物做得更好。然而,在20世纪80年代早期,W·福特·杜立德和理查德·道金斯分别反对盖亚假说的这一方面。杜立德认为,单个生物体的基因组中没有任何东西能够提供洛夫洛克提出的反馈机制,因此盖亚假说没有提出任何合理的机制,是不科学的。道金斯同时指出,要使有机体协同行动,就需要有远见和计划,这与当前科学界对进化论的理解相悖和杜立德一样,他也拒绝了反馈回路可以稳定系统的可能性。<br />
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[[Lynn Margulis]], a microbiologist who collaborated with Lovelock in supporting the Gaia hypothesis, argued in 1999, that "[[Charles Darwin|Darwin]]'s grand vision was not wrong, only incomplete. In accentuating the direct competition between individuals for resources as the primary selection mechanism, Darwin (and especially his followers) created the impression that the environment was simply a static arena". She wrote that the composition of the Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in [[homeostasis]], but those set points change with time.<ref name="ReferenceA">Margulis, Lynn. Symbiotic Planet: A New Look At Evolution. Houston: Basic Book 1999</ref><br />
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Lynn Margulis,一位与Lovelock合作支持盖亚假说的微生物学家,在1999年指出,“达尔文的宏伟愿景没有错,只是不完整。达尔文(特别是他的追随者)强调个人之间对资源的直接竞争是主要的选择机制,他给人的印象是环境只是一个静态的竞技场”。她写道,地球大气、水圈和岩石圈的组成都是围绕着“设定点”来调节的,就像在体内平衡中一样,但是这些设定点会随着时间的推移而变化 <br />
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Evolutionary biologist [[W. D. Hamilton]] called the concept of Gaia [[Nicolaus Copernicus|Copernican]], adding that it would take another [[Isaac Newton|Newton]] to explain how Gaian self-regulation takes place through Darwinian [[natural selection]].<ref name=vanish09>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, pp. 195-197. {{ISBN|978-0-465-01549-8}}</ref>{{better source|date=September 2012|reason=it should be possible to find the original place where Hamilton said this}} More recently [[Ford Doolittle]] building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal<ref name="ITSNTS">Doolittle WF, Inkpen SA. Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking. [https://www.pnas.org/content/115/16/4006 PNAS April 17, 2018 115 (16)] 4006-4014 </ref> proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis<ref name="Darwinizing Gaia">Doolittle WF. Darwinizing Gaia. [https://doi.org/10.1016/j.jtbi.2017.02.015 Journal of Theoretical BiologyVolume 434], 7 December 2017, Pages 11-19 </ref>. <br />
进化生物学家汉密尔顿称盖亚哥白尼为盖亚的概念,他补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。通过自然选择在进化过程中的繁殖,从而为自然选择理论和盖亚假说提供了可能的调和。 <br />
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===Criticism in the 21st century21世纪的批评===<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal ''Climatic Change'' in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it.<ref name="kirchner2002"/><ref name="volk2002"/> Several recent books have criticised the Gaia hypothesis, expressing views ranging from "... the Gaia hypothesis lacks unambiguous observational support and has significant theoretical difficulties"<ref>{{cite book |last=Waltham |first=David |authorlink=David Waltham |date=2014 |title=Lucky Planet: Why Earth is Exceptional – and What that Means for Life in the Universe |url=https://archive.org/details/luckyplanetwhyea0000walt |location= |publisher=Icon Books |page= |isbn=9781848316560 |accessdate= |url-access=registration }}</ref> to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background"<ref name="beerling2007"/> to "The Gaia hypothesis is supported neither by evolutionary theory nor by the empirical evidence of the geological record".<ref>{{cite book |last1=Cockell |first1=Charles |authorlink1=Charles Cockell |last2=Corfield |first2=Richard |last3=Dise |first3= Nancy |last4=Edwards |first4=Neil |last5=Harris |first5=Nigel |date=2008 |title= An Introduction to the Earth-Life System |url= http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/palaeontology-and-life-history/introduction-earth-life-system |location=Cambridge (UK) |publisher= Cambridge University Press |page= |isbn= 9780521729536 |accessdate= }}</ref> The [[CLAW hypothesis]],<ref name="CLAW87" /> initially suggested as a potential example of direct Gaian feedback, has subsequently been found to be less credible as understanding of [[cloud condensation nuclei]] has improved.<ref>{{Citation |last1= Quinn |first1=P.K. |last2= Bates |first2=T.S. |title =The case against climate regulation via oceanic phytoplankton sulphur emissions |journal =Nature |volume=480 |issue=7375 |pages =51–56 |date = 2011 |doi=10.1038/nature10580|bibcode = 2011Natur.480...51Q |pmid=22129724|url=https://zenodo.org/record/1233319 }}</ref> In 2009 the [[Medea hypothesis]] was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<ref>Peter Ward (2009), ''The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?'', {{ISBN|0-691-13075-2}}</ref><br />
盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论点是在许多例子中,生命对环境产生了有害或不稳定的影响,而不是采取行动来调节它。最近几本书批评了盖亚假说,譬如“盖亚假说缺乏明确的观察支持,并且有重大的理论困难”“(盖亚假说)令人不安地徘徊在污点、隐喻、事实和虚假科学之间,我宁愿把盖亚牢牢地放在原有的背景中”“盖亚假说既没有进化论的支持,也没有地质记录的经验证据的支持。爪假说最初被认为是盖亚直接反馈的一个潜在例子,后来被发现对云的理解不那么可信凝聚核已经得到了改善。2009年,美狄亚假说提出:生命对行星的状况非常有害,这与盖亚假说直接相反。 <br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it".<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=209 |isbn=9780691121581 |accessdate= }}</ref> Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works".<ref>{{Citation |last= Tyrrell |first = Toby |title =Gaia: the verdict is… |journal = New Scientist |volume = 220 |issue = 2940 |pages = 30–31 |date= 26 October 2013 |doi=10.1016/s0262-4079(13)62532-4}}</ref> This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=208 |isbn=9780691121581 |accessdate= }}</ref><br />
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2013年,托比·泰瑞尔在对盖亚假说的书评中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,认识到他大胆的概念有助于激发许多关于地球的新思想,并倡导一种研究地球的整体方法。”在其他地方,他提出了自己的结论:“盖亚假说并不是在精确地描述我们的世界在运转。”这种说法需要被理解为是指盖亚假说的“强大”和“温和”形式,生物群遵循的原则是使地球处于最佳状态(强度5)或有利于生命(强度4),或者它作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化德盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释 <br />
Category:Cybernetics<br />
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Category:Ecological theories<br />
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范畴: 生态学理论<br />
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==See also==<br />
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Category:Superorganisms<br />
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类别: 超级有机体<br />
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{{Portal|Environment|Earth sciences|Geography}}<br />
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Category:Climate change feedbacks<br />
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类别: 气候变化反馈<br />
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Category:1965 introductions<br />
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类别: 1965年引言<br />
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* {{annotated link|Biocoenosis}}<br />
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Category:Biogeochemistry<br />
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类别: 生物地球化学<br />
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* {{annotated link|Earth science}}<br />
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Category:Earth<br />
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类别: 地球<br />
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* {{annotated link|Environmentalism}}<br />
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Category:Biological hypotheses<br />
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类别: 生物学假说<br />
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* {{annotated link|Gaianism}}<br />
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Category:Astronomical hypotheses<br />
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* {{annotated link|Holism}}<br />
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Category:Meteorological hypotheses<br />
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类别: 气象假说<br />
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<small>This page was moved from [[wikipedia:en:Gaia hypothesis]]. Its edit history can be viewed at [[盖亚假说/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%96%E4%BA%9A%E5%81%87%E8%AF%B4&diff=21579盖亚假说2021-02-04T13:12:43Z<p>Vicky:/* Regulation of oxygen in the atmosphere大气层的氧气调节 */</p>
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<div>此词条由Henry第一次翻译。<br />
已由三奇同学完成校对。<br />
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{{short description|Hypothesis that living organisms interact with their surroundings in a self-regulating system}}<br />
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[[File:The Earth seen from Apollo 17.jpg|thumb|The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth]]'s conditions, as the Earth is the only planet currently known to harbour life (''[[The Blue Marble]]'', 1972 [[Apollo 17]] photograph)]]<br />
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The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth's conditions, as the Earth is the only planet currently known to harbour life (The Blue Marble, 1972 Apollo 17 photograph)]]<br />
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对行星可居住性的研究主要基于对[[地球条件]的了解进行推断,因为地球是目前已知的唯一一颗拥有生命的行星 <br />
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The '''Gaia hypothesis''' {{IPAc-en|ˈ|ɡ|aɪ|.|ə}}, also known as the '''Gaia theory''' or the '''Gaia principle''', proposes that living [[organism]]s interact with their [[Inorganic compound|inorganic]] surroundings on [[Earth]] to form a [[Synergy|synergistic]] and [[Homeostasis|self-regulating]], [[complex system]] that helps to maintain and perpetuate the conditions for [[life]] on the planet.<br />
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The Gaia hypothesis , also known as the Gaia theory or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.<br />
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盖亚假说(又称盖亚理论或盖亚原理)认为,生物体与地球上的无机环境相互作用,形成一个协同和自我调节的复杂系统,有助于维持和延续地球上的生命条件。<br />
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The hypothesis was formulated by the chemist [[James Lovelock]]<ref name="J1972" /> and co-developed by the microbiologist [[Lynn Margulis]] in the 1970s.<ref name="lovelock1974">{{cite journal|last1=Lovelock|first1=J.E.|last2=Margulis|first2=L.|title=Atmospheric homeostasis by and for the biosphere: the Gaia hypothesis|journal=Tellus|date=1974|volume=26|series=Series A|issue=1–2|pages=2–10|doi=10.1111/j.2153-3490.1974.tb01946.x|publisher=International Meteorological Institute|location=Stockholm|issn=1600-0870|ref=harv|bibcode=1974Tell...26....2L}}</ref> Lovelock named the idea after [[Gaia]], the primordial goddess who personified the Earth in [[Greek mythology]]. In 2006, the [[Geological Society of London]] awarded Lovelock the [[Wollaston Medal]] in part for his work on the Gaia hypothesis.<ref>{{cite web|title=Wollaston Award Lovelock|url=https://www.geolsoc.org.uk/About/History/Awards-Citations-Replies-2001-Onwards/2006-Awards-Citations-Replies|accessdate=19 October 2015}}</ref><br />
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The hypothesis was formulated by the chemist James Lovelock Lovelock named the idea after Gaia, the primordial goddess who personified the Earth in Greek mythology. In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.<br />
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这个假设是由化学家詹姆斯·洛夫洛克提出的,他以希腊神话中地球的化身盖亚的名字命名了这个想法。2006年,伦敦地质学会授予洛夫洛克沃拉斯顿勋章,以表彰他在<font color="#ff8000"> 盖亚假说Gaia hypothesis</font>方面的工作。 <br />
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Topics related to the hypothesis include how the [[biosphere]] and the [[evolution]] of organisms affect the stability of [[global temperature]], [[salinity]] of [[seawater]], [[atmospheric oxygen]] levels, the maintenance of a [[hydrosphere]] of liquid water and other environmental variables that affect the [[habitability of Earth]].<br />
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Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenance of a hydrosphere of liquid water and other environmental variables that affect the habitability of Earth.<br />
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与该假设有关的主题包括生物圈和生物体的进化如何影响全球温度的稳定性、海水的盐度、大气中的氧含量、液态水水圈的维持以及其他影响地球宜居性的环境变量。<br />
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The Gaia hypothesis was initially criticized for being [[teleological]] and against the principles of [[natural selection]], but later refinements aligned the Gaia hypothesis with ideas from fields such as [[Earth system science]], [[biogeochemistry]] and [[systems ecology]].<ref name="Turney, Jon 2003"/><ref name="Schwartzman2002">{{cite book |author=Schwartzman, David |title=Life, Temperature, and the Earth: The Self-Organizing Biosphere |publisher=Columbia University Press |date=2002 |isbn=978-0-231-10213-1 }}</ref><ref>Gribbin, John (1990), "Hothouse earth: The greenhouse effect and Gaia" (Weidenfeld & Nicolson)</ref> Lovelock also once described the "geophysiology" of the Earth.<ref name="agesofgaia">Lovelock, James, (1995) "The Ages of Gaia: A Biography of Our Living Earth" (W.W.Norton & Co)</ref>{{Explain|date=December 2017}} Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<ref name="kirchner2002">{{Citation |last= Kirchner |first = James W. |title =Toward a future for Gaia theory |journal=[[Climatic Change (journal)|Climatic Change]] |volume = 52 |issue = 4 |pages = 391–408 |date = 2002 | doi = 10.1023/a:1014237331082 }}</ref><ref name="volk2002">{{Citation |last= Volk |first = Tyler |title =The Gaia hypothesis: fact, theory, and wishful thinking |journal = Climatic Change |volume = 52 |issue = 4 |pages = 423–430 |date = 2002 | doi = 10.1023/a:1014218227825 }}</ref><ref name="beerling2007">{{cite book |last=Beerling |first=David |authorlink=David Beerling|date=2007 |title=The Emerald Planet: How plants changed Earth's history |url=http://ukcatalogue.oup.com/product/9780192806024.do |location=Oxford|publisher=Oxford University Press |page= |isbn= 978-0-19-280602-4 |accessdate= }}</ref><br />
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The Gaia hypothesis was initially criticized for being teleological and against the principles of natural selection, but later refinements aligned the Gaia hypothesis with ideas from fields such as Earth system science, biogeochemistry and systems ecology. Lovelock also once described the "geophysiology" of the Earth. Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<br />
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盖亚假说最初被诟病为目的论、反对自然选择的原则,但后来的改进使盖亚假说与来自地球系统科学、生物地球化学和系统生态学等领域的观点相一致。洛夫洛克还曾经描述过地球的“地球物理学”。即便如此,盖亚假说仍然受到一些批评,今天许多科学家认为只有少数证据支持这一理论,或与现有的证据相矛盾。<br />
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==Overview总览==<br />
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Gaian hypotheses suggest that organisms [[Co-evolution|co-evolve]] with their environment: that is, they "influence their [[abiotic]] environment, and that environment in turn influences the [[Biota (ecology)|biota]] by [[Darwinism|Darwinian process]]". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early [[Bacteria|thermo-acido-philic]] and [[methanogenic bacteria]] towards the oxygen-enriched [[atmosphere]] today that supports more [[Phanerozoic|complex life]].<br />
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Gaian hypotheses suggest that organisms co-evolve with their environment: that is, they "influence their abiotic environment, and that environment in turn influences the biota by Darwinian process". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early thermo-acido-philic and methanogenic bacteria towards the oxygen-enriched atmosphere today that supports more complex life.<br />
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盖亚假说认为,生物体与其环境共同进化。也就是说,生物“影响它们的非生物环境,而环境反过来又通过自然选择的过程影响生物群”。Lovelock(1995)在他的第二本书中提供了证据,展示了从早期嗜酸、产甲烷细菌的世界向今天支持更复杂生命的富氧大气的进化。<br />
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A reduced version of the hypothesis has been called "influential Gaia"<ref name=":02">{{Cite journal|last=Lapenis|first=Andrei G.|year=2002|title=Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?|url=|journal=The Professional Geographer|volume=54 |issue=3|pages=379–391|via=[Peer Reviewed Journal]|doi=10.1111/0033-0124.00337}}</ref> in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the [[Biota (ecology)|biota]] influence certain aspects of the abiotic world, e.g. [[temperature]] and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<ref name=":02" /> and biogeochemical processes. An example is how the activity of [[Photosynthesis|photosynthetic]] bacteria during Precambrian times completely modified the [[Earth's atmosphere|Earth atmosphere]] to turn it aerobic, and thus supports the evolution of life (in particular [[eukaryotic]] life).<br />
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A reduced version of the hypothesis has been called "influential Gaia" in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the biota influence certain aspects of the abiotic world, e.g. temperature and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<br />
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在《生物圈的定向进化: 生物地球化学选择还是盖亚? 》一书中,这一假说的简化版被称为“有影响力的盖亚”。安德烈·G·拉佩尼斯在这本书中指出生物影响着非生物世界的温度和大气等多个方面。这本书不是一个人的工作,而是一群俄罗斯科研人员的成果合并成这个通过同行评议的出版物。它通过“微观力量”阐述了生命与环境的共同进化。<br />
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Since barriers existed throughout the twentieth century between Russia and the rest of the world, it is only relatively recently that the early Russian scientists who introduced concepts overlapping the Gaia hypothesis have become better known to the Western scientific community.<ref name=":02" /> These scientists include [[Piotr Kropotkin|Piotr Alekseevich Kropotkin]] (1842–1921) (although he spent much of his professional life outside Russia), Vasil’evich Rizpolozhensky (1847–1918), [[Vladimir Ivanovich Vernadsky]] (1863–1945), and Vladimir Alexandrovich Kostitzin (1886–1963).<br />
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由于二十世纪苏联与西方国家存在隔阂,直到最近,在盖亚假说中引进重叠概念的早期苏联科学家才为西方科学界所熟知。<br />
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The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<br />
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盖亚假说认为,地球是一个自我调节的复杂系统,包括生物圈、大气层、水圈和土壤圈,作为一个进化的系统紧密结合在一起。这个假说认为,这个被称为盖亚的系统作为整体,寻求适合当代生命的物理和化学环境。<br />
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Biologists and Earth scientists usually view the factors that stabilize the characteristics of a period as an undirected [[emergent property]] or [[entelechy]] of the system; as each individual species pursues its own self-interest, for example, their combined actiYons may have counterbalancing effects on environmental change. Opponents of this view sometimes reference examples of events that resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth's atmosphere from a [[reducing environment]] to an [[oxygen]]-rich one at the end of the [[Archean|Archaean]] and the beginning of the [[Proterozoic]] periods.<br />
生物学家和地球科学家通常将平衡一个时期的特征的因素视为系统的无方向[[涌现属性]]或[[有目的行为]];例如,由于每个物种都追求自身利益,它们的联合行动可能对环境变化产生抵消作用。反对这一观点的人有时会举出一些导致了巨大变化而非平衡的事件作为反例,例如在[[太古宙|太古代]]末期和[[元古代]]时期开始时,地球大气从[[还原环境]]转变为富含[[氧气]]。 <br />
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Gaia evolves through a cybernetic feedback system operated unconsciously by the biota, leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially microorganisms, with inorganic elements. These processes establish a global control system that regulates Earth's surface temperature, atmosphere composition and ocean salinity, powered by the global thermodynamic disequilibrium state of the Earth system.<!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
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盖亚通过一个由生物群无意识操作的控制论反馈系统实现进化,在完全的内稳态中广泛获得稳定的可居住条件。地球表面的许多过程对生命的保障条件至关重要,这些过程依赖于生命形式,特别是微生物与无机元素的相互作用。这些过程建立了一个全球控制系统,由地球系统的全球热力学不平衡状态提供动力,调节地球表面温度、大气成分和海洋盐度。<br />
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Less accepted versions of the hypothesis claim that changes in the biosphere are brought about through the [[Superorganism|coordination of living organisms]] and maintain those conditions through [[homeostasis]]. In some versions of [[Gaia philosophy]], all lifeforms are considered part of one single living planetary being called ''Gaia''. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the [[Coevolution|coevolving]] diversity of living organisms.<br />
一种不太被接受的假说声称生物圈的变化是通过[[超级有机体|生物体的协调]]来实现的,并通过[[内稳态]]来维持这些条件。在一些版本的[[盖亚哲学]]中,所有的生命形式都是一个被称为“盖亚”的生命行星的一部分。在这种观点下,大气、海洋和地壳将是盖亚通过生物多样性进行干预的结果。 <br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of biogeochemistry, and it is being investigated also in other fields like Earth system science. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<br />
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以前在生物地球化学领域已经观察到受生命形式影响的行星内稳态的存在,而且地球系统科学等其他领域也在研究这一现象。盖亚假说的原创性依赖于这样一种观点: 即使地球或外部事件威胁到内稳态平衡,盖亚也会为了保持生命的最佳状态而积极追求这种平衡。<br />
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The Gaia hypothesis was an influence on the [[deep ecology]] movement.<ref>David Landis Barnhill, Roger S. Gottlieb (eds.), ''Deep Ecology and World Religions: New Essays on Sacred Ground'', SUNY Press, 2010, p. 32.</ref><br />
盖亚假说对[[深层生态学]]运动产生了影响 <br />
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==Details细节==<br />
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Rob Rohde's palaeotemperature graphs<br />
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罗布·罗德的古温度图<br />
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The Gaia hypothesis posits that the Earth is a self-regulating [[complex system]] involving the [[biosphere]], the [[Earth's atmosphere|atmosphere]], the [[hydrosphere]]s and the [[pedosphere]], tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<ref name="vanishing255">Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 255. {{ISBN|978-0-465-01549-8}}</ref><br />
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盖亚假说假设地球是一个自我调节的[[复杂系统]],包括[[生物圈]]、[[地球大气|大气]]、[[水圈]]和[[土壤圈]],作为一个进化系统紧密耦合。该假说认为,这个系统作为一个整体,称为盖亚,寻求一个最适合当代生活的物理和化学环境 <br />
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Since life started on Earth, the energy provided by the Sun has increased by 25% to 30%; however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on Titan. research has suggested that "oxygen shocks" and reduced methane levels led, during the Huronian, Sturtian and Marinoan/Varanger Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre Phanerozoic biosphere to fully self-regulate.<br />
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自从地球上有生命以来,太阳提供的能量增加了25%到30%;然而,地球表面温度一直保持在适宜居住的水平上,不曾突破上限或是下限。洛夫洛克还假设,产甲烷菌在早期大气中产生了较高水平的甲烷,这与在石化烟雾中发现的成分相似,在某些方面与土卫六上的大气相似。研究表明,在休伦期、斯图尔特期和马里诺/瓦朗格冰期,“氧冲击”和甲烷含量降低导致世界几乎变成了一个坚实的“雪球”。这些时代是前显生宙生物圈完全拥有自我调节能力的证据。<br />
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Gaia evolves through a [[Cybernetic#In biology|cybernetic]] [[feedback]] system operated unconsciously by the [[biota (ecology)|biota]], leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially [[microorganisms]], with inorganic elements. These processes establish a global control system that regulates Earth's [[Sea surface temperature|surface temperature]], [[atmosphere composition]] and [[ocean]] [[salinity]], powered by the global thermodynamic disequilibrium state of the Earth system.<ref>Kleidon, Axel. ''How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?''. Article submitted to the ''Philosophical Transactions of the Royal Society'' on Thu, 10 Mar 2011</ref><!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
盖亚通过一个[[控制论|生物学|控制论]][[反馈]]系统在[[生物群(生态学)|生物群]]的无意识运作中实现进化,导致在完全的内稳态中广泛存在稳定的可居住条件。地球表面对生命条件至关重要的许多过程都依赖于生物,特别是[微生物]与无机元素的相互作用。这些过程建立了一个全球控制系统,调节地球的[[海表温度|表面温度]]、[[大气组成]]和[[海洋]][[盐度]],其动力来自地球系统的全球热力学不平衡状态。<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
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温室气体CO<sub>2</sub>的处理在维持地球温度在可居住范围内起着关键作用(解释详见下文)。<br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of [[biogeochemistry]], and it is being investigated also in other fields like [[Earth system science]]. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 179. {{ISBN|978-0-465-01549-8}}</ref><br />
受生命形式影响的行星内稳态的存在,以前在[[生物地球化学]]领域就已被观察到,而且其他领域,如[[地球系统科学]]也在研究这种稳态。盖亚假说的独创性依赖于这样一种观点,即盖亚积极追求这种内平衡,以保持维护生命的最佳状态,即使是在地球或外部事件威胁它们的时候。<br />
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The CLAW hypothesis, inspired by the Gaia hypothesis, proposes a feedback loop that operates between ocean ecosystems and the Earth's climate. The hypothesis specifically proposes that particular phytoplankton that produce dimethyl sulfide are responsive to variations in climate forcing, and that these responses lead to a negative feedback loop that acts to stabilise the temperature of the Earth's atmosphere.<br />
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受盖亚假说的启发,CLAW 假说提出了一个在海洋生态系统和地球气候之间运行的反馈回路。该假说特别提出,产生二甲硫醚的浮游植物对气候变化有反应,这些反应导致了一个负反馈循环,稳定了地球大气的温度。<br />
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===Regulation of global surface temperature地球表面温度的调控===<br />
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[[File:All palaeotemps.png|thumb|480px|Rob Rohde's palaeotemperature graphs]]<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of greenhouse gases may cause negative feedbacks in the environment to become positive feedback. Lovelock has stated that this could bring an extremely accelerated global warming, but he has since stated the effects will likely occur more slowly.<br />
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目前,人口的增加及其活动对环境的影响,例如温室气体的增加,可能导致环境中的负反馈成为正反馈。洛夫洛克表示,这可能会极大地加速全球变暖,但他后来又表示,这种影响也可能发生得更慢。<br />
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{{See also|Paleoclimatology}}<br />
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Since life started on Earth, the energy provided by the [[Sun]] has increased by 25% to 30%;<ref name="Owen1979">{{cite journal | author = Owen, T. | author2 = Cess, R.D. | author3 = Ramanathan, V. | date = 1979 | title = Earth: An enhanced carbon dioxide greenhouse to compensate for reduced solar luminosity | journal = [[Nature (journal)|Nature]] | volume = 277 | pages = 640–2 | doi = 10.1038/277640a0 | issue=5698 | bibcode = 1979Natur.277..640O | ref = harv }}</ref> however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on [[Titan (moon)|Titan]].<ref name="agesofgaia"/> This, he suggests tended to screen out ultraviolet until the formation of the ozone screen, maintaining a degree of homeostasis. However, the [[Snowball Earth]]<ref>Hoffman, P.F. 2001. [http://www.snowballearth.org ''Snowball Earth theory'']</ref> research has suggested that "oxygen shocks" and reduced methane levels led, during the [[Huronian]], [[Sturtian]] and [[Marinoan]]/[[Cryogenian|Varanger]] Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre [[Phanerozoic]] biosphere to fully self-regulate.<br />
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Plots from a standard black and white [[Daisyworld simulation]]<br />
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从一个标准的黑白图[[雏菊世界模拟]]<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
说明了在温室气体维持低于临界温度的过程中,CO2起着至关重要的作用。 <br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic group selection and cooperation between organisms, James Lovelock and Andrew Watson developed a mathematical model, Daisyworld, in which ecological competition underpinned planetary temperature regulation.<br />
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有人批评盖亚假说似乎需要有机体之间不切实际的群体选择与合作,为了回应这种批评,James Lovelock 和 Andrew Watson建立了一个数学模型---- 雏菊世界,其中生态竞争支撑着地。<br />
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The [[CLAW hypothesis]], inspired by the Gaia hypothesis, proposes a [[feedback|feedback loop]] that operates between [[ocean]] [[ecosystem]]s and the [[Earth]]'s [[climate]].<ref name="CLAW87">{{cite journal |doi=10.1038/326655a0 |author=[[Robert Jay Charlson|Charlson, R. J.]], [[James Lovelock|Lovelock, J. E]], Andreae, M. O. and Warren, S. G. |title=Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate |journal=Nature |volume=326 |issue=6114 |pages=655–661 |date=1987 |bibcode=1987Natur.326..655C |ref=harv }}</ref> The [[hypothesis]] specifically proposes that particular [[phytoplankton]] that produce [[dimethyl sulfide]] are responsive to variations in [[climate forcing]], and that these responses lead to a [[negative feedback|negative feedback loop]] that acts to stabilise the [[temperature]] of the [[Earth's atmosphere]].<br />
受到盖亚假说启发的[[爪假说]]提出了一个在[[海洋]][[生态系统]]和[[地球]]的[[气候]]之间运行的[[反馈|反馈回路]]。<br />
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Daisyworld examines the energy budget of a planet populated by two different types of plants, black daisies and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the albedo of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
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《雏菊世界》调查了一个星球的能量预算,这个星球上生长着两种不同的植物,黑色雏菊和白色雏菊,这两种植物占据了星球表面的很大一部分。雏菊的颜色影响了地球的反照率,黑色的雏菊吸收更多的光线,使地球变暖,而白色的雏菊则反射更多的光线,使地球变冷。人们认为黑色雏菊在较低的温度下生长和繁殖最好,而白色雏菊则被认为在较高的温度下生长最好。当温度上升到接近白色雏菊所喜欢的温度时,白色雏菊繁殖率高于黑色雏菊,导致更大比例的白色表面,更多的阳光被反射,减少热量输入,最终使地球降温。相反,随着气温的下降,黑色雏菊繁殖率高于白色雏菊,吸收了更多的阳光,使地球变暖。因此,温度会收敛于两种植物繁殖率相等时对应温度的值。<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of [[greenhouse gases]] may cause [[negative feedback]]s in the environment to become [[positive feedback]]. Lovelock has stated that this could bring an [[James Lovelock#The revenge of Gaia|extremely accelerated global warming]],<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, {{ISBN|978-0-465-01549-8}}</ref> but he has since stated the effects will likely occur more slowly.<ref>Lovelock J., NBC News. [http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite Link] Published 23 April 2012, accessed 22 August 2012. {{Webarchive|url=https://web.archive.org/web/20120913163635/http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite |date=13 September 2012 }}</ref><br />
目前,人口的增加及其活动对环境的影响,如[[温室气体]]的倍增,可能导致环境中的[[负反馈]]变成[[正反馈]]。洛夫洛克曾表示,这可能会带来一场【【James Loveloc【《盖亚的复仇』极度加速的全球变暖】】 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this negative feedback due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
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洛夫洛克和沃森指出,在有限的条件下,如果太阳的能量输出发生变化,由于竞争产生的负反馈可以将地球温度稳定在支持生命存在的范围内,而没有生命的地球则会表现出巨大的温度波动。白色和黑色雏菊的百分比会不断变化,以保持植物繁殖率相等的温度值,使两种生命形式都能茁壮成长。<br />
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====Daisyworld simulations雏菊世界模拟====<br />
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[[File:StandardDaisyWorldRun2color.gif|thumb|280px|Plots from a standard black and white [[Daisyworld]] simulation]]<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<br />
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有人认为,这些结果是可以预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的答案。<br />
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{{Main|Daisyworld}}<br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic [[group selection]] and [[Cooperation (evolution)|cooperation]] between organisms, James Lovelock and [[Andrew Watson (scientist)|Andrew Watson]] developed a mathematical model, [[Daisyworld]], in which [[Competition (biology)|ecological competition]] underpinned planetary temperature regulation.<ref name="daisyworld">{{cite journal<br />
有人批评盖亚假说似乎需要有机体之间不切实际的[[群体选择]]和[[合作(进化)|合作]],詹姆斯·洛夫洛克和[[安德鲁·沃森(科学家)|安德鲁·沃森]]开发了一个数学模型,[[雏菊世界]],其中[[竞争(生物学)|生态竞争]]为基础行星温度调节。 <br />
|date = 1983<br />
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Ocean salinity has been constant at about 3.5% for a very long time. Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested that salinity may also be strongly influenced by seawater circulation through hot basaltic rocks, and emerging as hot water vents on mid-ocean ridges. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<br />
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长期以来,海洋盐度一直保持在3.5% 左右。海洋环境中盐度的稳定性很重要,因为大多数细胞需要相当恒定的盐度,一般不能耐受超过5% 的盐度值。海洋盐度为何恒定是一个长期的奥秘,因为没有任何方法可以抵消来自河流的流入盐。最近有人提出,盐分也会洋中脊的热水喷口排出,因此盐度可能受到穿过炽热玄武岩的海水循环的强烈影响。然而,海水的组成离平衡还很远,如果没有有机过程的影响,很难解释这一事实。有一种解释认为,地球历史上盐滩的形成是盐度平衡的原因之一。据推测,这些盐滩是由细菌菌落产生的,它们在生命过程中固定离子和重金属。<br />
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|title = Biological homeostasis of the global environment: the parable of Daisyworld<br />
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|journal = Tellus<br />
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|volume = 35B<br />
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Vostok, Antarctica research station. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
沃斯托克,南极洲研究站。当前期间在左边。<!--基于此图表的GIMP-FX版本的非源材料。现在的版本是正确的,原版的。必须删除这句话:请注意,当前CO2水平超过390ppm,远高于过去40万年来的任何时候-->] <br />
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|pages = 286–9<br />
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|bibcode = 1983TellB..35..284W<br />
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|doi = 10.1111/j.1600-0889.1983.tb00031.x<br />
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The Gaia hypothesis states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organisms or processed by them.<br />
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盖亚假说认为,地球的大气组成是由于生命的存在而保持在动态稳定的状态。大气成分提供了支持现代生命的条件。大气中除惰性气体以外的所有大气气体,要么是由生物体产生的,要么是由生物体加工的。<br />
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|last1 = Watson | first1= A.J. | last2= Lovelock | first2= J.E<br />
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|issue = 4<br />
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The stability of the atmosphere in Earth is not a consequence of chemical equilibrium. Oxygen is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the Great Oxygenation Event. Since the start of the Cambrian period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume. Traces of methane (at an amount of 100,000 tonnes produced per year) should not exist, as methane is combustible in an oxygen atmosphere.<br />
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地球大气层的稳定性不是化学平衡的结果。氧是一种活性化合物,最终会与地球大气层和地壳中的气体和矿物质结合。在大氧化事件开始之前,大约5000万年前,氧气才开始在大气中持续少量存在。自寒武纪以来,大气中氧浓度一直在大气体积的15% 至35% 之间波动。微量的甲烷(每年产生100,000吨)不适合存在,因为甲烷在氧气氛中是可燃的。<br />
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|ref = harv<br />
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}}</ref><br />
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Dry air in the atmosphere of Earth contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases including methane. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. <br />
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地球大气层中的干燥空气大致(按体积计算)含有78.09% 的氮气、20.95% 的氧气、0.93% 的氩气、0.039% 的二氧化碳以及少量的其他气体,包括甲烷。洛夫洛克最初推测,高于25% 的氧气浓度会增加森林大火和森林大火的发生频率。石炭纪和白垩纪煤系地质时期O2浓度确实超过了25%时,正是这一时期形成了火成木炭。这一结果支持了 Lovelock 的论点。<br />
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Daisyworld examines the [[Earth's energy budget|energy budget]] of a [[planet]] populated by two different types of plants, black [[Asteraceae|daisies]] and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the [[albedo]] of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
Daisyworld研究了居住着两种不同类型的植物的[[地球的能源预算|能源预算]],这两种植物是黑色的[[菊科的雏菊]]和白色的雏菊,这两种植物被认为占据了地表的很大一部分。雏菊的颜色影响着这个星球的[反照率],因此黑色雏菊吸收更多的光并温暖地球,而白色雏菊则反射更多的光并使地球降温。黑雏菊在较低温度下生长繁殖最好,而白雏菊在较高温度下生长繁殖最好。当温度上升到接近白色雏菊的最适生长温度时,白色雏菊的繁殖能力超过了黑色雏菊,导致白色表面的比例增大,更多的阳光被反射,减少了热量输入,最终使地球变冷。相反,随着温度的下降,黑雏菊的繁殖能力超过了白雏菊,吸收了更多的阳光,使地球变暖。因此,温度将收敛到两种植物繁殖率相等对应的温度值。 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this [[negative feedback]] due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
Lovelock和Watson表明,在有限的条件范围内,如果太阳的能量输出发生变化,由于竞争而产生的[[负反馈]]可以将地球的温度稳定在支持生命的值上,而没有生命的行星则会出现大范围的温度波动。白雏菊和黑雏菊的比例会不断变化,以使温度保持在植物繁殖率相等的值,从而使两种生命形式都能茁壮成长。 <br />
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Gaia scientists see the participation of living organisms in the carbon cycle as one of the complex processes that maintain conditions suitable for life. The only significant natural source of atmospheric carbon dioxide (CO<sub>2</sub>) is volcanic activity, while the only significant removal is through the precipitation of carbonate rocks. Carbon precipitation, solution and fixation are influenced by the bacteria and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
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盖亚假说的科学家们把生物体参与碳循环看作是维持适合生命条件的复杂过程之一。火山活动是大气中二氧化碳的最重要的自然来源,而碳酸盐岩的沉淀是大气中二氧化碳最重要的去除途径。碳沉淀、溶解和固定受到土壤中细菌和植物根系的影响,这些细菌和植物根系可以改善气体循环,或者在珊瑚礁中,碳酸钙以固体的形式沉积在海底。碳酸钙被活的有机体用来制造含碳的结构和外壳。一旦死亡,生物体的外壳就会沉到海底,在那里它们产生白垩和石灰石的沉淀物。<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<ref>{{cite journal | doi = 10.1023/A:1023494111532 | date = 2003 | last1 = Kirchner | first1 = James W. | journal = Climatic Change | volume = 58 |issue=1–2| pages = 21–45 |title=The Gaia Hypothesis: Conjectures and Refutations | ref = harv}}</ref><br />
有人认为,结果是可预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的反应。 <br />
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One of these organisms is Emiliania huxleyi, an abundant coccolithophore algae which also has a role in the formation of clouds. CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants. Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean algal blooms are also increasing.<br />
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其中一种是赫氏圆石藻,这是一种数量丰富的颗石藻类,也参与了云的形成。通过增加球石氟化物的寿命来补偿过量的CO < sub > 2 </sub > ,增加了锁定在海底的 CO < sub > 2 </sub > 的数量。球石粉会增加云量,从而控制地表温度,有助于降低整个地球的温度,有利于地球上植物所必需的降水。近年来,大气中 CO < < sub > 2 </sub > 浓度有所增加,有证据表明,海洋藻华的浓度也在增加。<br />
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===Regulation of oceanic salinity海洋盐度调节 ===<br />
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Lichen and other organisms accelerate the weathering of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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地衣和其他生物加速了岩石表面的风化,而岩石在土壤中的分解也加快了,这要归功于根、真菌、细菌和地下动物的活动。因此,二氧化碳从大气层流向土壤的过程是在生物的帮助下调节的。当大气中 CO2水平升高时,温度升高,植物生长。这种生长会增加植物对二氧化碳的消耗,植物会将二氧化碳处理到土壤中,从大气中排出。<br />
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Ocean [[salinity]] has been constant at about 3.5% for a very long time.<ref name=":0">{{Cite book|title=The Introduction to Ocean Sciences|last=Segar|first=Douglas|publisher=Library of Congress|year=2012|isbn=978-0-9857859-0-1|location=http://www.reefimages.com/oceans/SegarOcean3Chap05.pdf|pages=Chapter 5 3rd Edition|quote=|via=}}</ref> Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested<ref name="Gorham19912">{{cite journal|last=Gorham|first=Eville|date=1 January 1991|title=Biogeochemistry: its origins and development|journal=Biogeochemistry|publisher=Kluwer Academic|volume=13|issue=3|pages=199–239|doi=10.1007/BF00002942|issn=1573-515X|ref=harv}}</ref> that salinity may also be strongly influenced by [[seawater]] circulation through hot [[basalt]]ic rocks, and emerging as hot water vents on [[mid-ocean ridge]]s. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<ref name=":0" /><br />
在很长一段时间内,海洋盐度一直保持在3.5%左右。[23]海洋环境中的盐度稳定性非常重要,因为大多数细胞需要相当恒定的盐度,并且通常不能耐受超过5%的盐度值。恒定的海洋盐度是一个长期存在的谜团,因为没有任何过程可以抵消河流中的盐流入。大洋中脊上的热水喷口会排出盐分,有人认为[24]这说明盐分也会受到海水循环的强烈影响。然而,海水的组成远未达到平衡,如果没有有机过程的影响,很难解释这一事实。地球历史中盐滩的形成是一个常用的证据。据推测,这些盐滩是由在生命过程中固定离子和重金属的菌落产生的<br />
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In the biogeochemical processes of Earth, sources and sinks are the movement of elements. The composition of salt ions within our oceans and seas is: sodium (Na<sup>+</sup>), chlorine (Cl<sup>−</sup>), sulfate (SO<sub>4</sub><sup>2−</sup>), magnesium (Mg<sup>2+</sup>), calcium (Ca<sup>2+</sup>) and potassium (K<sup>+</sup>). The elements that comprise salinity do not readily change and are a conservative property of seawater.<ref name=":0" /> There are many mechanisms that change salinity from a particulate form to a dissolved form and back. The known sources of sodium i.e. salts are when weathering, erosion, and dissolution of rocks are transported into rivers and deposited into the oceans.<br />
在地球的生物地球化学过程中,源和汇是元素的运动。我们海洋中盐离子的组成是:钠(Na+)、氯(Cl-)、硫酸盐(SO42-)、镁(Mg2+)、钙(Ca2+)和钾(K+)。构成盐度的元素不易变化,是海水的一种保守属性。[23]有许多机制可以将盐度从颗粒形态改变为溶解形态,然后再返回。已知的钠(即盐)因为岩石的风化、侵蚀和溶解作用被输送到河流中并沉积到海洋中。 <br />
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The [[Mediterranean Sea]] as being Gaia's kidney is found ([http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/ here]) by Kenneth J. Hsue, a correspondence author in 2001. The "[[desiccation]]" of the Mediterranean is the evidence of a functioning kidney. Earlier "kidney functions" were performed during the "[[Deposition (geology)|deposition]] of the [[Cretaceous]] ([[Atlantic Ocean|South Atlantic]]), [[Jurassic]] ([[Gulf of Mexico]]), [[Permian–Triassic extinction event|Permo-Triassic]] ([[Europe]]), [[Devonian]] ([[Canada]]), [[Cambrian]]/[[Precambrian]] ([[Gondwana]]) saline giants."<ref>{{Cite web|url=http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/|title=Scientia Marina: List of Issues|last=http://www.webviva.com|first=Justino Martinez. Web Viva 2007|website=scimar.icm.csic.es|language=English|access-date=2017-02-04}}</ref><br />
地中海是盖亚的肾脏,由肯尼斯·J·休伊(KennethJ.Hsue)在2001年发现的。地中海的“干涸”是肾功能正常的证据。早期的“肾功能”是在“白垩纪(南大西洋)、侏罗纪(墨西哥湾)、二叠纪-三叠纪(欧洲)、泥盆纪(加拿大)、寒武纪/前寒武纪(冈瓦纳)盐沼沉积时期进行的。” <br />
[[Earthrise taken from Apollo 8 on December 24, 1968]]<br />
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[1968年12月24日阿波罗8号拍摄的地出]<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = <br />
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地球是一个完整的整体,一个有生命的存在,这个观念有着悠久的传统。神话中的盖亚是拟人化地球的原始希腊女神,是希腊版本的“自然母亲”(来自 Ge = 地球,和 Aia = <br />
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===Regulation of oxygen in the atmosphere大气层的氧气调节===<br />
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PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a suggestion from the novelist William Golding, who was living in the same village as Lovelock at the time (Bowerchalke, Wiltshire, UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of living organisms, climate, and Earth's crust. His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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派祖母,或地球母亲。詹姆斯·洛夫洛克根据小说家威廉·戈尔丁的建议给他的假设起了这个名字,他当时和洛夫洛克住在同一个村子里(英国威尔特郡鲍尔查尔克)。戈尔丁的建议是以Gea为基础的,Gea是希腊女神名字的另一种拼写,在地质学、地球物理和地球化学中,Gea是前缀。后来,博物学家和探险家亚历山大·冯·洪堡认识到生物、气候和地壳的共同进化。他的远见卓识的声明在西方没有被广泛接受,几十年后,盖亚假说刚提出时同样受到了科学界的抵制。<br />
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[[File:Vostok 420ky 4curves insolation.jpg|thumb|280px|Levels of gases in the atmosphere in 420,000 years of ice core data from [[Vostok Station|Vostok, Antarctica research station]]. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
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{{See also|Geological history of oxygen}}<br />
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Also in the turn to the 20th century Aldo Leopold, pioneer in the development of modern environmental ethics and in the movement for wilderness conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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同样在20世纪之交,现代环境伦理学发展的先驱、荒野保护运动的先驱奥尔多 · 利奥波德在他的生物中心或整体的土地伦理学中提出了一个有生命的地球。<br />
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The Gaia hypothesis states that the Earth's [[Atmospheric chemistry#Atmospheric composition|atmospheric composition]] is kept at a dynamically steady state by the presence of life.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 163. {{ISBN|978-0-465-01549-8}}</ref> The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than [[noble gas]]es present in the atmosphere are either made by organisms or processed by them.<br />
盖亚假说指出,地球的大气成分由于生命的存在而保持在动态稳定的状态。大气中除惰性气体以外的所有大气气体都是由生物体制造或加工而成。<br />
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The stability of the atmosphere in Earth is not a consequence of [[chemical equilibrium]]. [[Oxygen]] is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the [[Great Oxygenation Event]].<ref name=Anabar2007>{{Cite journal| last4 = Arnold| last6 = Creaser| last3 = Lyons| first1 = A. | first2 = Y.| last9 = Scott| last2 = Duan | first3 = T. | first4 = G.| last8 = Gordon | first5 = B. | first10 = J. | first6 = R.| last10 = Garvin | first7 = A.| last11 = Buick | first8 = G. | first11 = R. | first9 = C.| title = A whiff of oxygen before the great oxidation event?| journal = Science| volume = 317| issue = 5846| year = 2007| last7 = Kaufman| pages = 1903–1906| last5 = Kendall| pmid = 17901330| last1 = Anbar | doi = 10.1126/science.1140325|bibcode = 2007Sci...317.1903A }}</ref> Since the start of the [[Cambrian]] period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume.<br />
地球大气的稳定性不是化学平衡造成的。氧气是一种活性化合物,最终会与地球大气层和地壳上的气体和矿物质结合。在大氧化事件开始前的5000万年,氧气才在大气中少量存在。自寒武纪开始以来,大气氧浓度值一直在大气体积的15%到35%之间波动。甲烷的痕迹(每年产生10万吨)是不存在的,因为甲烷在氧气环境中是可燃的。<br />
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Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut William Anders in 1968 during the Apollo 8 mission became, through the Overview Effect an early symbol for the global ecology movement.<br />
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盖亚假说和环境运动的另一个影响来自于苏联和美利坚合众国之间太空竞赛。在20世纪60年代,第一批进入太空的人类可以看到地球作为一个整体的样子。1968年,宇航员威廉 · 安德斯在阿波罗8号任务期间拍摄的地出照片,通过总体效应成为全球生态运动的早期象征。<br />
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| pmid = 10500106<br />
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| date=Sep 1999 | last1 = Berner | first1 = R. A.<br />
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| title = Atmospheric oxygen over Phanerozoic time<br />
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[[James Lovelock, 2005]]<br />
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[ James Lovelock,2005]<br />
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| volume = 96<br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the Jet Propulsion Laboratory in California on methods of detecting life on Mars. The first paper to mention it was Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life, co-authored with C.E. Giffin. A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the Pic du Midi observatory, planets like Mars or Venus had atmospheres in chemical equilibrium. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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65年9月,洛夫洛克在加利福尼亚喷气推进实验室研究探测火星生命的方法时,开始定义由生物群落控制的自我调节地球的概念。第一篇提到它的论文是行星大气:与C.E.Giffin合著的与生命存在有关的成分和其他变化。一个主要的概念是,通过大气的化学成分可以在行星尺度上探测到生命。根据picdumidi天文台收集的数据,像火星或金星这样的行星,其大气层处于化学平衡状态。这种与地球大气的差异被认为是这些行星上没有生命的证据。 <br />
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| issue = 20<br />
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| pages = 10955–10957<br />
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Lovelock formulated the Gaia Hypothesis in journal articles in 1972 and 1974, and a popular book length version of the hypothesis, published in 1979 as The Quest for Gaia, began to attract scientific and critical attention.<br />
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洛夫洛克在1972年和1974年的期刊文章中提出了盖亚假说,并在1979年出版了一本畅销书,名为《寻找盖亚》 ,开始引起科学界和批判界的关注。<br />
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| journal = Proceedings of the National Academy of Sciences of the United States of America<br />
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Lovelock called it first the Earth feedback hypothesis, and it was a way to explain the fact that combinations of chemicals including oxygen and methane persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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洛夫洛克首先将其称为地球反馈假说,解释氧气和甲烷等化学物质在地球大气中如何保持稳定浓度。洛夫洛克认为,在其他行星的大气层中探测这种组合,是一种相对便宜可靠的探测生命的方法。<br />
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| doi = 10.1073/pnas.96.20.10955<br />
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[[Lynn Margulis]]<br />
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[琳 · 玛格丽丝]<br />
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|bibcode = 1999PNAS...9610955B }}</ref> Traces of [[Atmospheric methane|methane]] (at an amount of 100,000 tonnes produced per year)<ref name="Cicerone1988">{{cite journal |last1=Cicerone |first1=R.J. |last2=Oremland |first2=R.S. |date=1988 |title=Biogeochemical aspects of atmospheric methane |journal=Global Biogeochemical Cycles |volume=2 |issue=4 |pages=299–327 |url=//webfiles.uci.edu/setrumbo/public/Methane_papers/Cicerone_Global%20Biogeochem%20Cy_1988.pdf |doi=10.1029/GB002i004p00299 |bibcode=1988GBioC...2..299C}}</ref> should not exist, as methane is combustible in an oxygen atmosphere.<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<br />
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后来出现了其他关系,例如海洋生物产生的硫和碘的数量与陆地生物所需的数量大致相同,这些都支持了这一假说。<br />
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Dry air in the [[atmosphere of Earth]] contains roughly (by volume) 78.09% [[nitrogen]], 20.95% oxygen, 0.93% [[argon]], 0.039% [[Carbon dioxide in the Earth's atmosphere|carbon dioxide]], and small amounts of other gases including [[methane]]. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. {{citation needed|date=June 2012}}<br />
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[[地球大气]]中的干空气大约(按体积)包含78.09%[[氮]],20.95%的氧,0.93%[[氩]],0.039%[地球大气中的二氧化碳|二氧化碳]],以及少量其他气体,包括[[甲烷]]。洛夫洛克最初推测,氧气浓度超过25%会增加森林火灾和火灾的发生率。最近在石炭纪和白垩纪煤系中火成木炭的研究(这两个地质时期O<sub>2</sub>浓度超过25%)支持了Lovelock的观点 <br />
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In 1971 microbiologist Dr. Lynn Margulis joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet. The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of eukaryotic organelles and her contributions to the endosymbiotic theory, nowadays accepted. Margulis dedicated the last of eight chapters in her book, The Symbiotic Planet, to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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1971年,微生物学家 Lynn Margulis 博士加入了 Lovelock 的行列,努力将最初的假设充实为科学证明的概念。Margulis 贡献了她关于微生物如何影响大气层和地球表面不同层次的知识。这位美国生物学家也唤受到科学界的批评,因为她倡导真核细胞器起源的理论,以及她对美国共生发源学会的贡献——现在被接受了。玛格丽丝在她的书《共生星球》中将最后八章用于描述盖亚。然而,她反对对盖亚的广泛拟人化,并强调盖亚“不是一个有机体” ,而是“有机体之间相互作用的一个新兴属性”。她将盖亚定义为“组成地球表面一个巨大生态系统的一系列相互作用的生态系统”。句号”。这本书最令人难忘的“口号”实际上是由马古利斯的一个学生打趣说的: “从太空看,盖亚只是共生而已。”。<br />
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===Processing of CO<sub>2</sub>二氧化碳处理===<br />
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{{See also|Carbon cycle}}<br />
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James Lovelock called his first proposal the Gaia hypothesis but has also used the term Gaia theory. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments and provided a number of useful predictions. In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating. The principal sponsor was the National Audubon Society. Speakers included James Lovelock, George Wald, Mary Catherine Bateson, Lewis Thomas, John Todd, Donald Michael, Christopher Bird, Thomas Berry, David Abram, Michael Cohen, and William Fields. Some 500 people attended.<br />
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詹姆斯 · 洛夫洛克称他的第一个提议为盖亚假说,但也使用了盖亚理论这个术语。洛夫洛克说,最初的提法是基于观察,但仍然缺乏科学的解释。盖亚假说从那以后得到了一些科学实验的支持,并提供了一些有用的预测。事实上,更广泛的研究证明了最初的假设是错误的,在这个意义上,不是生命本身,而是整个地球系统在调节。主要赞助者是奥杜邦学会。讲者包括 James Lovelock、 George Wald、 Mary Catherine Bateson、 Lewis Thomas、 John Todd、 Donald Michael、 Christopher Bird、 Thomas Berry、 David Abram、 Michael Cohen 和 William Fields。大约有500人参加。<br />
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Gaia scientists see the participation of living organisms in the [[carbon cycle]] as one of the complex processes that maintain conditions suitable for life. The only significant natural source of [[Carbon dioxide in Earth's atmosphere|atmospheric carbon dioxide]] ([[Carbon dioxide|CO<sub>2</sub>]]) is [[volcanic activity]], while the only significant removal is through the precipitation of [[carbonate rocks]].<ref name="Karhu1996">{{cite journal | author = Karhu, J.A. | author2 = Holland, H.D. | date = 1 October 1996 | title = Carbon isotopes and the rise of atmospheric oxygen | journal = [[Geology (journal)|Geology]] | volume = 24 | issue = 10 | pages = 867–870 | doi = 10.1130/0091-7613(1996)024<0867:CIATRO>2.3.CO;2|bibcode = 1996Geo....24..867K | ref = harv}}</ref> Carbon precipitation, solution and [[Carbon fixation|fixation]] are influenced by the [[bacteria]] and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
盖亚的科学家认为,生物参与[[碳循环]是维持适宜生命条件的复杂过程之一。[[地球大气中的二氧化碳|大气二氧化碳]]([[二氧化碳| CO2]])最重要的自然来源是[[火山活动]],而最重要的去除过程是[[碳酸盐岩]]的沉淀,溶液和[[固碳|固碳]]受土壤中的[[细菌]]和植物根系的影响,它们改善了气体循环,珊瑚礁中碳酸钙以固体形式沉积在海底。碳酸钙被生物用来制造含碳结构和贝壳。一旦死亡,这些生物的壳就会落到海底,在那里它们会产生白垩和石灰岩的沉积物。 <br />
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One of these organisms is ''[[Emiliania huxleyi]]'', an abundant [[coccolithophore]] [[algae]] which also has a role in the formation of [[cloud]]s.<ref name="Harding2006">{{cite book |author=Harding, Stephan |title=Animate Earth |publisher=Chelsea Green Publishing |date=2006 |pages=65 |isbn=978-1-933392-29-5 }}</ref> CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants.{{citation needed|date=July 2015}} Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean [[algal bloom]]s are also increasing.<ref>{{Cite web | date = 12 September 2007 | title = Interagency Report Says Harmful Algal Blooms Increasing | url = http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | url-status = dead | archiveurl = https://web.archive.org/web/20080209234239/http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | archivedate = 9 February 2008 }}</ref><br />
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In 1988, climatologist Stephen Schneider organised a conference of the American Geophysical Union. The first Chapman Conference on Gaia,<br />
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在1988年,气候学家史蒂芬·史奈德组织了一次美国美国地球物理联盟协会的会议。关于盖亚假说的第一次查普曼会议,<br />
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[[Lichen]] and other organisms accelerate the [[weathering]] of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the Daisyworld Model (and its modifications, above) as evidence against most of these criticisms.<br />
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然而,洛夫洛克和其他支持盖亚理论的科学家确实试图反驳这样一种说法,即这种假设不科学,因为不可能通过控制实验来检验它。例如,针对盖亚假说是目的论的指责,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修正,上文)反驳这些批评。<br />
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==History历史==<br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of teleologism ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,这一版本中盖亚并不是有意地在她的环境中维持生命赖以生存的复杂平衡。看起来,盖亚假说“故意”行为的说法只是他那本广受欢迎的书中的一个比喻性陈述,并不是字面意义上的理解。这种对盖亚假说的新陈述更能为科学界所接受。在这次会议之后,大多数关于目的论的指责都停止了。<br />
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===Precedents先例===<br />
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[[File:NASA-Apollo8-Dec24-Earthrise.jpg|thumb|''[[Earthrise]]'' taken from [[Apollo 8]] on December 24, 1968]]<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000, the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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到2000年6月23日在西班牙巴伦西亚举行关于盖亚假说的第二次查普曼会议时,情况发生了重大变化。与其讨论盖亚假说的目的论观点,或盖亚假说的“类型” ,不如将重点放在具体的机制上,通过这些机制,短期内基本稳态在重要的进化长期结构变化的框架内得以维持。<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The [[Gaia (mythology)|mythical Gaia]] was the primal Greek goddess personifying the [[Earth]], the Greek version of "[[Mother Nature]]" (from Ge = Earth, and Aia = <br />
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[[PIE]] grandmother), or the [[Earth Mother]]. James Lovelock gave this name to his hypothesis after a suggestion from the novelist [[William Golding]], who was living in the same village as Lovelock at the time ([[Bowerchalke]], [[Wiltshire]], UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry.<ref name=vanish09 /> Golding later made reference to Gaia in his [[Nobel prize]] acceptance speech.<br />
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The major questions were:<br />
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主要的问题是:<br />
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In the eighteenth century, as [[geology]] consolidated as a modern science, [[James Hutton]] maintained that geological and biological processes are interlinked.<ref name=CapraWeb>{{cite book |author=Capra, Fritjof |title=The web of life: a new scientific understanding of living systems |publisher=Anchor Books |location=Garden City, N.Y |date=1996 |page=[https://archive.org/details/weboflifenewscie00capr/page/23 23] |isbn=978-0-385-47675-1 |url=https://archive.org/details/weboflifenewscie00capr/page/23 }}</ref> Later, the [[naturalist]] and explorer [[Alexander von Humboldt]] recognized the coevolution of living organisms, climate, and Earth's crust.<ref name=CapraWeb /> In the twentieth century, [[Vladimir Vernadsky]] formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian [[geochemist]] and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological processes. During the 1920s he published works arguing that living organisms could reshape the planet as surely as any physical force. Vernadsky was a pioneer of the scientific bases for the environmental sciences.<ref>S.R. Weart, 2003, ''The Discovery of Global Warming'', Cambridge, Harvard Press</ref> His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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"How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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“被称为盖亚的全球生物地球化学/气候系统是如何及时发生变化的?它的历史是什么?盖亚假说能够在一个时间尺度上保持系统的稳定性,但是在更长的时间尺度上仍然经历矢量变化吗?如何利用地质记录来检验这些问题? ”<br />
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"What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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“盖亚假说的结构是什么?这些反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由在任何特定时间进行的学科研究务实地决定的,还是有一些部分应该被认为是最真实的,以了解盖亚假说随着时间的推移包含进化中的生物体?盖亚系统这些不同部分之间的反馈是什么? 对盖亚假说作为全球生态系统的结构和生命的生产力来说,物质的近乎封闭意味着什么? ”<br />
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Also in the turn to the 20th century [[Aldo Leopold]], pioneer in the development of modern [[environmental ethics]] and in the movement for [[wilderness]] conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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"How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
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“盖亚假说过程和现象的模型如何与现实相关,它们如何帮助解决和理解盖亚?雏菊世界的成果如何转移到现实世界?什么是“雏菊”的主要候选人?我们发现雏菊与否对盖亚理论重要吗?我们应该怎样寻找雏菊,我们应该加紧寻找吗?如何利用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制? ”<br />
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{{quotation|It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated functions, but possibly also that process of consumption as replacement which in biology we call metabolism, or growth. In such case we would have all the visible attributes of a living thing, which we do not realize to be such because it is too big, and its life processes too slow.| Stephan Harding | ''Animate Earth''.<ref>Harding, Stephan. ''Animate Earth Science, Intuition and Gaia''. Chelsea Green Publishing, 2006, p. 44. {{ISBN|1-933392-29-0}}</ref>}}<br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise entropy production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
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1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是一种向远离平衡的稳态演化的结果,这种平衡状态使熵产生最大化,克莱顿(2004)同意这样的说法:“自稳态行为可以从与行星反照率相关的MEP状态中产生”;“……一个如盖亚假说所述,处于MEP状态的生物地球很可能导致地球系统在长时间尺度上的近稳态行为。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。<br />
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Another influence for the Gaia hypothesis and the [[environmental movement]] in general came as a side effect of the [[Space Race]] between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph ''[[Earthrise]]'' taken by astronaut [[William Anders]] in 1968 during the [[Apollo 8]] mission became, through the [[Overview Effect]] an early symbol for the global ecology movement.<ref>[http://digitaljournalist.org/issue0309/lm11.html 100 Photographs that Changed the World by Life - The Digital Journalist]</ref><br />
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盖亚假说和[[环境运动]]的另一个总体影响来自苏联和美利坚合众国之间[[太空竞赛]]的副作用。在20世纪60年代,第一批进入太空的人类可以看到地球的整体面貌。1968年宇航员[[William Anders]]在[[Apollo 8]]任务期间拍摄的照片“[[地球升起]”,通过[[概述效果]]成为全球生态运动的早期标志<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<br />
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第四次关于盖亚假说的国际会议,由北弗吉尼亚地区公园管理局和其他机构主办,于2006年10月在弗吉尼亚州乔治梅森大学的阿灵顿校区举行。<br />
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===Formulation of the hypothesis假说形成===<br />
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[[File:James Lovelock in 2005.jpg|thumb|[[James Lovelock]], 2005]]<br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
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马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。Lynn Margulis是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the [[Jet Propulsion Laboratory]] in California on methods of detecting [[life on Mars (planet)|life on Mars]].<ref name="Lovelock1965">{{cite journal | author = Lovelock, J.E. | date = 1965 | title = A physical basis for life detection experiments | journal = [[Nature (journal)|Nature]] | volume = 207 | issue = 7 | pages = 568–570 | doi = 10.1038/207568a0 | pmid=5883628|bibcode = 1965Natur.207..568L | ref = harv}}</ref><ref>{{Cite web |url=http://www.jameslovelock.org/page4.html |title=Geophysiology |access-date=2007-05-05 |archive-url=https://web.archive.org/web/20070506073502/http://www.jameslovelock.org/page4.html |archive-date=2007-05-06 |url-status=dead }}</ref> The first paper to mention it was ''Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life'', co-authored with C.E. Giffin.<ref>{{cite journal | author1 = Lovelock, J.E. | author2 = Giffin, C.E. | date = 1969 | title = Planetary Atmospheres: Compositional and other changes associated with the presence of Life | journal = Advances in the Astronautical Sciences | volume = 25 | pages = 179–193 | isbn = 978-0-87703-028-7 | ref = harv}}</ref> A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the [[Pic du Midi de Bigorre|Pic du Midi observatory]], planets like Mars or Venus had atmospheres in [[chemical equilibrium]]. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
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这次会议将盖亚假说作为一种科学和隐喻的手段,来理解我们如何开始解决21世纪的问题,如气候变化和持续的环境破坏。<br />
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Lovelock formulated the ''Gaia Hypothesis'' in journal articles in 1972<ref name="J1972">{{cite journal | author = J. E. Lovelock | title = Gaia as seen through the atmosphere | date = 1972 | journal = [[Atmospheric Environment]] | volume = 6 | issue = 8 | pages = 579–580 | doi = 10.1016/0004-6981(72)90076-5 | ref = harv|bibcode = 1972AtmEn...6..579L }}</ref> and 1974,<ref name="lovelock1974" /> followed by a popularizing 1979 book ''Gaia: A new look at life on Earth''. An article in the ''[[New Scientist]]'' of February 6, 1975,<ref>Lovelock, John and Sidney Epton, (February 8, 1975). "The quest for Gaia". [https://books.google.com/books?id=pnV6UYEkU4YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false New Scientist], p. 304.</ref> and a popular book length version of the hypothesis, published in 1979 as ''The Quest for Gaia'', began to attract scientific and critical attention.<br />
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Lovelock called it first the Earth feedback hypothesis,<ref name="Lovelock01">{{harvnb|Lovelock, James|2001}}</ref> and it was a way to explain the fact that combinations of chemicals including [[oxygen]] and [[methane]] persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as Ford Doolittle, Richard Dawkins and Stephen Jay Gould. Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists, He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoietic or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole. With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<br />
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在最初几乎没有引起科学家的注意之后(从1969年到1977年) ,有一段时间,最初的盖亚假说受到了一些科学家的批评,如福特杜利特,理查德道金斯和史蒂芬·古尔德。洛夫洛克说,因为他的假说是以一位希腊女神的名字命名的,并得到许多非科学家的拥护,他想知道实现自我调节体内平衡的实际机制。在为盖亚辩护时,戴维•阿布拉姆认为,古尔德忽视了一个事实,即“机制”本身就是一个隐喻——尽管这个隐喻极其常见,而且往往不为人所知——这个隐喻让我们把自然和生命系统看作是由外部组织和建造的机器(而不是自动生成或自组织现象)。根据阿布拉姆的说法,机械隐喻使我们忽略了生命实体的活跃性或代表性,而盖亚假说的有机隐喻强调了生物群和整个生物圈的活跃性。关于盖亚的因果关系,洛夫洛克认为没有单一的机制是负责任的,各种已知机制之间的联系可能永远不会被人知道,这在生物学和生态学的其他领域是理所当然地被接受的,并且由于其他原因,特定的敌意是保留给他自己的假设的。<br />
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[[File:Lynn Margulis.jpg|thumb|left|[[Lynn Margulis]]]]<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of greedy reductionism in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<br />
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除了澄清他的语言和理解什么是生命形式,洛夫洛克自己把大部分的批评归因于他的批评者缺乏对非线性数学的理解,以及贪婪还原主义的线性化形式,在这种形式中,所有事件都必须立即归因于事件发生之前的特定原因。他还表示,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,以及一些自我调节现象可能无法在数学上解释。<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<ref>{{cite journal | first1=W.D. | last1=Hamilton | first2=T.M. | last2=Lenton | title=Spora and Gaia: how microbes fly with their clouds | journal=Ethology Ecology & Evolution | volume=10 | pages=1–16 | date=1998 | issue=1 | url=http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | format=PDF | doi=10.1080/08927014.1998.9522867 | ref=harv | url-status=dead | archiveurl=https://web.archive.org/web/20110723055017/http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | archivedate=2011-07-23 }}</ref><br />
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Evolutionary biologist W. D. Hamilton called the concept of Gaia Copernican, adding that it would take another Newton to explain how Gaian self-regulation takes place through Darwinian natural selection. More recently Ford Doolittle building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis. <br />
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进化生物学家W.D.Hamilton称盖亚假说为哥白尼式的概念,并补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。最近,Ford Doolittle在他和Inkpen的ITSNTS(这是歌手而不是歌曲)的建议中提出,差异持续性可以在自然选择进化中起到与差异生殖相似的作用,从而为自然选择理论和盖亚假说之间提供了一种可能的调和。 <br />
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In 1971 [[microbiologist]] Dr. [[Lynn Margulis]] joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet.<ref name="Turney, Jon 2003">{{cite book |author=Turney, Jon |title=Lovelock and Gaia: Signs of Life |publisher=Icon Books |location=UK |date=2003 |isbn=978-1-84046-458-0 |url-access=registration |url=https://archive.org/details/lovelockgaiasign0000turn }}</ref> The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of [[eukaryote|eukaryotic]] [[organelle]]s and her contributions to the [[endosymbiotic theory]], nowadays accepted. Margulis dedicated the last of eight chapters in her book, ''The Symbiotic Planet'', to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal Climatic Change in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it. to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background" The CLAW hypothesis, In 2009 the Medea hypothesis was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<br />
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盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论据是,生命对环境产生了有害或不稳定的影响,而不是采取行动加以调节。为了“令人不安地徘徊在污点隐喻、事实和虚假科学之间,我宁愿把盖亚假说牢牢地放在背景下。”爪假说,2009年提出的美狄亚假说:生命对行星条件有高度有害的(生物杀灭)影响,与盖亚假说直接相反。 <br />
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James Lovelock called his first proposal the ''Gaia hypothesis'' but has also used the term ''Gaia theory''. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments<ref name="J1990">{{cite journal | author = J. E. Lovelock | title = Hands up for the Gaia hypothesis | date = 1990 | journal = [[Nature (journal)|Nature]] | volume = 344 | issue = 6262 | pages = 100–2 | doi = 10.1038/344100a0|bibcode = 1990Natur.344..100L | ref = harv}}</ref> and provided a number of useful predictions.<ref name="Volk2003">{{cite book |author=Volk, Tyler |title=Gaia's Body: Toward a Physiology of Earth |publisher=[[MIT Press]] |location=Cambridge, Massachusetts |date=2003 |isbn=978-0-262-72042-7 }}</ref> In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating.<ref name="vanishing255"/><br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it". Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works". This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<br />
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2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新想法,并倡导一种整体的方法来研究地球”。在其他地方,他提出了自己的结论:“盖亚假说并不是我们这个世界如何运转的精确图像”。这种说法需要被理解为是指盖亚假说的“强”和“中”形式,生物群遵循的原则是使地球成为最佳(强度5)或有利于生命(强度4),或是作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化的盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释。<br />
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===First Gaia conference第一次盖亚会议===<br />
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In 1985, the first public symposium on the Gaia hypothesis, ''Is The Earth A Living Organism?'' was held at [[University of Massachusetts Amherst]], August 1–6.<ref>{{cite news |last=Joseph |first=Lawrence E. |title=Britain's Whole Earth Guru |work=The New York Times Magazine |date=November 23, 1986 |url=https://www.nytimes.com/1986/11/23/magazine/britain-s-whole-earth-guru.html |accessdate=1 December 2013}}</ref> The principal sponsor was the [[National Audubon Society]]. Speakers included James Lovelock, [[George Wald]], [[Mary Catherine Bateson]], [[Lewis Thomas]], [[John Todd (Canadian biologist)|John Todd]], Donald Michael, [[Christopher Bird]], [[Thomas Berry]], [[David Abram]], [[Michael A. Cohen|Michael Cohen]], and William Fields. Some 500 people attended.<ref>Bunyard, Peter (1996), "Gaia in Action: Science of the Living Earth" (Floris Books)</ref><br />
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1985年,关于盖亚假说的第一次公开研讨会,“地球是一个活的有机体吗?”在马萨诸塞大学阿默斯特举行 <br />
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===Second Gaia conference第二次盖亚会议===<br />
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In 1988, [[climatology|climatologist]] [[Stephen Schneider]] organised a conference of the [[American Geophysical Union]]. The first Chapman Conference on Gaia,<ref name="ReferenceB"/> was held in San Diego, California on March 7, 1988.<br />
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1988年,climatology和Stephen Schneider组织了一次美国地球物理联合会会议。关于盖亚假说的第一次查普曼会议 <br />
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During the "philosophical foundations" session of the conference, [[David Abram]] spoke on the influence of metaphor in science, and of the Gaia hypothesis as offering a new and potentially game-changing metaphorics, while [[James Kirchner]] criticised the Gaia hypothesis for its imprecision. Kirchner claimed that Lovelock and Margulis had not presented one Gaia hypothesis, but four -<br />
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在会议的“哲学基础”会议上,David Abram谈到了隐喻在科学中的影响,盖亚假说提供了一种新的、可能改变游戏规则的隐喻,而James Kirchner则批评盖亚假说的不精确性。基什纳声称,洛夫洛克和马古利斯提出的盖亚假说不是一个,而是四个- <br />
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* [[Coevolution|CoEvolutionary]] Gaia: that life and the environment had evolved in a coupled way. Kirchner claimed that this was already accepted scientifically and was not new.<br />
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* [[Homeostatic]] Gaia: that life maintained the stability of the natural environment, and that this stability enabled life to continue to exist.<br />
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* [[Geophysics|Geophysical]] Gaia: that the Gaia hypothesis generated interest in geophysical cycles and therefore led to interesting new research in terrestrial geophysical dynamics.<br />
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* Optimising Gaia: that Gaia shaped the planet in a way that made it an optimal environment for life as a whole. Kirchner claimed that this was not testable and therefore was not scientific.<br />
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盖亚:生命和环境是以耦合的方式进化的。基什内尔声称,这已经被科学界接受,并不是什么新鲜事。 <br />
盖亚:生命维持着自然环境的稳定,这种稳定性使生命得以继续存在。 <br />
盖亚:盖亚假说引起了人们对地球物理周期的兴趣,因此导致了地球物理动力学中有趣的新研究。 <br />
优化盖亚:盖亚塑造了地球,使之成为整个生命的最佳环境。基什内尔声称,这是不可测试的,因此是不科学的。 <br />
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Of Homeostatic Gaia, Kirchner recognised two alternatives. "Weak Gaia" asserted that life tends to make the environment stable for the flourishing of all life. "Strong Gaia" according to Kirchner, asserted that life tends to make the environment stable, ''to enable'' the flourishing of all life. Strong Gaia, Kirchner claimed, was untestable and therefore not scientific.<ref>{{cite journal | bibcode=1989RvGeo..27..223K | doi = 10.1029/RG027i002p00223 | title=The Gaia hypothesis: Can it be tested? | date=1989 | last1=Kirchner | first1=James W. | journal=Reviews of Geophysics | volume=27 | issue=2 | pages=223 | ref=harv}}</ref><br />
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基什内尔发现了两种选择“软弱的盖亚”断言,为了所有生命的繁衍,生命往往会使环境变得稳定根据基什内尔的说法,“强大的盖亚”断言,生命趋向于使环境稳定,“使”所有生命繁荣昌盛。基什内尔声称,强大的盖亚是不稳定的,因此不科学。 <br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the [[Daisyworld]] Model (and its modifications, above) as evidence against most of these criticisms.<ref name="daisyworld"/> Lovelock said that the Daisyworld model "demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways".<ref>{{cite journal | pmid=10968941 | date=2000 | last1=Lenton | first1=TM | last2=Lovelock | first2=JE | s2cid=5486128 | title=Daisyworld is Darwinian: Constraints on adaptation are important for planetary self-regulation | volume=206 | issue=1 | pages=109–14 | doi=10.1006/jtbi.2000.2105 | journal=Journal of Theoretical Biology | ref=harv}}</ref><br />
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然而,洛夫洛克和其他支持盖亚假说的科学家,确实试图反驳这种说法,即这个假设是不科学的,因为不可能通过受控实验来检验它。例如,针对盖亚假说是目的论的指控,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修改,洛夫洛克说,雏菊世界模型“证明了全球环境的自我调节可以通过不同方式改变当地环境的生活类型之间的竞争产生”。 <br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of [[teleology|teleologism]] ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,没有声称盖亚有意或有意识地维持着生命生存所需的复杂平衡。看来盖亚假说“故意”的行为是他最受欢迎的第一本书中的隐喻性陈述,并不是字面意思。盖亚假说的这一新说法更为科学界所接受。在这次会议之后,[[目的论|目的论]]的大多数指控都停止了。<br />
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===Third Gaia conference第三次盖亚会议===<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000,<ref>{{cite news|last=Simón|first=Federico|title=GEOLOGÍA Enfoque multidisciplinar La hipótesis Gaia madura en Valencia con los últimos avances científicos|journal=El País|date=21 June 2000|url=http://elpais.com/diario/2000/06/21/futuro/961538404_850215.html|accessdate=1 December 2013|language=spanish}}</ref> the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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The major questions were:<ref>{{cite web|title=General Information Chapman Conference on the Gaia Hypothesis University of Valencia Valencia, Spain June 19-23, 2000 (Monday through Friday) |url=http://www.agu.org/meetings/chapman/chapman_archive/cc00bcall.html |work=AGU Meetings |accessdate=7 January 2017 |author=American Geophysical Union }}</ref><br />
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# "How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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# "What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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# "How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
“被称为盖亚的全球生物地球化学/气候系统是如何随时间变化的?它的历史是什么?盖亚能在一个时间尺度上保持系统的稳定性,但在较长的时间尺度上仍能经历向量变化吗?如何利用地质记录来检验这些问题?” <br />
“盖亚假说的结构是什么?反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由任何给定时间正在进行的任何学科研究实际确定的,还是有一组应该被视为最真实的部分来理解盖亚假说,即随着时间的推移包含进化中的有机体?盖亚系统的这些不同部分之间的反馈是什么?物质的接近封闭对盖亚作为全球生态系统的结构和生命的生产力意味着什么?” <br />
“盖亚假说过程和现象的模型如何与现实联系起来,它们如何帮助解决和理解盖亚假说?雏菊世界的结果如何传递到真实世界?“雏菊”的主要候选对象是什么?我们是否找到雏菊对盖亚理论有意义吗?我们应该如何寻找雏菊,我们应该加强搜索?如何使用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制?” <br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise [[entropy]] production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是朝着使熵产量最大化的远非平衡的状态演化的结果,克莱顿(2004)同意这样的说法:“自稳行为可以从与行星反照率相关的MEP状态中产生”;“……生物地球在MEP状态下的行为很可能导致地球系统在长时间尺度上的近稳态行为,正如盖亚假说所述”。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。 <br />
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===Fourth Gaia conference第四次盖亚会议===<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<ref>{{cite web|title=Gaia Theory Conference at George Mason University Law School|url=http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|accessdate=1 December 2013|author=Official Site of Arlington County Virginia|archive-url=https://web.archive.org/web/20131203043657/http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|archive-date=2013-12-03|url-status=dead}}</ref><br />
第四届盖亚假说国际会议于2006年10月在乔治梅森大学阿灵顿分校举行,会议由北弗吉尼亚州公园管理局和其他机构赞助。 <br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。林恩 马古拉斯是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
这次会议将盖亚假说作为一种科学和隐喻来探讨,以此来理解我们如何着手解决21世纪的问题,如气候变化和持续的环境破坏<br />
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==Criticism批评==<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as [[Ford Doolittle]],<ref name=":1">{{Cite journal|last=Doolittle|first=W. F.|year=1981|title=Is Nature Really Motherly|url=|journal=The Coevolution Quarterly|volume=Spring|pages=58–63|via=}}</ref> [[Richard Dawkins]]<ref name=":2">{{Cite book|title=The Extended Phenotype: the Long Reach of the Gene|last=Dawkins|first=Richard|publisher=Oxford University Press|year=1982|isbn=978-0-19-286088-0|location=|pages=}}</ref> and [[Stephen Jay Gould]].<ref name="ReferenceB">Turney, Jon. "Lovelock and Gaia: Signs of Life" (Revolutions in Science)</ref> Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists,<ref name="Lovelock01"/> the Gaia hypothesis was interpreted as a [[neo-Pagan]] [[religion]]. Many scientists in particular also criticised the approach taken in his popular book ''Gaia, a New Look at Life on Earth'' for being [[teleology|teleological]]—a belief that things are purposeful and aimed towards a goal. Responding to this critique in 1990, Lovelock stated, "Nowhere in our writings do we express the idea that planetary self-regulation is purposeful, or involves foresight or planning by the [[biota (ecology)|biota]]".<br />
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最初很少受到科学家的关注(从1969年到1977年),此后的一段时间里,最初的盖亚假说受到了许多科学家的批评,比如福特·杜利特,理查德·道金斯和斯蒂芬·杰伊·古尔德洛夫洛克曾说过,因为他的假设是以希腊女神的名字命名的,新盖亚假说被许多非教派的科学家解释为。特别是许多科学家还批评了他的畅销书《盖亚》中采用的方法,认为地球上的生命是目的论的,认为事物是有目的的,是有目的的。洛夫洛克在1990年回应这一批评时说:“在我们的著作中我们没有任何地方表达行星自我调节是有目的的,或涉及生物群的远见或计划。”<br />
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[[Stephen Jay Gould]] criticised Gaia as being "a metaphor, not a mechanism."<ref name="Gould 1997">{{cite journal |author=Gould S.J. |title=Kropotkin was no crackpot |journal=Natural History |volume=106 |pages=12–21 |date=June 1997 |url=http://libcom.org/library/kropotkin-was-no-crackpot |ref=harv}}</ref> He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as [[autopoiesis|autopoietic]] or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole.<ref>Abram, D. (1988) "The Mechanical and the Organic: On the Impact of Metaphor in Science" in Scientists on Gaia, edited by Stephen Schneider and Penelope Boston, Cambridge, Massachusetts: MIT Press, 1991</ref><ref>{{cite web|url=http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |title=The Mechanical and the Organic |accessdate=August 27, 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120223165936/http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |archivedate=February 23, 2012 }}</ref> With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<ref name="Lovelock, James 2001">Lovelock, James (2001), ''Homage to Gaia: The Life of an Independent Scientist'' (Oxford University Press)</ref><br />
史蒂芬·杰伊·古尔德批评盖亚假说是“一种隐喻,而不是一种机制。”他想知道实现自我调节内稳态的实际机制。在为盖亚假说辩护时,大卫·艾布拉姆认为古尔德忽略了一个事实,即“机制”本身就是一个隐喻——尽管这是一个非常常见且常常未被人认识的隐喻——它使我们把自然和生命系统看作是从外部组织和建造的机器(而不是自动或自组织的)现象)。艾布拉姆认为,机械隐喻使我们忽视了生命实体的活动性或能动性,而盖亚假说的有机体隐喻强调了生物群和生物圈作为一个整体的能动性。关于盖亚假说的因果关系,洛夫洛克认为没有单一的机制负责各种已知机制之间的联系可能永远不为人所知,这一点在其他生物学和生态学领域都是理所当然的,而具体的敌意是出于其他原因留给他自己的假设的<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of [[greedy reductionism]] in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<ref name="Lovelock, James 2001"/><br />
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除了澄清自己的语言和对生命形式的理解之外,洛夫洛克自己将大部分批评归咎于批评家对非线性数学缺乏理解,以及贪婪还原论的线性化形式,在这种形式中,所有事件都必须在事实发生之前立即归因于特定的原因。他还指出,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,有些自我调节的现象可能无法用数学解释 <br />
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===Natural selection and evolution自然选择和进化===<br />
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Lovelock has suggested that global biological feedback mechanisms could evolve by [[natural selection]], stating that organisms that improve their environment for their survival do better than those that damage their environment. However, in the early 1980s, [[Ford Doolittle|W. Ford Doolittle]] and [[Richard Dawkins]] separately argued against this aspect of Gaia. Doolittle argued that nothing in the [[genome]] of individual organisms could provide the feedback mechanisms proposed by Lovelock, and therefore the Gaia hypothesis proposed no plausible mechanism and was unscientific.<ref name=":1" /> Dawkins meanwhile stated that for organisms to act in concert would require foresight and planning, which is contrary to the current scientific understanding of evolution.<ref name=":2" /> Like Doolittle, he also rejected the possibility that feedback loops could stabilize the system.<br />
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洛夫洛克提出,全球生物反馈机制可以通过自然选择而进化,他指出,为生存而改善环境的生物比那些破坏环境的生物做得更好。然而,在20世纪80年代早期,W·福特·杜立德和理查德·道金斯分别反对盖亚假说的这一方面。杜立德认为,单个生物体的基因组中没有任何东西能够提供洛夫洛克提出的反馈机制,因此盖亚假说没有提出任何合理的机制,是不科学的。道金斯同时指出,要使有机体协同行动,就需要有远见和计划,这与当前科学界对进化论的理解相悖和杜立德一样,他也拒绝了反馈回路可以稳定系统的可能性。<br />
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[[Lynn Margulis]], a microbiologist who collaborated with Lovelock in supporting the Gaia hypothesis, argued in 1999, that "[[Charles Darwin|Darwin]]'s grand vision was not wrong, only incomplete. In accentuating the direct competition between individuals for resources as the primary selection mechanism, Darwin (and especially his followers) created the impression that the environment was simply a static arena". She wrote that the composition of the Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in [[homeostasis]], but those set points change with time.<ref name="ReferenceA">Margulis, Lynn. Symbiotic Planet: A New Look At Evolution. Houston: Basic Book 1999</ref><br />
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Lynn Margulis,一位与Lovelock合作支持盖亚假说的微生物学家,在1999年指出,“达尔文的宏伟愿景没有错,只是不完整。达尔文(特别是他的追随者)强调个人之间对资源的直接竞争是主要的选择机制,他给人的印象是环境只是一个静态的竞技场”。她写道,地球大气、水圈和岩石圈的组成都是围绕着“设定点”来调节的,就像在体内平衡中一样,但是这些设定点会随着时间的推移而变化 <br />
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Evolutionary biologist [[W. D. Hamilton]] called the concept of Gaia [[Nicolaus Copernicus|Copernican]], adding that it would take another [[Isaac Newton|Newton]] to explain how Gaian self-regulation takes place through Darwinian [[natural selection]].<ref name=vanish09>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, pp. 195-197. {{ISBN|978-0-465-01549-8}}</ref>{{better source|date=September 2012|reason=it should be possible to find the original place where Hamilton said this}} More recently [[Ford Doolittle]] building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal<ref name="ITSNTS">Doolittle WF, Inkpen SA. Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking. [https://www.pnas.org/content/115/16/4006 PNAS April 17, 2018 115 (16)] 4006-4014 </ref> proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis<ref name="Darwinizing Gaia">Doolittle WF. Darwinizing Gaia. [https://doi.org/10.1016/j.jtbi.2017.02.015 Journal of Theoretical BiologyVolume 434], 7 December 2017, Pages 11-19 </ref>. <br />
进化生物学家汉密尔顿称盖亚哥白尼为盖亚的概念,他补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。通过自然选择在进化过程中的繁殖,从而为自然选择理论和盖亚假说提供了可能的调和。 <br />
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===Criticism in the 21st century21世纪的批评===<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal ''Climatic Change'' in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it.<ref name="kirchner2002"/><ref name="volk2002"/> Several recent books have criticised the Gaia hypothesis, expressing views ranging from "... the Gaia hypothesis lacks unambiguous observational support and has significant theoretical difficulties"<ref>{{cite book |last=Waltham |first=David |authorlink=David Waltham |date=2014 |title=Lucky Planet: Why Earth is Exceptional – and What that Means for Life in the Universe |url=https://archive.org/details/luckyplanetwhyea0000walt |location= |publisher=Icon Books |page= |isbn=9781848316560 |accessdate= |url-access=registration }}</ref> to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background"<ref name="beerling2007"/> to "The Gaia hypothesis is supported neither by evolutionary theory nor by the empirical evidence of the geological record".<ref>{{cite book |last1=Cockell |first1=Charles |authorlink1=Charles Cockell |last2=Corfield |first2=Richard |last3=Dise |first3= Nancy |last4=Edwards |first4=Neil |last5=Harris |first5=Nigel |date=2008 |title= An Introduction to the Earth-Life System |url= http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/palaeontology-and-life-history/introduction-earth-life-system |location=Cambridge (UK) |publisher= Cambridge University Press |page= |isbn= 9780521729536 |accessdate= }}</ref> The [[CLAW hypothesis]],<ref name="CLAW87" /> initially suggested as a potential example of direct Gaian feedback, has subsequently been found to be less credible as understanding of [[cloud condensation nuclei]] has improved.<ref>{{Citation |last1= Quinn |first1=P.K. |last2= Bates |first2=T.S. |title =The case against climate regulation via oceanic phytoplankton sulphur emissions |journal =Nature |volume=480 |issue=7375 |pages =51–56 |date = 2011 |doi=10.1038/nature10580|bibcode = 2011Natur.480...51Q |pmid=22129724|url=https://zenodo.org/record/1233319 }}</ref> In 2009 the [[Medea hypothesis]] was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<ref>Peter Ward (2009), ''The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?'', {{ISBN|0-691-13075-2}}</ref><br />
盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论点是在许多例子中,生命对环境产生了有害或不稳定的影响,而不是采取行动来调节它。最近几本书批评了盖亚假说,譬如“盖亚假说缺乏明确的观察支持,并且有重大的理论困难”“(盖亚假说)令人不安地徘徊在污点、隐喻、事实和虚假科学之间,我宁愿把盖亚牢牢地放在原有的背景中”“盖亚假说既没有进化论的支持,也没有地质记录的经验证据的支持。爪假说最初被认为是盖亚直接反馈的一个潜在例子,后来被发现对云的理解不那么可信凝聚核已经得到了改善。2009年,美狄亚假说提出:生命对行星的状况非常有害,这与盖亚假说直接相反。 <br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it".<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=209 |isbn=9780691121581 |accessdate= }}</ref> Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works".<ref>{{Citation |last= Tyrrell |first = Toby |title =Gaia: the verdict is… |journal = New Scientist |volume = 220 |issue = 2940 |pages = 30–31 |date= 26 October 2013 |doi=10.1016/s0262-4079(13)62532-4}}</ref> This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=208 |isbn=9780691121581 |accessdate= }}</ref><br />
2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新思想,并倡导一种研究地球的整体方法。”在其他地方,他提出了自己的结论:“盖亚假说并不是一个关于如何进行的精确描述我们的世界在运转。”这种说法需要被理解为是指盖亚假说的“强大”和“温和”形式,生物群遵循的原则是使地球处于最佳状态(强度5)或有利于生命(强度4),或者它作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化德盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释 <br />
Category:Cybernetics<br />
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类别: 控制论<br />
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Category:Ecological theories<br />
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范畴: 生态学理论<br />
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==See also==<br />
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Category:Superorganisms<br />
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类别: 超级有机体<br />
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{{Portal|Environment|Earth sciences|Geography}}<br />
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Category:Climate change feedbacks<br />
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类别: 气候变化反馈<br />
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Category:1965 introductions<br />
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类别: 1965年引言<br />
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* {{annotated link|Biocoenosis}}<br />
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Category:Biogeochemistry<br />
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* {{annotated link|Earth science}}<br />
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Category:Biological hypotheses<br />
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Category:Astronomical hypotheses<br />
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Category:Meteorological hypotheses<br />
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类别: 气象假说<br />
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<small>This page was moved from [[wikipedia:en:Gaia hypothesis]]. Its edit history can be viewed at [[盖亚假说/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%96%E4%BA%9A%E5%81%87%E8%AF%B4&diff=21575盖亚假说2021-02-04T13:10:12Z<p>Vicky:/* Regulation of oxygen in the atmosphere大气层的氧气调节 */</p>
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<div>此词条由Henry第一次翻译。<br />
已由三奇同学完成校对。<br />
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{{short description|Hypothesis that living organisms interact with their surroundings in a self-regulating system}}<br />
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[[File:The Earth seen from Apollo 17.jpg|thumb|The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth]]'s conditions, as the Earth is the only planet currently known to harbour life (''[[The Blue Marble]]'', 1972 [[Apollo 17]] photograph)]]<br />
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The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth's conditions, as the Earth is the only planet currently known to harbour life (The Blue Marble, 1972 Apollo 17 photograph)]]<br />
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对行星可居住性的研究主要基于对[[地球条件]的了解进行推断,因为地球是目前已知的唯一一颗拥有生命的行星 <br />
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The '''Gaia hypothesis''' {{IPAc-en|ˈ|ɡ|aɪ|.|ə}}, also known as the '''Gaia theory''' or the '''Gaia principle''', proposes that living [[organism]]s interact with their [[Inorganic compound|inorganic]] surroundings on [[Earth]] to form a [[Synergy|synergistic]] and [[Homeostasis|self-regulating]], [[complex system]] that helps to maintain and perpetuate the conditions for [[life]] on the planet.<br />
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The Gaia hypothesis , also known as the Gaia theory or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.<br />
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盖亚假说(又称盖亚理论或盖亚原理)认为,生物体与地球上的无机环境相互作用,形成一个协同和自我调节的复杂系统,有助于维持和延续地球上的生命条件。<br />
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The hypothesis was formulated by the chemist [[James Lovelock]]<ref name="J1972" /> and co-developed by the microbiologist [[Lynn Margulis]] in the 1970s.<ref name="lovelock1974">{{cite journal|last1=Lovelock|first1=J.E.|last2=Margulis|first2=L.|title=Atmospheric homeostasis by and for the biosphere: the Gaia hypothesis|journal=Tellus|date=1974|volume=26|series=Series A|issue=1–2|pages=2–10|doi=10.1111/j.2153-3490.1974.tb01946.x|publisher=International Meteorological Institute|location=Stockholm|issn=1600-0870|ref=harv|bibcode=1974Tell...26....2L}}</ref> Lovelock named the idea after [[Gaia]], the primordial goddess who personified the Earth in [[Greek mythology]]. In 2006, the [[Geological Society of London]] awarded Lovelock the [[Wollaston Medal]] in part for his work on the Gaia hypothesis.<ref>{{cite web|title=Wollaston Award Lovelock|url=https://www.geolsoc.org.uk/About/History/Awards-Citations-Replies-2001-Onwards/2006-Awards-Citations-Replies|accessdate=19 October 2015}}</ref><br />
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The hypothesis was formulated by the chemist James Lovelock Lovelock named the idea after Gaia, the primordial goddess who personified the Earth in Greek mythology. In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.<br />
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这个假设是由化学家詹姆斯·洛夫洛克提出的,他以希腊神话中地球的化身盖亚的名字命名了这个想法。2006年,伦敦地质学会授予洛夫洛克沃拉斯顿勋章,以表彰他在<font color="#ff8000"> 盖亚假说Gaia hypothesis</font>方面的工作。 <br />
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Topics related to the hypothesis include how the [[biosphere]] and the [[evolution]] of organisms affect the stability of [[global temperature]], [[salinity]] of [[seawater]], [[atmospheric oxygen]] levels, the maintenance of a [[hydrosphere]] of liquid water and other environmental variables that affect the [[habitability of Earth]].<br />
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Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenance of a hydrosphere of liquid water and other environmental variables that affect the habitability of Earth.<br />
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与该假设有关的主题包括生物圈和生物体的进化如何影响全球温度的稳定性、海水的盐度、大气中的氧含量、液态水水圈的维持以及其他影响地球宜居性的环境变量。<br />
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The Gaia hypothesis was initially criticized for being [[teleological]] and against the principles of [[natural selection]], but later refinements aligned the Gaia hypothesis with ideas from fields such as [[Earth system science]], [[biogeochemistry]] and [[systems ecology]].<ref name="Turney, Jon 2003"/><ref name="Schwartzman2002">{{cite book |author=Schwartzman, David |title=Life, Temperature, and the Earth: The Self-Organizing Biosphere |publisher=Columbia University Press |date=2002 |isbn=978-0-231-10213-1 }}</ref><ref>Gribbin, John (1990), "Hothouse earth: The greenhouse effect and Gaia" (Weidenfeld & Nicolson)</ref> Lovelock also once described the "geophysiology" of the Earth.<ref name="agesofgaia">Lovelock, James, (1995) "The Ages of Gaia: A Biography of Our Living Earth" (W.W.Norton & Co)</ref>{{Explain|date=December 2017}} Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<ref name="kirchner2002">{{Citation |last= Kirchner |first = James W. |title =Toward a future for Gaia theory |journal=[[Climatic Change (journal)|Climatic Change]] |volume = 52 |issue = 4 |pages = 391–408 |date = 2002 | doi = 10.1023/a:1014237331082 }}</ref><ref name="volk2002">{{Citation |last= Volk |first = Tyler |title =The Gaia hypothesis: fact, theory, and wishful thinking |journal = Climatic Change |volume = 52 |issue = 4 |pages = 423–430 |date = 2002 | doi = 10.1023/a:1014218227825 }}</ref><ref name="beerling2007">{{cite book |last=Beerling |first=David |authorlink=David Beerling|date=2007 |title=The Emerald Planet: How plants changed Earth's history |url=http://ukcatalogue.oup.com/product/9780192806024.do |location=Oxford|publisher=Oxford University Press |page= |isbn= 978-0-19-280602-4 |accessdate= }}</ref><br />
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The Gaia hypothesis was initially criticized for being teleological and against the principles of natural selection, but later refinements aligned the Gaia hypothesis with ideas from fields such as Earth system science, biogeochemistry and systems ecology. Lovelock also once described the "geophysiology" of the Earth. Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<br />
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盖亚假说最初被诟病为目的论、反对自然选择的原则,但后来的改进使盖亚假说与来自地球系统科学、生物地球化学和系统生态学等领域的观点相一致。洛夫洛克还曾经描述过地球的“地球物理学”。即便如此,盖亚假说仍然受到一些批评,今天许多科学家认为只有少数证据支持这一理论,或与现有的证据相矛盾。<br />
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==Overview总览==<br />
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Gaian hypotheses suggest that organisms [[Co-evolution|co-evolve]] with their environment: that is, they "influence their [[abiotic]] environment, and that environment in turn influences the [[Biota (ecology)|biota]] by [[Darwinism|Darwinian process]]". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early [[Bacteria|thermo-acido-philic]] and [[methanogenic bacteria]] towards the oxygen-enriched [[atmosphere]] today that supports more [[Phanerozoic|complex life]].<br />
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Gaian hypotheses suggest that organisms co-evolve with their environment: that is, they "influence their abiotic environment, and that environment in turn influences the biota by Darwinian process". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early thermo-acido-philic and methanogenic bacteria towards the oxygen-enriched atmosphere today that supports more complex life.<br />
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盖亚假说认为,生物体与其环境共同进化。也就是说,生物“影响它们的非生物环境,而环境反过来又通过自然选择的过程影响生物群”。Lovelock(1995)在他的第二本书中提供了证据,展示了从早期嗜酸、产甲烷细菌的世界向今天支持更复杂生命的富氧大气的进化。<br />
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A reduced version of the hypothesis has been called "influential Gaia"<ref name=":02">{{Cite journal|last=Lapenis|first=Andrei G.|year=2002|title=Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?|url=|journal=The Professional Geographer|volume=54 |issue=3|pages=379–391|via=[Peer Reviewed Journal]|doi=10.1111/0033-0124.00337}}</ref> in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the [[Biota (ecology)|biota]] influence certain aspects of the abiotic world, e.g. [[temperature]] and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<ref name=":02" /> and biogeochemical processes. An example is how the activity of [[Photosynthesis|photosynthetic]] bacteria during Precambrian times completely modified the [[Earth's atmosphere|Earth atmosphere]] to turn it aerobic, and thus supports the evolution of life (in particular [[eukaryotic]] life).<br />
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A reduced version of the hypothesis has been called "influential Gaia" in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the biota influence certain aspects of the abiotic world, e.g. temperature and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<br />
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在《生物圈的定向进化: 生物地球化学选择还是盖亚? 》一书中,这一假说的简化版被称为“有影响力的盖亚”。安德烈·G·拉佩尼斯在这本书中指出生物影响着非生物世界的温度和大气等多个方面。这本书不是一个人的工作,而是一群俄罗斯科研人员的成果合并成这个通过同行评议的出版物。它通过“微观力量”阐述了生命与环境的共同进化。<br />
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Since barriers existed throughout the twentieth century between Russia and the rest of the world, it is only relatively recently that the early Russian scientists who introduced concepts overlapping the Gaia hypothesis have become better known to the Western scientific community.<ref name=":02" /> These scientists include [[Piotr Kropotkin|Piotr Alekseevich Kropotkin]] (1842–1921) (although he spent much of his professional life outside Russia), Vasil’evich Rizpolozhensky (1847–1918), [[Vladimir Ivanovich Vernadsky]] (1863–1945), and Vladimir Alexandrovich Kostitzin (1886–1963).<br />
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由于二十世纪苏联与西方国家存在隔阂,直到最近,在盖亚假说中引进重叠概念的早期苏联科学家才为西方科学界所熟知。<br />
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The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<br />
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盖亚假说认为,地球是一个自我调节的复杂系统,包括生物圈、大气层、水圈和土壤圈,作为一个进化的系统紧密结合在一起。这个假说认为,这个被称为盖亚的系统作为整体,寻求适合当代生命的物理和化学环境。<br />
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Biologists and Earth scientists usually view the factors that stabilize the characteristics of a period as an undirected [[emergent property]] or [[entelechy]] of the system; as each individual species pursues its own self-interest, for example, their combined actiYons may have counterbalancing effects on environmental change. Opponents of this view sometimes reference examples of events that resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth's atmosphere from a [[reducing environment]] to an [[oxygen]]-rich one at the end of the [[Archean|Archaean]] and the beginning of the [[Proterozoic]] periods.<br />
生物学家和地球科学家通常将平衡一个时期的特征的因素视为系统的无方向[[涌现属性]]或[[有目的行为]];例如,由于每个物种都追求自身利益,它们的联合行动可能对环境变化产生抵消作用。反对这一观点的人有时会举出一些导致了巨大变化而非平衡的事件作为反例,例如在[[太古宙|太古代]]末期和[[元古代]]时期开始时,地球大气从[[还原环境]]转变为富含[[氧气]]。 <br />
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Gaia evolves through a cybernetic feedback system operated unconsciously by the biota, leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially microorganisms, with inorganic elements. These processes establish a global control system that regulates Earth's surface temperature, atmosphere composition and ocean salinity, powered by the global thermodynamic disequilibrium state of the Earth system.<!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
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盖亚通过一个由生物群无意识操作的控制论反馈系统实现进化,在完全的内稳态中广泛获得稳定的可居住条件。地球表面的许多过程对生命的保障条件至关重要,这些过程依赖于生命形式,特别是微生物与无机元素的相互作用。这些过程建立了一个全球控制系统,由地球系统的全球热力学不平衡状态提供动力,调节地球表面温度、大气成分和海洋盐度。<br />
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Less accepted versions of the hypothesis claim that changes in the biosphere are brought about through the [[Superorganism|coordination of living organisms]] and maintain those conditions through [[homeostasis]]. In some versions of [[Gaia philosophy]], all lifeforms are considered part of one single living planetary being called ''Gaia''. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the [[Coevolution|coevolving]] diversity of living organisms.<br />
一种不太被接受的假说声称生物圈的变化是通过[[超级有机体|生物体的协调]]来实现的,并通过[[内稳态]]来维持这些条件。在一些版本的[[盖亚哲学]]中,所有的生命形式都是一个被称为“盖亚”的生命行星的一部分。在这种观点下,大气、海洋和地壳将是盖亚通过生物多样性进行干预的结果。 <br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of biogeochemistry, and it is being investigated also in other fields like Earth system science. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<br />
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以前在生物地球化学领域已经观察到受生命形式影响的行星内稳态的存在,而且地球系统科学等其他领域也在研究这一现象。盖亚假说的原创性依赖于这样一种观点: 即使地球或外部事件威胁到内稳态平衡,盖亚也会为了保持生命的最佳状态而积极追求这种平衡。<br />
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The Gaia hypothesis was an influence on the [[deep ecology]] movement.<ref>David Landis Barnhill, Roger S. Gottlieb (eds.), ''Deep Ecology and World Religions: New Essays on Sacred Ground'', SUNY Press, 2010, p. 32.</ref><br />
盖亚假说对[[深层生态学]]运动产生了影响 <br />
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==Details细节==<br />
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Rob Rohde's palaeotemperature graphs<br />
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罗布·罗德的古温度图<br />
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The Gaia hypothesis posits that the Earth is a self-regulating [[complex system]] involving the [[biosphere]], the [[Earth's atmosphere|atmosphere]], the [[hydrosphere]]s and the [[pedosphere]], tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<ref name="vanishing255">Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 255. {{ISBN|978-0-465-01549-8}}</ref><br />
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盖亚假说假设地球是一个自我调节的[[复杂系统]],包括[[生物圈]]、[[地球大气|大气]]、[[水圈]]和[[土壤圈]],作为一个进化系统紧密耦合。该假说认为,这个系统作为一个整体,称为盖亚,寻求一个最适合当代生活的物理和化学环境 <br />
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Since life started on Earth, the energy provided by the Sun has increased by 25% to 30%; however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on Titan. research has suggested that "oxygen shocks" and reduced methane levels led, during the Huronian, Sturtian and Marinoan/Varanger Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre Phanerozoic biosphere to fully self-regulate.<br />
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自从地球上有生命以来,太阳提供的能量增加了25%到30%;然而,地球表面温度一直保持在适宜居住的水平上,不曾突破上限或是下限。洛夫洛克还假设,产甲烷菌在早期大气中产生了较高水平的甲烷,这与在石化烟雾中发现的成分相似,在某些方面与土卫六上的大气相似。研究表明,在休伦期、斯图尔特期和马里诺/瓦朗格冰期,“氧冲击”和甲烷含量降低导致世界几乎变成了一个坚实的“雪球”。这些时代是前显生宙生物圈完全拥有自我调节能力的证据。<br />
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Gaia evolves through a [[Cybernetic#In biology|cybernetic]] [[feedback]] system operated unconsciously by the [[biota (ecology)|biota]], leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially [[microorganisms]], with inorganic elements. These processes establish a global control system that regulates Earth's [[Sea surface temperature|surface temperature]], [[atmosphere composition]] and [[ocean]] [[salinity]], powered by the global thermodynamic disequilibrium state of the Earth system.<ref>Kleidon, Axel. ''How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?''. Article submitted to the ''Philosophical Transactions of the Royal Society'' on Thu, 10 Mar 2011</ref><!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
盖亚通过一个[[控制论|生物学|控制论]][[反馈]]系统在[[生物群(生态学)|生物群]]的无意识运作中实现进化,导致在完全的内稳态中广泛存在稳定的可居住条件。地球表面对生命条件至关重要的许多过程都依赖于生物,特别是[微生物]与无机元素的相互作用。这些过程建立了一个全球控制系统,调节地球的[[海表温度|表面温度]]、[[大气组成]]和[[海洋]][[盐度]],其动力来自地球系统的全球热力学不平衡状态。<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
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温室气体CO<sub>2</sub>的处理在维持地球温度在可居住范围内起着关键作用(解释详见下文)。<br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of [[biogeochemistry]], and it is being investigated also in other fields like [[Earth system science]]. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 179. {{ISBN|978-0-465-01549-8}}</ref><br />
受生命形式影响的行星内稳态的存在,以前在[[生物地球化学]]领域就已被观察到,而且其他领域,如[[地球系统科学]]也在研究这种稳态。盖亚假说的独创性依赖于这样一种观点,即盖亚积极追求这种内平衡,以保持维护生命的最佳状态,即使是在地球或外部事件威胁它们的时候。<br />
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The CLAW hypothesis, inspired by the Gaia hypothesis, proposes a feedback loop that operates between ocean ecosystems and the Earth's climate. The hypothesis specifically proposes that particular phytoplankton that produce dimethyl sulfide are responsive to variations in climate forcing, and that these responses lead to a negative feedback loop that acts to stabilise the temperature of the Earth's atmosphere.<br />
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受盖亚假说的启发,CLAW 假说提出了一个在海洋生态系统和地球气候之间运行的反馈回路。该假说特别提出,产生二甲硫醚的浮游植物对气候变化有反应,这些反应导致了一个负反馈循环,稳定了地球大气的温度。<br />
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===Regulation of global surface temperature地球表面温度的调控===<br />
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[[File:All palaeotemps.png|thumb|480px|Rob Rohde's palaeotemperature graphs]]<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of greenhouse gases may cause negative feedbacks in the environment to become positive feedback. Lovelock has stated that this could bring an extremely accelerated global warming, but he has since stated the effects will likely occur more slowly.<br />
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目前,人口的增加及其活动对环境的影响,例如温室气体的增加,可能导致环境中的负反馈成为正反馈。洛夫洛克表示,这可能会极大地加速全球变暖,但他后来又表示,这种影响也可能发生得更慢。<br />
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{{See also|Paleoclimatology}}<br />
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Since life started on Earth, the energy provided by the [[Sun]] has increased by 25% to 30%;<ref name="Owen1979">{{cite journal | author = Owen, T. | author2 = Cess, R.D. | author3 = Ramanathan, V. | date = 1979 | title = Earth: An enhanced carbon dioxide greenhouse to compensate for reduced solar luminosity | journal = [[Nature (journal)|Nature]] | volume = 277 | pages = 640–2 | doi = 10.1038/277640a0 | issue=5698 | bibcode = 1979Natur.277..640O | ref = harv }}</ref> however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on [[Titan (moon)|Titan]].<ref name="agesofgaia"/> This, he suggests tended to screen out ultraviolet until the formation of the ozone screen, maintaining a degree of homeostasis. However, the [[Snowball Earth]]<ref>Hoffman, P.F. 2001. [http://www.snowballearth.org ''Snowball Earth theory'']</ref> research has suggested that "oxygen shocks" and reduced methane levels led, during the [[Huronian]], [[Sturtian]] and [[Marinoan]]/[[Cryogenian|Varanger]] Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre [[Phanerozoic]] biosphere to fully self-regulate.<br />
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Plots from a standard black and white [[Daisyworld simulation]]<br />
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从一个标准的黑白图[[雏菊世界模拟]]<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
说明了在温室气体维持低于临界温度的过程中,CO2起着至关重要的作用。 <br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic group selection and cooperation between organisms, James Lovelock and Andrew Watson developed a mathematical model, Daisyworld, in which ecological competition underpinned planetary temperature regulation.<br />
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有人批评盖亚假说似乎需要有机体之间不切实际的群体选择与合作,为了回应这种批评,James Lovelock 和 Andrew Watson建立了一个数学模型---- 雏菊世界,其中生态竞争支撑着地。<br />
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The [[CLAW hypothesis]], inspired by the Gaia hypothesis, proposes a [[feedback|feedback loop]] that operates between [[ocean]] [[ecosystem]]s and the [[Earth]]'s [[climate]].<ref name="CLAW87">{{cite journal |doi=10.1038/326655a0 |author=[[Robert Jay Charlson|Charlson, R. J.]], [[James Lovelock|Lovelock, J. E]], Andreae, M. O. and Warren, S. G. |title=Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate |journal=Nature |volume=326 |issue=6114 |pages=655–661 |date=1987 |bibcode=1987Natur.326..655C |ref=harv }}</ref> The [[hypothesis]] specifically proposes that particular [[phytoplankton]] that produce [[dimethyl sulfide]] are responsive to variations in [[climate forcing]], and that these responses lead to a [[negative feedback|negative feedback loop]] that acts to stabilise the [[temperature]] of the [[Earth's atmosphere]].<br />
受到盖亚假说启发的[[爪假说]]提出了一个在[[海洋]][[生态系统]]和[[地球]]的[[气候]]之间运行的[[反馈|反馈回路]]。<br />
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Daisyworld examines the energy budget of a planet populated by two different types of plants, black daisies and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the albedo of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
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《雏菊世界》调查了一个星球的能量预算,这个星球上生长着两种不同的植物,黑色雏菊和白色雏菊,这两种植物占据了星球表面的很大一部分。雏菊的颜色影响了地球的反照率,黑色的雏菊吸收更多的光线,使地球变暖,而白色的雏菊则反射更多的光线,使地球变冷。人们认为黑色雏菊在较低的温度下生长和繁殖最好,而白色雏菊则被认为在较高的温度下生长最好。当温度上升到接近白色雏菊所喜欢的温度时,白色雏菊繁殖率高于黑色雏菊,导致更大比例的白色表面,更多的阳光被反射,减少热量输入,最终使地球降温。相反,随着气温的下降,黑色雏菊繁殖率高于白色雏菊,吸收了更多的阳光,使地球变暖。因此,温度会收敛于两种植物繁殖率相等时对应温度的值。<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of [[greenhouse gases]] may cause [[negative feedback]]s in the environment to become [[positive feedback]]. Lovelock has stated that this could bring an [[James Lovelock#The revenge of Gaia|extremely accelerated global warming]],<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, {{ISBN|978-0-465-01549-8}}</ref> but he has since stated the effects will likely occur more slowly.<ref>Lovelock J., NBC News. [http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite Link] Published 23 April 2012, accessed 22 August 2012. {{Webarchive|url=https://web.archive.org/web/20120913163635/http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite |date=13 September 2012 }}</ref><br />
目前,人口的增加及其活动对环境的影响,如[[温室气体]]的倍增,可能导致环境中的[[负反馈]]变成[[正反馈]]。洛夫洛克曾表示,这可能会带来一场【【James Loveloc【《盖亚的复仇』极度加速的全球变暖】】 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this negative feedback due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
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洛夫洛克和沃森指出,在有限的条件下,如果太阳的能量输出发生变化,由于竞争产生的负反馈可以将地球温度稳定在支持生命存在的范围内,而没有生命的地球则会表现出巨大的温度波动。白色和黑色雏菊的百分比会不断变化,以保持植物繁殖率相等的温度值,使两种生命形式都能茁壮成长。<br />
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====Daisyworld simulations雏菊世界模拟====<br />
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[[File:StandardDaisyWorldRun2color.gif|thumb|280px|Plots from a standard black and white [[Daisyworld]] simulation]]<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<br />
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有人认为,这些结果是可以预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的答案。<br />
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{{Main|Daisyworld}}<br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic [[group selection]] and [[Cooperation (evolution)|cooperation]] between organisms, James Lovelock and [[Andrew Watson (scientist)|Andrew Watson]] developed a mathematical model, [[Daisyworld]], in which [[Competition (biology)|ecological competition]] underpinned planetary temperature regulation.<ref name="daisyworld">{{cite journal<br />
有人批评盖亚假说似乎需要有机体之间不切实际的[[群体选择]]和[[合作(进化)|合作]],詹姆斯·洛夫洛克和[[安德鲁·沃森(科学家)|安德鲁·沃森]]开发了一个数学模型,[[雏菊世界]],其中[[竞争(生物学)|生态竞争]]为基础行星温度调节。 <br />
|date = 1983<br />
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Ocean salinity has been constant at about 3.5% for a very long time. Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested that salinity may also be strongly influenced by seawater circulation through hot basaltic rocks, and emerging as hot water vents on mid-ocean ridges. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<br />
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长期以来,海洋盐度一直保持在3.5% 左右。海洋环境中盐度的稳定性很重要,因为大多数细胞需要相当恒定的盐度,一般不能耐受超过5% 的盐度值。海洋盐度为何恒定是一个长期的奥秘,因为没有任何方法可以抵消来自河流的流入盐。最近有人提出,盐分也会洋中脊的热水喷口排出,因此盐度可能受到穿过炽热玄武岩的海水循环的强烈影响。然而,海水的组成离平衡还很远,如果没有有机过程的影响,很难解释这一事实。有一种解释认为,地球历史上盐滩的形成是盐度平衡的原因之一。据推测,这些盐滩是由细菌菌落产生的,它们在生命过程中固定离子和重金属。<br />
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|title = Biological homeostasis of the global environment: the parable of Daisyworld<br />
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|journal = Tellus<br />
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|volume = 35B<br />
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Vostok, Antarctica research station. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
沃斯托克,南极洲研究站。当前期间在左边。<!--基于此图表的GIMP-FX版本的非源材料。现在的版本是正确的,原版的。必须删除这句话:请注意,当前CO2水平超过390ppm,远高于过去40万年来的任何时候-->] <br />
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|pages = 286–9<br />
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|bibcode = 1983TellB..35..284W<br />
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|doi = 10.1111/j.1600-0889.1983.tb00031.x<br />
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The Gaia hypothesis states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organisms or processed by them.<br />
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盖亚假说认为,地球的大气组成是由于生命的存在而保持在动态稳定的状态。大气成分提供了支持现代生命的条件。大气中除惰性气体以外的所有大气气体,要么是由生物体产生的,要么是由生物体加工的。<br />
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|last1 = Watson | first1= A.J. | last2= Lovelock | first2= J.E<br />
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|issue = 4<br />
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The stability of the atmosphere in Earth is not a consequence of chemical equilibrium. Oxygen is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the Great Oxygenation Event. Since the start of the Cambrian period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume. Traces of methane (at an amount of 100,000 tonnes produced per year) should not exist, as methane is combustible in an oxygen atmosphere.<br />
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地球大气层的稳定性不是化学平衡的结果。氧是一种活性化合物,最终会与地球大气层和地壳中的气体和矿物质结合。在大氧化事件开始之前,大约5000万年前,氧气才开始在大气中持续少量存在。自寒武纪以来,大气中氧浓度一直在大气体积的15% 至35% 之间波动。微量的甲烷(每年产生100,000吨)不适合存在,因为甲烷在氧气氛中是可燃的。<br />
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|ref = harv<br />
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}}</ref><br />
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Dry air in the atmosphere of Earth contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases including methane. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. <br />
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地球大气层中的干燥空气大致(按体积计算)含有78.09% 的氮气、20.95% 的氧气、0.93% 的氩气、0.039% 的二氧化碳以及少量的其他气体,包括甲烷。洛夫洛克最初推测,高于25% 的氧气浓度会增加森林大火和森林大火的发生频率。石炭纪和白垩纪煤系地质时期O2浓度确实超过了25%时,正是这一时期形成了火成木炭。这一结果支持了 Lovelock 的论点。<br />
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Daisyworld examines the [[Earth's energy budget|energy budget]] of a [[planet]] populated by two different types of plants, black [[Asteraceae|daisies]] and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the [[albedo]] of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
Daisyworld研究了居住着两种不同类型的植物的[[地球的能源预算|能源预算]],这两种植物是黑色的[[菊科的雏菊]]和白色的雏菊,这两种植物被认为占据了地表的很大一部分。雏菊的颜色影响着这个星球的[反照率],因此黑色雏菊吸收更多的光并温暖地球,而白色雏菊则反射更多的光并使地球降温。黑雏菊在较低温度下生长繁殖最好,而白雏菊在较高温度下生长繁殖最好。当温度上升到接近白色雏菊的最适生长温度时,白色雏菊的繁殖能力超过了黑色雏菊,导致白色表面的比例增大,更多的阳光被反射,减少了热量输入,最终使地球变冷。相反,随着温度的下降,黑雏菊的繁殖能力超过了白雏菊,吸收了更多的阳光,使地球变暖。因此,温度将收敛到两种植物繁殖率相等对应的温度值。 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this [[negative feedback]] due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
Lovelock和Watson表明,在有限的条件范围内,如果太阳的能量输出发生变化,由于竞争而产生的[[负反馈]]可以将地球的温度稳定在支持生命的值上,而没有生命的行星则会出现大范围的温度波动。白雏菊和黑雏菊的比例会不断变化,以使温度保持在植物繁殖率相等的值,从而使两种生命形式都能茁壮成长。 <br />
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Gaia scientists see the participation of living organisms in the carbon cycle as one of the complex processes that maintain conditions suitable for life. The only significant natural source of atmospheric carbon dioxide (CO<sub>2</sub>) is volcanic activity, while the only significant removal is through the precipitation of carbonate rocks. Carbon precipitation, solution and fixation are influenced by the bacteria and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
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盖亚假说的科学家们把生物体参与碳循环看作是维持适合生命条件的复杂过程之一。火山活动是大气中二氧化碳的最重要的自然来源,而碳酸盐岩的沉淀是大气中二氧化碳最重要的去除途径。碳沉淀、溶解和固定受到土壤中细菌和植物根系的影响,这些细菌和植物根系可以改善气体循环,或者在珊瑚礁中,碳酸钙以固体的形式沉积在海底。碳酸钙被活的有机体用来制造含碳的结构和外壳。一旦死亡,生物体的外壳就会沉到海底,在那里它们产生白垩和石灰石的沉淀物。<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<ref>{{cite journal | doi = 10.1023/A:1023494111532 | date = 2003 | last1 = Kirchner | first1 = James W. | journal = Climatic Change | volume = 58 |issue=1–2| pages = 21–45 |title=The Gaia Hypothesis: Conjectures and Refutations | ref = harv}}</ref><br />
有人认为,结果是可预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的反应。 <br />
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One of these organisms is Emiliania huxleyi, an abundant coccolithophore algae which also has a role in the formation of clouds. CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants. Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean algal blooms are also increasing.<br />
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其中一种是赫氏圆石藻,这是一种数量丰富的颗石藻类,也参与了云的形成。通过增加球石氟化物的寿命来补偿过量的CO < sub > 2 </sub > ,增加了锁定在海底的 CO < sub > 2 </sub > 的数量。球石粉会增加云量,从而控制地表温度,有助于降低整个地球的温度,有利于地球上植物所必需的降水。近年来,大气中 CO < < sub > 2 </sub > 浓度有所增加,有证据表明,海洋藻华的浓度也在增加。<br />
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===Regulation of oceanic salinity海洋盐度调节 ===<br />
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Lichen and other organisms accelerate the weathering of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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地衣和其他生物加速了岩石表面的风化,而岩石在土壤中的分解也加快了,这要归功于根、真菌、细菌和地下动物的活动。因此,二氧化碳从大气层流向土壤的过程是在生物的帮助下调节的。当大气中 CO2水平升高时,温度升高,植物生长。这种生长会增加植物对二氧化碳的消耗,植物会将二氧化碳处理到土壤中,从大气中排出。<br />
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Ocean [[salinity]] has been constant at about 3.5% for a very long time.<ref name=":0">{{Cite book|title=The Introduction to Ocean Sciences|last=Segar|first=Douglas|publisher=Library of Congress|year=2012|isbn=978-0-9857859-0-1|location=http://www.reefimages.com/oceans/SegarOcean3Chap05.pdf|pages=Chapter 5 3rd Edition|quote=|via=}}</ref> Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested<ref name="Gorham19912">{{cite journal|last=Gorham|first=Eville|date=1 January 1991|title=Biogeochemistry: its origins and development|journal=Biogeochemistry|publisher=Kluwer Academic|volume=13|issue=3|pages=199–239|doi=10.1007/BF00002942|issn=1573-515X|ref=harv}}</ref> that salinity may also be strongly influenced by [[seawater]] circulation through hot [[basalt]]ic rocks, and emerging as hot water vents on [[mid-ocean ridge]]s. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<ref name=":0" /><br />
在很长一段时间内,海洋盐度一直保持在3.5%左右。[23]海洋环境中的盐度稳定性非常重要,因为大多数细胞需要相当恒定的盐度,并且通常不能耐受超过5%的盐度值。恒定的海洋盐度是一个长期存在的谜团,因为没有任何过程可以抵消河流中的盐流入。大洋中脊上的热水喷口会排出盐分,有人认为[24]这说明盐分也会受到海水循环的强烈影响。然而,海水的组成远未达到平衡,如果没有有机过程的影响,很难解释这一事实。地球历史中盐滩的形成是一个常用的证据。据推测,这些盐滩是由在生命过程中固定离子和重金属的菌落产生的<br />
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In the biogeochemical processes of Earth, sources and sinks are the movement of elements. The composition of salt ions within our oceans and seas is: sodium (Na<sup>+</sup>), chlorine (Cl<sup>−</sup>), sulfate (SO<sub>4</sub><sup>2−</sup>), magnesium (Mg<sup>2+</sup>), calcium (Ca<sup>2+</sup>) and potassium (K<sup>+</sup>). The elements that comprise salinity do not readily change and are a conservative property of seawater.<ref name=":0" /> There are many mechanisms that change salinity from a particulate form to a dissolved form and back. The known sources of sodium i.e. salts are when weathering, erosion, and dissolution of rocks are transported into rivers and deposited into the oceans.<br />
在地球的生物地球化学过程中,源和汇是元素的运动。我们海洋中盐离子的组成是:钠(Na+)、氯(Cl-)、硫酸盐(SO42-)、镁(Mg2+)、钙(Ca2+)和钾(K+)。构成盐度的元素不易变化,是海水的一种保守属性。[23]有许多机制可以将盐度从颗粒形态改变为溶解形态,然后再返回。已知的钠(即盐)因为岩石的风化、侵蚀和溶解作用被输送到河流中并沉积到海洋中。 <br />
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The [[Mediterranean Sea]] as being Gaia's kidney is found ([http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/ here]) by Kenneth J. Hsue, a correspondence author in 2001. The "[[desiccation]]" of the Mediterranean is the evidence of a functioning kidney. Earlier "kidney functions" were performed during the "[[Deposition (geology)|deposition]] of the [[Cretaceous]] ([[Atlantic Ocean|South Atlantic]]), [[Jurassic]] ([[Gulf of Mexico]]), [[Permian–Triassic extinction event|Permo-Triassic]] ([[Europe]]), [[Devonian]] ([[Canada]]), [[Cambrian]]/[[Precambrian]] ([[Gondwana]]) saline giants."<ref>{{Cite web|url=http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/|title=Scientia Marina: List of Issues|last=http://www.webviva.com|first=Justino Martinez. Web Viva 2007|website=scimar.icm.csic.es|language=English|access-date=2017-02-04}}</ref><br />
地中海是盖亚的肾脏,由肯尼斯·J·休伊(KennethJ.Hsue)在2001年发现的。地中海的“干涸”是肾功能正常的证据。早期的“肾功能”是在“白垩纪(南大西洋)、侏罗纪(墨西哥湾)、二叠纪-三叠纪(欧洲)、泥盆纪(加拿大)、寒武纪/前寒武纪(冈瓦纳)盐沼沉积时期进行的。” <br />
[[Earthrise taken from Apollo 8 on December 24, 1968]]<br />
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[1968年12月24日阿波罗8号拍摄的地出]<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = <br />
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地球是一个完整的整体,一个有生命的存在,这个观念有着悠久的传统。神话中的盖亚是拟人化地球的原始希腊女神,是希腊版本的“自然母亲”(来自 Ge = 地球,和 Aia = <br />
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===Regulation of oxygen in the atmosphere大气层的氧气调节===<br />
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PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a suggestion from the novelist William Golding, who was living in the same village as Lovelock at the time (Bowerchalke, Wiltshire, UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of living organisms, climate, and Earth's crust. His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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派祖母,或地球母亲。詹姆斯·洛夫洛克根据小说家威廉·戈尔丁的建议给他的假设起了这个名字,他当时和洛夫洛克住在同一个村子里(英国威尔特郡鲍尔查尔克)。戈尔丁的建议是以Gea为基础的,Gea是希腊女神名字的另一种拼写,在地质学、地球物理和地球化学中,Gea是前缀。后来,博物学家和探险家亚历山大·冯·洪堡认识到生物、气候和地壳的共同进化。他的远见卓识的声明在西方没有被广泛接受,几十年后,盖亚假说刚提出时同样受到了科学界的抵制。<br />
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[[File:Vostok 420ky 4curves insolation.jpg|thumb|280px|Levels of gases in the atmosphere in 420,000 years of ice core data from [[Vostok Station|Vostok, Antarctica research station]]. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
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{{See also|Geological history of oxygen}}<br />
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Also in the turn to the 20th century Aldo Leopold, pioneer in the development of modern environmental ethics and in the movement for wilderness conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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同样在20世纪之交,现代环境伦理学发展的先驱、荒野保护运动的先驱奥尔多 · 利奥波德在他的生物中心或整体的土地伦理学中提出了一个有生命的地球。<br />
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The Gaia hypothesis states that the Earth's [[Atmospheric chemistry#Atmospheric composition|atmospheric composition]] is kept at a dynamically steady state by the presence of life.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 163. {{ISBN|978-0-465-01549-8}}</ref> The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than [[noble gas]]es present in the atmosphere are either made by organisms or processed by them.<br />
盖亚假说指出,地球的大气成分由于生命的存在而保持在动态稳定的状态。大气中除惰性气体以外的所有大气气体都是由生物体制造或加工而成。<br />
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The stability of the atmosphere in Earth is not a consequence of [[chemical equilibrium]]. [[Oxygen]] is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the [[Great Oxygenation Event]].<ref name=Anabar2007>{{Cite journal| last4 = Arnold| last6 = Creaser| last3 = Lyons| first1 = A. | first2 = Y.| last9 = Scott| last2 = Duan | first3 = T. | first4 = G.| last8 = Gordon | first5 = B. | first10 = J. | first6 = R.| last10 = Garvin | first7 = A.| last11 = Buick | first8 = G. | first11 = R. | first9 = C.| title = A whiff of oxygen before the great oxidation event?| journal = Science| volume = 317| issue = 5846| year = 2007| last7 = Kaufman| pages = 1903–1906| last5 = Kendall| pmid = 17901330| last1 = Anbar | doi = 10.1126/science.1140325|bibcode = 2007Sci...317.1903A }}</ref> Since the start of the [[Cambrian]] period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume.<ref name=Berner1999>{{Cite journal<br />
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地球大气的稳定性不是化学平衡造成的。氧气是一种活性化合物,最终会与地球大气层和地壳上的气体和矿物质结合。在大氧化事件开始前的5000万年,氧气才在大气中少量存在。自寒武纪开始以来,大气氧浓度值一直在大气体积的15%到35%之间波动。甲烷的痕迹(每年产生10万吨)是不存在的,因为甲烷在氧气环境中是可燃的。<br />
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Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut William Anders in 1968 during the Apollo 8 mission became, through the Overview Effect an early symbol for the global ecology movement.<br />
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盖亚假说和环境运动的另一个影响来自于苏联和美利坚合众国之间太空竞赛。在20世纪60年代,第一批进入太空的人类可以看到地球作为一个整体的样子。1968年,宇航员威廉 · 安德斯在阿波罗8号任务期间拍摄的地出照片,通过总体效应成为全球生态运动的早期象征。<br />
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| pmid = 10500106<br />
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| date=Sep 1999 | last1 = Berner | first1 = R. A.<br />
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| title = Atmospheric oxygen over Phanerozoic time<br />
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[[James Lovelock, 2005]]<br />
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[ James Lovelock,2005]<br />
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| volume = 96<br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the Jet Propulsion Laboratory in California on methods of detecting life on Mars. The first paper to mention it was Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life, co-authored with C.E. Giffin. A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the Pic du Midi observatory, planets like Mars or Venus had atmospheres in chemical equilibrium. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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65年9月,洛夫洛克在加利福尼亚喷气推进实验室研究探测火星生命的方法时,开始定义由生物群落控制的自我调节地球的概念。第一篇提到它的论文是行星大气:与C.E.Giffin合著的与生命存在有关的成分和其他变化。一个主要的概念是,通过大气的化学成分可以在行星尺度上探测到生命。根据picdumidi天文台收集的数据,像火星或金星这样的行星,其大气层处于化学平衡状态。这种与地球大气的差异被认为是这些行星上没有生命的证据。 <br />
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| issue = 20<br />
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| pages = 10955–10957<br />
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Lovelock formulated the Gaia Hypothesis in journal articles in 1972 and 1974, and a popular book length version of the hypothesis, published in 1979 as The Quest for Gaia, began to attract scientific and critical attention.<br />
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洛夫洛克在1972年和1974年的期刊文章中提出了盖亚假说,并在1979年出版了一本畅销书,名为《寻找盖亚》 ,开始引起科学界和批判界的关注。<br />
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| issn = 0027-8424<br />
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| journal = Proceedings of the National Academy of Sciences of the United States of America<br />
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Lovelock called it first the Earth feedback hypothesis, and it was a way to explain the fact that combinations of chemicals including oxygen and methane persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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洛夫洛克首先将其称为地球反馈假说,解释氧气和甲烷等化学物质在地球大气中如何保持稳定浓度。洛夫洛克认为,在其他行星的大气层中探测这种组合,是一种相对便宜可靠的探测生命的方法。<br />
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| doi = 10.1073/pnas.96.20.10955<br />
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| pmc = 34224<br />
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[[Lynn Margulis]]<br />
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[琳 · 玛格丽丝]<br />
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|bibcode = 1999PNAS...9610955B }}</ref> Traces of [[Atmospheric methane|methane]] (at an amount of 100,000 tonnes produced per year)<ref name="Cicerone1988">{{cite journal |last1=Cicerone |first1=R.J. |last2=Oremland |first2=R.S. |date=1988 |title=Biogeochemical aspects of atmospheric methane |journal=Global Biogeochemical Cycles |volume=2 |issue=4 |pages=299–327 |url=//webfiles.uci.edu/setrumbo/public/Methane_papers/Cicerone_Global%20Biogeochem%20Cy_1988.pdf |doi=10.1029/GB002i004p00299 |bibcode=1988GBioC...2..299C}}</ref> should not exist, as methane is combustible in an oxygen atmosphere.<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<br />
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后来出现了其他关系,例如海洋生物产生的硫和碘的数量与陆地生物所需的数量大致相同,这些都支持了这一假说。<br />
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Dry air in the [[atmosphere of Earth]] contains roughly (by volume) 78.09% [[nitrogen]], 20.95% oxygen, 0.93% [[argon]], 0.039% [[Carbon dioxide in the Earth's atmosphere|carbon dioxide]], and small amounts of other gases including [[methane]]. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. {{citation needed|date=June 2012}}<br />
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[[地球大气]]中的干空气大约(按体积)包含78.09%[[氮]],20.95%的氧,0.93%[[氩]],0.039%[地球大气中的二氧化碳|二氧化碳]],以及少量其他气体,包括[[甲烷]]。洛夫洛克最初推测,氧气浓度超过25%会增加森林火灾和火灾的发生率。最近在石炭纪和白垩纪煤系中火成木炭的研究(这两个地质时期O<sub>2</sub>浓度超过25%)支持了Lovelock的观点 <br />
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In 1971 microbiologist Dr. Lynn Margulis joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet. The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of eukaryotic organelles and her contributions to the endosymbiotic theory, nowadays accepted. Margulis dedicated the last of eight chapters in her book, The Symbiotic Planet, to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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1971年,微生物学家 Lynn Margulis 博士加入了 Lovelock 的行列,努力将最初的假设充实为科学证明的概念。Margulis 贡献了她关于微生物如何影响大气层和地球表面不同层次的知识。这位美国生物学家也唤受到科学界的批评,因为她倡导真核细胞器起源的理论,以及她对美国共生发源学会的贡献——现在被接受了。玛格丽丝在她的书《共生星球》中将最后八章用于描述盖亚。然而,她反对对盖亚的广泛拟人化,并强调盖亚“不是一个有机体” ,而是“有机体之间相互作用的一个新兴属性”。她将盖亚定义为“组成地球表面一个巨大生态系统的一系列相互作用的生态系统”。句号”。这本书最令人难忘的“口号”实际上是由马古利斯的一个学生打趣说的: “从太空看,盖亚只是共生而已。”。<br />
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===Processing of CO<sub>2</sub>二氧化碳处理===<br />
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{{See also|Carbon cycle}}<br />
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James Lovelock called his first proposal the Gaia hypothesis but has also used the term Gaia theory. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments and provided a number of useful predictions. In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating. The principal sponsor was the National Audubon Society. Speakers included James Lovelock, George Wald, Mary Catherine Bateson, Lewis Thomas, John Todd, Donald Michael, Christopher Bird, Thomas Berry, David Abram, Michael Cohen, and William Fields. Some 500 people attended.<br />
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詹姆斯 · 洛夫洛克称他的第一个提议为盖亚假说,但也使用了盖亚理论这个术语。洛夫洛克说,最初的提法是基于观察,但仍然缺乏科学的解释。盖亚假说从那以后得到了一些科学实验的支持,并提供了一些有用的预测。事实上,更广泛的研究证明了最初的假设是错误的,在这个意义上,不是生命本身,而是整个地球系统在调节。主要赞助者是奥杜邦学会。讲者包括 James Lovelock、 George Wald、 Mary Catherine Bateson、 Lewis Thomas、 John Todd、 Donald Michael、 Christopher Bird、 Thomas Berry、 David Abram、 Michael Cohen 和 William Fields。大约有500人参加。<br />
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Gaia scientists see the participation of living organisms in the [[carbon cycle]] as one of the complex processes that maintain conditions suitable for life. The only significant natural source of [[Carbon dioxide in Earth's atmosphere|atmospheric carbon dioxide]] ([[Carbon dioxide|CO<sub>2</sub>]]) is [[volcanic activity]], while the only significant removal is through the precipitation of [[carbonate rocks]].<ref name="Karhu1996">{{cite journal | author = Karhu, J.A. | author2 = Holland, H.D. | date = 1 October 1996 | title = Carbon isotopes and the rise of atmospheric oxygen | journal = [[Geology (journal)|Geology]] | volume = 24 | issue = 10 | pages = 867–870 | doi = 10.1130/0091-7613(1996)024<0867:CIATRO>2.3.CO;2|bibcode = 1996Geo....24..867K | ref = harv}}</ref> Carbon precipitation, solution and [[Carbon fixation|fixation]] are influenced by the [[bacteria]] and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
盖亚的科学家认为,生物参与[[碳循环]是维持适宜生命条件的复杂过程之一。[[地球大气中的二氧化碳|大气二氧化碳]]([[二氧化碳| CO2]])最重要的自然来源是[[火山活动]],而最重要的去除过程是[[碳酸盐岩]]的沉淀,溶液和[[固碳|固碳]]受土壤中的[[细菌]]和植物根系的影响,它们改善了气体循环,珊瑚礁中碳酸钙以固体形式沉积在海底。碳酸钙被生物用来制造含碳结构和贝壳。一旦死亡,这些生物的壳就会落到海底,在那里它们会产生白垩和石灰岩的沉积物。 <br />
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One of these organisms is ''[[Emiliania huxleyi]]'', an abundant [[coccolithophore]] [[algae]] which also has a role in the formation of [[cloud]]s.<ref name="Harding2006">{{cite book |author=Harding, Stephan |title=Animate Earth |publisher=Chelsea Green Publishing |date=2006 |pages=65 |isbn=978-1-933392-29-5 }}</ref> CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants.{{citation needed|date=July 2015}} Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean [[algal bloom]]s are also increasing.<ref>{{Cite web | date = 12 September 2007 | title = Interagency Report Says Harmful Algal Blooms Increasing | url = http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | url-status = dead | archiveurl = https://web.archive.org/web/20080209234239/http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | archivedate = 9 February 2008 }}</ref><br />
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In 1988, climatologist Stephen Schneider organised a conference of the American Geophysical Union. The first Chapman Conference on Gaia,<br />
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在1988年,气候学家史蒂芬·史奈德组织了一次美国美国地球物理联盟协会的会议。关于盖亚假说的第一次查普曼会议,<br />
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[[Lichen]] and other organisms accelerate the [[weathering]] of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the Daisyworld Model (and its modifications, above) as evidence against most of these criticisms.<br />
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然而,洛夫洛克和其他支持盖亚理论的科学家确实试图反驳这样一种说法,即这种假设不科学,因为不可能通过控制实验来检验它。例如,针对盖亚假说是目的论的指责,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修正,上文)反驳这些批评。<br />
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==History历史==<br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of teleologism ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,这一版本中盖亚并不是有意地在她的环境中维持生命赖以生存的复杂平衡。看起来,盖亚假说“故意”行为的说法只是他那本广受欢迎的书中的一个比喻性陈述,并不是字面意义上的理解。这种对盖亚假说的新陈述更能为科学界所接受。在这次会议之后,大多数关于目的论的指责都停止了。<br />
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===Precedents先例===<br />
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[[File:NASA-Apollo8-Dec24-Earthrise.jpg|thumb|''[[Earthrise]]'' taken from [[Apollo 8]] on December 24, 1968]]<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000, the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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到2000年6月23日在西班牙巴伦西亚举行关于盖亚假说的第二次查普曼会议时,情况发生了重大变化。与其讨论盖亚假说的目的论观点,或盖亚假说的“类型” ,不如将重点放在具体的机制上,通过这些机制,短期内基本稳态在重要的进化长期结构变化的框架内得以维持。<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The [[Gaia (mythology)|mythical Gaia]] was the primal Greek goddess personifying the [[Earth]], the Greek version of "[[Mother Nature]]" (from Ge = Earth, and Aia = <br />
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[[PIE]] grandmother), or the [[Earth Mother]]. James Lovelock gave this name to his hypothesis after a suggestion from the novelist [[William Golding]], who was living in the same village as Lovelock at the time ([[Bowerchalke]], [[Wiltshire]], UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry.<ref name=vanish09 /> Golding later made reference to Gaia in his [[Nobel prize]] acceptance speech.<br />
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The major questions were:<br />
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主要的问题是:<br />
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In the eighteenth century, as [[geology]] consolidated as a modern science, [[James Hutton]] maintained that geological and biological processes are interlinked.<ref name=CapraWeb>{{cite book |author=Capra, Fritjof |title=The web of life: a new scientific understanding of living systems |publisher=Anchor Books |location=Garden City, N.Y |date=1996 |page=[https://archive.org/details/weboflifenewscie00capr/page/23 23] |isbn=978-0-385-47675-1 |url=https://archive.org/details/weboflifenewscie00capr/page/23 }}</ref> Later, the [[naturalist]] and explorer [[Alexander von Humboldt]] recognized the coevolution of living organisms, climate, and Earth's crust.<ref name=CapraWeb /> In the twentieth century, [[Vladimir Vernadsky]] formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian [[geochemist]] and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological processes. During the 1920s he published works arguing that living organisms could reshape the planet as surely as any physical force. Vernadsky was a pioneer of the scientific bases for the environmental sciences.<ref>S.R. Weart, 2003, ''The Discovery of Global Warming'', Cambridge, Harvard Press</ref> His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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"How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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“被称为盖亚的全球生物地球化学/气候系统是如何及时发生变化的?它的历史是什么?盖亚假说能够在一个时间尺度上保持系统的稳定性,但是在更长的时间尺度上仍然经历矢量变化吗?如何利用地质记录来检验这些问题? ”<br />
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"What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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“盖亚假说的结构是什么?这些反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由在任何特定时间进行的学科研究务实地决定的,还是有一些部分应该被认为是最真实的,以了解盖亚假说随着时间的推移包含进化中的生物体?盖亚系统这些不同部分之间的反馈是什么? 对盖亚假说作为全球生态系统的结构和生命的生产力来说,物质的近乎封闭意味着什么? ”<br />
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Also in the turn to the 20th century [[Aldo Leopold]], pioneer in the development of modern [[environmental ethics]] and in the movement for [[wilderness]] conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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"How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
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“盖亚假说过程和现象的模型如何与现实相关,它们如何帮助解决和理解盖亚?雏菊世界的成果如何转移到现实世界?什么是“雏菊”的主要候选人?我们发现雏菊与否对盖亚理论重要吗?我们应该怎样寻找雏菊,我们应该加紧寻找吗?如何利用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制? ”<br />
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{{quotation|It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated functions, but possibly also that process of consumption as replacement which in biology we call metabolism, or growth. In such case we would have all the visible attributes of a living thing, which we do not realize to be such because it is too big, and its life processes too slow.| Stephan Harding | ''Animate Earth''.<ref>Harding, Stephan. ''Animate Earth Science, Intuition and Gaia''. Chelsea Green Publishing, 2006, p. 44. {{ISBN|1-933392-29-0}}</ref>}}<br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise entropy production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
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1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是一种向远离平衡的稳态演化的结果,这种平衡状态使熵产生最大化,克莱顿(2004)同意这样的说法:“自稳态行为可以从与行星反照率相关的MEP状态中产生”;“……一个如盖亚假说所述,处于MEP状态的生物地球很可能导致地球系统在长时间尺度上的近稳态行为。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。<br />
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Another influence for the Gaia hypothesis and the [[environmental movement]] in general came as a side effect of the [[Space Race]] between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph ''[[Earthrise]]'' taken by astronaut [[William Anders]] in 1968 during the [[Apollo 8]] mission became, through the [[Overview Effect]] an early symbol for the global ecology movement.<ref>[http://digitaljournalist.org/issue0309/lm11.html 100 Photographs that Changed the World by Life - The Digital Journalist]</ref><br />
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盖亚假说和[[环境运动]]的另一个总体影响来自苏联和美利坚合众国之间[[太空竞赛]]的副作用。在20世纪60年代,第一批进入太空的人类可以看到地球的整体面貌。1968年宇航员[[William Anders]]在[[Apollo 8]]任务期间拍摄的照片“[[地球升起]”,通过[[概述效果]]成为全球生态运动的早期标志<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<br />
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第四次关于盖亚假说的国际会议,由北弗吉尼亚地区公园管理局和其他机构主办,于2006年10月在弗吉尼亚州乔治梅森大学的阿灵顿校区举行。<br />
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===Formulation of the hypothesis假说形成===<br />
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[[File:James Lovelock in 2005.jpg|thumb|[[James Lovelock]], 2005]]<br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
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马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。Lynn Margulis是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the [[Jet Propulsion Laboratory]] in California on methods of detecting [[life on Mars (planet)|life on Mars]].<ref name="Lovelock1965">{{cite journal | author = Lovelock, J.E. | date = 1965 | title = A physical basis for life detection experiments | journal = [[Nature (journal)|Nature]] | volume = 207 | issue = 7 | pages = 568–570 | doi = 10.1038/207568a0 | pmid=5883628|bibcode = 1965Natur.207..568L | ref = harv}}</ref><ref>{{Cite web |url=http://www.jameslovelock.org/page4.html |title=Geophysiology |access-date=2007-05-05 |archive-url=https://web.archive.org/web/20070506073502/http://www.jameslovelock.org/page4.html |archive-date=2007-05-06 |url-status=dead }}</ref> The first paper to mention it was ''Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life'', co-authored with C.E. Giffin.<ref>{{cite journal | author1 = Lovelock, J.E. | author2 = Giffin, C.E. | date = 1969 | title = Planetary Atmospheres: Compositional and other changes associated with the presence of Life | journal = Advances in the Astronautical Sciences | volume = 25 | pages = 179–193 | isbn = 978-0-87703-028-7 | ref = harv}}</ref> A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the [[Pic du Midi de Bigorre|Pic du Midi observatory]], planets like Mars or Venus had atmospheres in [[chemical equilibrium]]. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
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这次会议将盖亚假说作为一种科学和隐喻的手段,来理解我们如何开始解决21世纪的问题,如气候变化和持续的环境破坏。<br />
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Lovelock formulated the ''Gaia Hypothesis'' in journal articles in 1972<ref name="J1972">{{cite journal | author = J. E. Lovelock | title = Gaia as seen through the atmosphere | date = 1972 | journal = [[Atmospheric Environment]] | volume = 6 | issue = 8 | pages = 579–580 | doi = 10.1016/0004-6981(72)90076-5 | ref = harv|bibcode = 1972AtmEn...6..579L }}</ref> and 1974,<ref name="lovelock1974" /> followed by a popularizing 1979 book ''Gaia: A new look at life on Earth''. An article in the ''[[New Scientist]]'' of February 6, 1975,<ref>Lovelock, John and Sidney Epton, (February 8, 1975). "The quest for Gaia". [https://books.google.com/books?id=pnV6UYEkU4YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false New Scientist], p. 304.</ref> and a popular book length version of the hypothesis, published in 1979 as ''The Quest for Gaia'', began to attract scientific and critical attention.<br />
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Lovelock called it first the Earth feedback hypothesis,<ref name="Lovelock01">{{harvnb|Lovelock, James|2001}}</ref> and it was a way to explain the fact that combinations of chemicals including [[oxygen]] and [[methane]] persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as Ford Doolittle, Richard Dawkins and Stephen Jay Gould. Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists, He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoietic or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole. With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<br />
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在最初几乎没有引起科学家的注意之后(从1969年到1977年) ,有一段时间,最初的盖亚假说受到了一些科学家的批评,如福特杜利特,理查德道金斯和史蒂芬·古尔德。洛夫洛克说,因为他的假说是以一位希腊女神的名字命名的,并得到许多非科学家的拥护,他想知道实现自我调节体内平衡的实际机制。在为盖亚辩护时,戴维•阿布拉姆认为,古尔德忽视了一个事实,即“机制”本身就是一个隐喻——尽管这个隐喻极其常见,而且往往不为人所知——这个隐喻让我们把自然和生命系统看作是由外部组织和建造的机器(而不是自动生成或自组织现象)。根据阿布拉姆的说法,机械隐喻使我们忽略了生命实体的活跃性或代表性,而盖亚假说的有机隐喻强调了生物群和整个生物圈的活跃性。关于盖亚的因果关系,洛夫洛克认为没有单一的机制是负责任的,各种已知机制之间的联系可能永远不会被人知道,这在生物学和生态学的其他领域是理所当然地被接受的,并且由于其他原因,特定的敌意是保留给他自己的假设的。<br />
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[[File:Lynn Margulis.jpg|thumb|left|[[Lynn Margulis]]]]<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of greedy reductionism in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<br />
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除了澄清他的语言和理解什么是生命形式,洛夫洛克自己把大部分的批评归因于他的批评者缺乏对非线性数学的理解,以及贪婪还原主义的线性化形式,在这种形式中,所有事件都必须立即归因于事件发生之前的特定原因。他还表示,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,以及一些自我调节现象可能无法在数学上解释。<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<ref>{{cite journal | first1=W.D. | last1=Hamilton | first2=T.M. | last2=Lenton | title=Spora and Gaia: how microbes fly with their clouds | journal=Ethology Ecology & Evolution | volume=10 | pages=1–16 | date=1998 | issue=1 | url=http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | format=PDF | doi=10.1080/08927014.1998.9522867 | ref=harv | url-status=dead | archiveurl=https://web.archive.org/web/20110723055017/http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | archivedate=2011-07-23 }}</ref><br />
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Evolutionary biologist W. D. Hamilton called the concept of Gaia Copernican, adding that it would take another Newton to explain how Gaian self-regulation takes place through Darwinian natural selection. More recently Ford Doolittle building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis. <br />
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进化生物学家W.D.Hamilton称盖亚假说为哥白尼式的概念,并补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。最近,Ford Doolittle在他和Inkpen的ITSNTS(这是歌手而不是歌曲)的建议中提出,差异持续性可以在自然选择进化中起到与差异生殖相似的作用,从而为自然选择理论和盖亚假说之间提供了一种可能的调和。 <br />
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In 1971 [[microbiologist]] Dr. [[Lynn Margulis]] joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet.<ref name="Turney, Jon 2003">{{cite book |author=Turney, Jon |title=Lovelock and Gaia: Signs of Life |publisher=Icon Books |location=UK |date=2003 |isbn=978-1-84046-458-0 |url-access=registration |url=https://archive.org/details/lovelockgaiasign0000turn }}</ref> The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of [[eukaryote|eukaryotic]] [[organelle]]s and her contributions to the [[endosymbiotic theory]], nowadays accepted. Margulis dedicated the last of eight chapters in her book, ''The Symbiotic Planet'', to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal Climatic Change in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it. to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background" The CLAW hypothesis, In 2009 the Medea hypothesis was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<br />
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盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论据是,生命对环境产生了有害或不稳定的影响,而不是采取行动加以调节。为了“令人不安地徘徊在污点隐喻、事实和虚假科学之间,我宁愿把盖亚假说牢牢地放在背景下。”爪假说,2009年提出的美狄亚假说:生命对行星条件有高度有害的(生物杀灭)影响,与盖亚假说直接相反。 <br />
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James Lovelock called his first proposal the ''Gaia hypothesis'' but has also used the term ''Gaia theory''. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments<ref name="J1990">{{cite journal | author = J. E. Lovelock | title = Hands up for the Gaia hypothesis | date = 1990 | journal = [[Nature (journal)|Nature]] | volume = 344 | issue = 6262 | pages = 100–2 | doi = 10.1038/344100a0|bibcode = 1990Natur.344..100L | ref = harv}}</ref> and provided a number of useful predictions.<ref name="Volk2003">{{cite book |author=Volk, Tyler |title=Gaia's Body: Toward a Physiology of Earth |publisher=[[MIT Press]] |location=Cambridge, Massachusetts |date=2003 |isbn=978-0-262-72042-7 }}</ref> In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating.<ref name="vanishing255"/><br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it". Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works". This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<br />
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2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新想法,并倡导一种整体的方法来研究地球”。在其他地方,他提出了自己的结论:“盖亚假说并不是我们这个世界如何运转的精确图像”。这种说法需要被理解为是指盖亚假说的“强”和“中”形式,生物群遵循的原则是使地球成为最佳(强度5)或有利于生命(强度4),或是作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化的盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释。<br />
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===First Gaia conference第一次盖亚会议===<br />
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In 1985, the first public symposium on the Gaia hypothesis, ''Is The Earth A Living Organism?'' was held at [[University of Massachusetts Amherst]], August 1–6.<ref>{{cite news |last=Joseph |first=Lawrence E. |title=Britain's Whole Earth Guru |work=The New York Times Magazine |date=November 23, 1986 |url=https://www.nytimes.com/1986/11/23/magazine/britain-s-whole-earth-guru.html |accessdate=1 December 2013}}</ref> The principal sponsor was the [[National Audubon Society]]. Speakers included James Lovelock, [[George Wald]], [[Mary Catherine Bateson]], [[Lewis Thomas]], [[John Todd (Canadian biologist)|John Todd]], Donald Michael, [[Christopher Bird]], [[Thomas Berry]], [[David Abram]], [[Michael A. Cohen|Michael Cohen]], and William Fields. Some 500 people attended.<ref>Bunyard, Peter (1996), "Gaia in Action: Science of the Living Earth" (Floris Books)</ref><br />
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1985年,关于盖亚假说的第一次公开研讨会,“地球是一个活的有机体吗?”在马萨诸塞大学阿默斯特举行 <br />
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===Second Gaia conference第二次盖亚会议===<br />
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In 1988, [[climatology|climatologist]] [[Stephen Schneider]] organised a conference of the [[American Geophysical Union]]. The first Chapman Conference on Gaia,<ref name="ReferenceB"/> was held in San Diego, California on March 7, 1988.<br />
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1988年,climatology和Stephen Schneider组织了一次美国地球物理联合会会议。关于盖亚假说的第一次查普曼会议 <br />
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During the "philosophical foundations" session of the conference, [[David Abram]] spoke on the influence of metaphor in science, and of the Gaia hypothesis as offering a new and potentially game-changing metaphorics, while [[James Kirchner]] criticised the Gaia hypothesis for its imprecision. Kirchner claimed that Lovelock and Margulis had not presented one Gaia hypothesis, but four -<br />
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在会议的“哲学基础”会议上,David Abram谈到了隐喻在科学中的影响,盖亚假说提供了一种新的、可能改变游戏规则的隐喻,而James Kirchner则批评盖亚假说的不精确性。基什纳声称,洛夫洛克和马古利斯提出的盖亚假说不是一个,而是四个- <br />
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* [[Coevolution|CoEvolutionary]] Gaia: that life and the environment had evolved in a coupled way. Kirchner claimed that this was already accepted scientifically and was not new.<br />
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* [[Homeostatic]] Gaia: that life maintained the stability of the natural environment, and that this stability enabled life to continue to exist.<br />
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* [[Geophysics|Geophysical]] Gaia: that the Gaia hypothesis generated interest in geophysical cycles and therefore led to interesting new research in terrestrial geophysical dynamics.<br />
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* Optimising Gaia: that Gaia shaped the planet in a way that made it an optimal environment for life as a whole. Kirchner claimed that this was not testable and therefore was not scientific.<br />
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盖亚:生命和环境是以耦合的方式进化的。基什内尔声称,这已经被科学界接受,并不是什么新鲜事。 <br />
盖亚:生命维持着自然环境的稳定,这种稳定性使生命得以继续存在。 <br />
盖亚:盖亚假说引起了人们对地球物理周期的兴趣,因此导致了地球物理动力学中有趣的新研究。 <br />
优化盖亚:盖亚塑造了地球,使之成为整个生命的最佳环境。基什内尔声称,这是不可测试的,因此是不科学的。 <br />
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Of Homeostatic Gaia, Kirchner recognised two alternatives. "Weak Gaia" asserted that life tends to make the environment stable for the flourishing of all life. "Strong Gaia" according to Kirchner, asserted that life tends to make the environment stable, ''to enable'' the flourishing of all life. Strong Gaia, Kirchner claimed, was untestable and therefore not scientific.<ref>{{cite journal | bibcode=1989RvGeo..27..223K | doi = 10.1029/RG027i002p00223 | title=The Gaia hypothesis: Can it be tested? | date=1989 | last1=Kirchner | first1=James W. | journal=Reviews of Geophysics | volume=27 | issue=2 | pages=223 | ref=harv}}</ref><br />
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基什内尔发现了两种选择“软弱的盖亚”断言,为了所有生命的繁衍,生命往往会使环境变得稳定根据基什内尔的说法,“强大的盖亚”断言,生命趋向于使环境稳定,“使”所有生命繁荣昌盛。基什内尔声称,强大的盖亚是不稳定的,因此不科学。 <br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the [[Daisyworld]] Model (and its modifications, above) as evidence against most of these criticisms.<ref name="daisyworld"/> Lovelock said that the Daisyworld model "demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways".<ref>{{cite journal | pmid=10968941 | date=2000 | last1=Lenton | first1=TM | last2=Lovelock | first2=JE | s2cid=5486128 | title=Daisyworld is Darwinian: Constraints on adaptation are important for planetary self-regulation | volume=206 | issue=1 | pages=109–14 | doi=10.1006/jtbi.2000.2105 | journal=Journal of Theoretical Biology | ref=harv}}</ref><br />
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然而,洛夫洛克和其他支持盖亚假说的科学家,确实试图反驳这种说法,即这个假设是不科学的,因为不可能通过受控实验来检验它。例如,针对盖亚假说是目的论的指控,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修改,洛夫洛克说,雏菊世界模型“证明了全球环境的自我调节可以通过不同方式改变当地环境的生活类型之间的竞争产生”。 <br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of [[teleology|teleologism]] ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,没有声称盖亚有意或有意识地维持着生命生存所需的复杂平衡。看来盖亚假说“故意”的行为是他最受欢迎的第一本书中的隐喻性陈述,并不是字面意思。盖亚假说的这一新说法更为科学界所接受。在这次会议之后,[[目的论|目的论]]的大多数指控都停止了。<br />
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===Third Gaia conference第三次盖亚会议===<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000,<ref>{{cite news|last=Simón|first=Federico|title=GEOLOGÍA Enfoque multidisciplinar La hipótesis Gaia madura en Valencia con los últimos avances científicos|journal=El País|date=21 June 2000|url=http://elpais.com/diario/2000/06/21/futuro/961538404_850215.html|accessdate=1 December 2013|language=spanish}}</ref> the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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The major questions were:<ref>{{cite web|title=General Information Chapman Conference on the Gaia Hypothesis University of Valencia Valencia, Spain June 19-23, 2000 (Monday through Friday) |url=http://www.agu.org/meetings/chapman/chapman_archive/cc00bcall.html |work=AGU Meetings |accessdate=7 January 2017 |author=American Geophysical Union }}</ref><br />
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# "How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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# "What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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# "How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
“被称为盖亚的全球生物地球化学/气候系统是如何随时间变化的?它的历史是什么?盖亚能在一个时间尺度上保持系统的稳定性,但在较长的时间尺度上仍能经历向量变化吗?如何利用地质记录来检验这些问题?” <br />
“盖亚假说的结构是什么?反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由任何给定时间正在进行的任何学科研究实际确定的,还是有一组应该被视为最真实的部分来理解盖亚假说,即随着时间的推移包含进化中的有机体?盖亚系统的这些不同部分之间的反馈是什么?物质的接近封闭对盖亚作为全球生态系统的结构和生命的生产力意味着什么?” <br />
“盖亚假说过程和现象的模型如何与现实联系起来,它们如何帮助解决和理解盖亚假说?雏菊世界的结果如何传递到真实世界?“雏菊”的主要候选对象是什么?我们是否找到雏菊对盖亚理论有意义吗?我们应该如何寻找雏菊,我们应该加强搜索?如何使用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制?” <br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise [[entropy]] production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是朝着使熵产量最大化的远非平衡的状态演化的结果,克莱顿(2004)同意这样的说法:“自稳行为可以从与行星反照率相关的MEP状态中产生”;“……生物地球在MEP状态下的行为很可能导致地球系统在长时间尺度上的近稳态行为,正如盖亚假说所述”。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。 <br />
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===Fourth Gaia conference第四次盖亚会议===<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<ref>{{cite web|title=Gaia Theory Conference at George Mason University Law School|url=http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|accessdate=1 December 2013|author=Official Site of Arlington County Virginia|archive-url=https://web.archive.org/web/20131203043657/http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|archive-date=2013-12-03|url-status=dead}}</ref><br />
第四届盖亚假说国际会议于2006年10月在乔治梅森大学阿灵顿分校举行,会议由北弗吉尼亚州公园管理局和其他机构赞助。 <br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。林恩 马古拉斯是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
这次会议将盖亚假说作为一种科学和隐喻来探讨,以此来理解我们如何着手解决21世纪的问题,如气候变化和持续的环境破坏<br />
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==Criticism批评==<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as [[Ford Doolittle]],<ref name=":1">{{Cite journal|last=Doolittle|first=W. F.|year=1981|title=Is Nature Really Motherly|url=|journal=The Coevolution Quarterly|volume=Spring|pages=58–63|via=}}</ref> [[Richard Dawkins]]<ref name=":2">{{Cite book|title=The Extended Phenotype: the Long Reach of the Gene|last=Dawkins|first=Richard|publisher=Oxford University Press|year=1982|isbn=978-0-19-286088-0|location=|pages=}}</ref> and [[Stephen Jay Gould]].<ref name="ReferenceB">Turney, Jon. "Lovelock and Gaia: Signs of Life" (Revolutions in Science)</ref> Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists,<ref name="Lovelock01"/> the Gaia hypothesis was interpreted as a [[neo-Pagan]] [[religion]]. Many scientists in particular also criticised the approach taken in his popular book ''Gaia, a New Look at Life on Earth'' for being [[teleology|teleological]]—a belief that things are purposeful and aimed towards a goal. Responding to this critique in 1990, Lovelock stated, "Nowhere in our writings do we express the idea that planetary self-regulation is purposeful, or involves foresight or planning by the [[biota (ecology)|biota]]".<br />
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最初很少受到科学家的关注(从1969年到1977年),此后的一段时间里,最初的盖亚假说受到了许多科学家的批评,比如福特·杜利特,理查德·道金斯和斯蒂芬·杰伊·古尔德洛夫洛克曾说过,因为他的假设是以希腊女神的名字命名的,新盖亚假说被许多非教派的科学家解释为。特别是许多科学家还批评了他的畅销书《盖亚》中采用的方法,认为地球上的生命是目的论的,认为事物是有目的的,是有目的的。洛夫洛克在1990年回应这一批评时说:“在我们的著作中我们没有任何地方表达行星自我调节是有目的的,或涉及生物群的远见或计划。”<br />
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[[Stephen Jay Gould]] criticised Gaia as being "a metaphor, not a mechanism."<ref name="Gould 1997">{{cite journal |author=Gould S.J. |title=Kropotkin was no crackpot |journal=Natural History |volume=106 |pages=12–21 |date=June 1997 |url=http://libcom.org/library/kropotkin-was-no-crackpot |ref=harv}}</ref> He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as [[autopoiesis|autopoietic]] or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole.<ref>Abram, D. (1988) "The Mechanical and the Organic: On the Impact of Metaphor in Science" in Scientists on Gaia, edited by Stephen Schneider and Penelope Boston, Cambridge, Massachusetts: MIT Press, 1991</ref><ref>{{cite web|url=http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |title=The Mechanical and the Organic |accessdate=August 27, 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120223165936/http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |archivedate=February 23, 2012 }}</ref> With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<ref name="Lovelock, James 2001">Lovelock, James (2001), ''Homage to Gaia: The Life of an Independent Scientist'' (Oxford University Press)</ref><br />
史蒂芬·杰伊·古尔德批评盖亚假说是“一种隐喻,而不是一种机制。”他想知道实现自我调节内稳态的实际机制。在为盖亚假说辩护时,大卫·艾布拉姆认为古尔德忽略了一个事实,即“机制”本身就是一个隐喻——尽管这是一个非常常见且常常未被人认识的隐喻——它使我们把自然和生命系统看作是从外部组织和建造的机器(而不是自动或自组织的)现象)。艾布拉姆认为,机械隐喻使我们忽视了生命实体的活动性或能动性,而盖亚假说的有机体隐喻强调了生物群和生物圈作为一个整体的能动性。关于盖亚假说的因果关系,洛夫洛克认为没有单一的机制负责各种已知机制之间的联系可能永远不为人所知,这一点在其他生物学和生态学领域都是理所当然的,而具体的敌意是出于其他原因留给他自己的假设的<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of [[greedy reductionism]] in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<ref name="Lovelock, James 2001"/><br />
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除了澄清自己的语言和对生命形式的理解之外,洛夫洛克自己将大部分批评归咎于批评家对非线性数学缺乏理解,以及贪婪还原论的线性化形式,在这种形式中,所有事件都必须在事实发生之前立即归因于特定的原因。他还指出,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,有些自我调节的现象可能无法用数学解释 <br />
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===Natural selection and evolution自然选择和进化===<br />
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Lovelock has suggested that global biological feedback mechanisms could evolve by [[natural selection]], stating that organisms that improve their environment for their survival do better than those that damage their environment. However, in the early 1980s, [[Ford Doolittle|W. Ford Doolittle]] and [[Richard Dawkins]] separately argued against this aspect of Gaia. Doolittle argued that nothing in the [[genome]] of individual organisms could provide the feedback mechanisms proposed by Lovelock, and therefore the Gaia hypothesis proposed no plausible mechanism and was unscientific.<ref name=":1" /> Dawkins meanwhile stated that for organisms to act in concert would require foresight and planning, which is contrary to the current scientific understanding of evolution.<ref name=":2" /> Like Doolittle, he also rejected the possibility that feedback loops could stabilize the system.<br />
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洛夫洛克提出,全球生物反馈机制可以通过自然选择而进化,他指出,为生存而改善环境的生物比那些破坏环境的生物做得更好。然而,在20世纪80年代早期,W·福特·杜立德和理查德·道金斯分别反对盖亚假说的这一方面。杜立德认为,单个生物体的基因组中没有任何东西能够提供洛夫洛克提出的反馈机制,因此盖亚假说没有提出任何合理的机制,是不科学的。道金斯同时指出,要使有机体协同行动,就需要有远见和计划,这与当前科学界对进化论的理解相悖和杜立德一样,他也拒绝了反馈回路可以稳定系统的可能性。<br />
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[[Lynn Margulis]], a microbiologist who collaborated with Lovelock in supporting the Gaia hypothesis, argued in 1999, that "[[Charles Darwin|Darwin]]'s grand vision was not wrong, only incomplete. In accentuating the direct competition between individuals for resources as the primary selection mechanism, Darwin (and especially his followers) created the impression that the environment was simply a static arena". She wrote that the composition of the Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in [[homeostasis]], but those set points change with time.<ref name="ReferenceA">Margulis, Lynn. Symbiotic Planet: A New Look At Evolution. Houston: Basic Book 1999</ref><br />
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Lynn Margulis,一位与Lovelock合作支持盖亚假说的微生物学家,在1999年指出,“达尔文的宏伟愿景没有错,只是不完整。达尔文(特别是他的追随者)强调个人之间对资源的直接竞争是主要的选择机制,他给人的印象是环境只是一个静态的竞技场”。她写道,地球大气、水圈和岩石圈的组成都是围绕着“设定点”来调节的,就像在体内平衡中一样,但是这些设定点会随着时间的推移而变化 <br />
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Evolutionary biologist [[W. D. Hamilton]] called the concept of Gaia [[Nicolaus Copernicus|Copernican]], adding that it would take another [[Isaac Newton|Newton]] to explain how Gaian self-regulation takes place through Darwinian [[natural selection]].<ref name=vanish09>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, pp. 195-197. {{ISBN|978-0-465-01549-8}}</ref>{{better source|date=September 2012|reason=it should be possible to find the original place where Hamilton said this}} More recently [[Ford Doolittle]] building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal<ref name="ITSNTS">Doolittle WF, Inkpen SA. Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking. [https://www.pnas.org/content/115/16/4006 PNAS April 17, 2018 115 (16)] 4006-4014 </ref> proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis<ref name="Darwinizing Gaia">Doolittle WF. Darwinizing Gaia. [https://doi.org/10.1016/j.jtbi.2017.02.015 Journal of Theoretical BiologyVolume 434], 7 December 2017, Pages 11-19 </ref>. <br />
进化生物学家汉密尔顿称盖亚哥白尼为盖亚的概念,他补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。通过自然选择在进化过程中的繁殖,从而为自然选择理论和盖亚假说提供了可能的调和。 <br />
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===Criticism in the 21st century21世纪的批评===<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal ''Climatic Change'' in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it.<ref name="kirchner2002"/><ref name="volk2002"/> Several recent books have criticised the Gaia hypothesis, expressing views ranging from "... the Gaia hypothesis lacks unambiguous observational support and has significant theoretical difficulties"<ref>{{cite book |last=Waltham |first=David |authorlink=David Waltham |date=2014 |title=Lucky Planet: Why Earth is Exceptional – and What that Means for Life in the Universe |url=https://archive.org/details/luckyplanetwhyea0000walt |location= |publisher=Icon Books |page= |isbn=9781848316560 |accessdate= |url-access=registration }}</ref> to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background"<ref name="beerling2007"/> to "The Gaia hypothesis is supported neither by evolutionary theory nor by the empirical evidence of the geological record".<ref>{{cite book |last1=Cockell |first1=Charles |authorlink1=Charles Cockell |last2=Corfield |first2=Richard |last3=Dise |first3= Nancy |last4=Edwards |first4=Neil |last5=Harris |first5=Nigel |date=2008 |title= An Introduction to the Earth-Life System |url= http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/palaeontology-and-life-history/introduction-earth-life-system |location=Cambridge (UK) |publisher= Cambridge University Press |page= |isbn= 9780521729536 |accessdate= }}</ref> The [[CLAW hypothesis]],<ref name="CLAW87" /> initially suggested as a potential example of direct Gaian feedback, has subsequently been found to be less credible as understanding of [[cloud condensation nuclei]] has improved.<ref>{{Citation |last1= Quinn |first1=P.K. |last2= Bates |first2=T.S. |title =The case against climate regulation via oceanic phytoplankton sulphur emissions |journal =Nature |volume=480 |issue=7375 |pages =51–56 |date = 2011 |doi=10.1038/nature10580|bibcode = 2011Natur.480...51Q |pmid=22129724|url=https://zenodo.org/record/1233319 }}</ref> In 2009 the [[Medea hypothesis]] was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<ref>Peter Ward (2009), ''The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?'', {{ISBN|0-691-13075-2}}</ref><br />
盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论点是在许多例子中,生命对环境产生了有害或不稳定的影响,而不是采取行动来调节它。最近几本书批评了盖亚假说,譬如“盖亚假说缺乏明确的观察支持,并且有重大的理论困难”“(盖亚假说)令人不安地徘徊在污点、隐喻、事实和虚假科学之间,我宁愿把盖亚牢牢地放在原有的背景中”“盖亚假说既没有进化论的支持,也没有地质记录的经验证据的支持。爪假说最初被认为是盖亚直接反馈的一个潜在例子,后来被发现对云的理解不那么可信凝聚核已经得到了改善。2009年,美狄亚假说提出:生命对行星的状况非常有害,这与盖亚假说直接相反。 <br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it".<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=209 |isbn=9780691121581 |accessdate= }}</ref> Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works".<ref>{{Citation |last= Tyrrell |first = Toby |title =Gaia: the verdict is… |journal = New Scientist |volume = 220 |issue = 2940 |pages = 30–31 |date= 26 October 2013 |doi=10.1016/s0262-4079(13)62532-4}}</ref> This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=208 |isbn=9780691121581 |accessdate= }}</ref><br />
2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新思想,并倡导一种研究地球的整体方法。”在其他地方,他提出了自己的结论:“盖亚假说并不是一个关于如何进行的精确描述我们的世界在运转。”这种说法需要被理解为是指盖亚假说的“强大”和“温和”形式,生物群遵循的原则是使地球处于最佳状态(强度5)或有利于生命(强度4),或者它作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化德盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释 <br />
Category:Cybernetics<br />
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类别: 控制论<br />
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Category:Ecological theories<br />
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范畴: 生态学理论<br />
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==See also==<br />
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Category:Superorganisms<br />
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类别: 超级有机体<br />
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{{Portal|Environment|Earth sciences|Geography}}<br />
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Category:Climate change feedbacks<br />
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类别: 气候变化反馈<br />
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Category:1965 introductions<br />
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类别: 1965年引言<br />
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* {{annotated link|Biocoenosis}}<br />
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Category:Biogeochemistry<br />
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类别: 生物地球化学<br />
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* {{annotated link|Earth science}}<br />
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Category:Earth<br />
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类别: 地球<br />
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* {{annotated link|Environmentalism}}<br />
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Category:Biological hypotheses<br />
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类别: 生物学假说<br />
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* {{annotated link|Gaianism}}<br />
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Category:Astronomical hypotheses<br />
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类别: 天文学假设<br />
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* {{annotated link|Holism}}<br />
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Category:Meteorological hypotheses<br />
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类别: 气象假说<br />
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<small>This page was moved from [[wikipedia:en:Gaia hypothesis]]. Its edit history can be viewed at [[盖亚假说/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%96%E4%BA%9A%E5%81%87%E8%AF%B4&diff=21548盖亚假说2021-02-04T02:54:44Z<p>Vicky:/* Details细节 */</p>
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<div>此词条由Henry第一次翻译。<br />
已由三奇同学完成校对。<br />
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{{short description|Hypothesis that living organisms interact with their surroundings in a self-regulating system}}<br />
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[[File:The Earth seen from Apollo 17.jpg|thumb|The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth]]'s conditions, as the Earth is the only planet currently known to harbour life (''[[The Blue Marble]]'', 1972 [[Apollo 17]] photograph)]]<br />
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The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth's conditions, as the Earth is the only planet currently known to harbour life (The Blue Marble, 1972 Apollo 17 photograph)]]<br />
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对行星可居住性的研究主要基于对[[地球条件]的了解进行推断,因为地球是目前已知的唯一一颗拥有生命的行星 <br />
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The '''Gaia hypothesis''' {{IPAc-en|ˈ|ɡ|aɪ|.|ə}}, also known as the '''Gaia theory''' or the '''Gaia principle''', proposes that living [[organism]]s interact with their [[Inorganic compound|inorganic]] surroundings on [[Earth]] to form a [[Synergy|synergistic]] and [[Homeostasis|self-regulating]], [[complex system]] that helps to maintain and perpetuate the conditions for [[life]] on the planet.<br />
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The Gaia hypothesis , also known as the Gaia theory or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.<br />
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盖亚假说(又称盖亚理论或盖亚原理)认为,生物体与地球上的无机环境相互作用,形成一个协同和自我调节的复杂系统,有助于维持和延续地球上的生命条件。<br />
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The hypothesis was formulated by the chemist [[James Lovelock]]<ref name="J1972" /> and co-developed by the microbiologist [[Lynn Margulis]] in the 1970s.<ref name="lovelock1974">{{cite journal|last1=Lovelock|first1=J.E.|last2=Margulis|first2=L.|title=Atmospheric homeostasis by and for the biosphere: the Gaia hypothesis|journal=Tellus|date=1974|volume=26|series=Series A|issue=1–2|pages=2–10|doi=10.1111/j.2153-3490.1974.tb01946.x|publisher=International Meteorological Institute|location=Stockholm|issn=1600-0870|ref=harv|bibcode=1974Tell...26....2L}}</ref> Lovelock named the idea after [[Gaia]], the primordial goddess who personified the Earth in [[Greek mythology]]. In 2006, the [[Geological Society of London]] awarded Lovelock the [[Wollaston Medal]] in part for his work on the Gaia hypothesis.<ref>{{cite web|title=Wollaston Award Lovelock|url=https://www.geolsoc.org.uk/About/History/Awards-Citations-Replies-2001-Onwards/2006-Awards-Citations-Replies|accessdate=19 October 2015}}</ref><br />
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The hypothesis was formulated by the chemist James Lovelock Lovelock named the idea after Gaia, the primordial goddess who personified the Earth in Greek mythology. In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.<br />
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这个假设是由化学家詹姆斯·洛夫洛克提出的,他以希腊神话中地球的化身盖亚的名字命名了这个想法。2006年,伦敦地质学会授予洛夫洛克沃拉斯顿勋章,以表彰他在<font color="#ff8000"> 盖亚假说Gaia hypothesis</font>方面的工作。 <br />
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Topics related to the hypothesis include how the [[biosphere]] and the [[evolution]] of organisms affect the stability of [[global temperature]], [[salinity]] of [[seawater]], [[atmospheric oxygen]] levels, the maintenance of a [[hydrosphere]] of liquid water and other environmental variables that affect the [[habitability of Earth]].<br />
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Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenance of a hydrosphere of liquid water and other environmental variables that affect the habitability of Earth.<br />
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与该假设有关的主题包括生物圈和生物体的进化如何影响全球温度的稳定性、海水的盐度、大气中的氧含量、液态水水圈的维持以及其他影响地球宜居性的环境变量。<br />
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The Gaia hypothesis was initially criticized for being [[teleological]] and against the principles of [[natural selection]], but later refinements aligned the Gaia hypothesis with ideas from fields such as [[Earth system science]], [[biogeochemistry]] and [[systems ecology]].<ref name="Turney, Jon 2003"/><ref name="Schwartzman2002">{{cite book |author=Schwartzman, David |title=Life, Temperature, and the Earth: The Self-Organizing Biosphere |publisher=Columbia University Press |date=2002 |isbn=978-0-231-10213-1 }}</ref><ref>Gribbin, John (1990), "Hothouse earth: The greenhouse effect and Gaia" (Weidenfeld & Nicolson)</ref> Lovelock also once described the "geophysiology" of the Earth.<ref name="agesofgaia">Lovelock, James, (1995) "The Ages of Gaia: A Biography of Our Living Earth" (W.W.Norton & Co)</ref>{{Explain|date=December 2017}} Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<ref name="kirchner2002">{{Citation |last= Kirchner |first = James W. |title =Toward a future for Gaia theory |journal=[[Climatic Change (journal)|Climatic Change]] |volume = 52 |issue = 4 |pages = 391–408 |date = 2002 | doi = 10.1023/a:1014237331082 }}</ref><ref name="volk2002">{{Citation |last= Volk |first = Tyler |title =The Gaia hypothesis: fact, theory, and wishful thinking |journal = Climatic Change |volume = 52 |issue = 4 |pages = 423–430 |date = 2002 | doi = 10.1023/a:1014218227825 }}</ref><ref name="beerling2007">{{cite book |last=Beerling |first=David |authorlink=David Beerling|date=2007 |title=The Emerald Planet: How plants changed Earth's history |url=http://ukcatalogue.oup.com/product/9780192806024.do |location=Oxford|publisher=Oxford University Press |page= |isbn= 978-0-19-280602-4 |accessdate= }}</ref><br />
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The Gaia hypothesis was initially criticized for being teleological and against the principles of natural selection, but later refinements aligned the Gaia hypothesis with ideas from fields such as Earth system science, biogeochemistry and systems ecology. Lovelock also once described the "geophysiology" of the Earth. Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<br />
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盖亚假说最初被诟病为目的论、反对自然选择的原则,但后来的改进使盖亚假说与来自地球系统科学、生物地球化学和系统生态学等领域的观点相一致。洛夫洛克还曾经描述过地球的“地球物理学”。即便如此,盖亚假说仍然受到一些批评,今天许多科学家认为只有少数证据支持这一理论,或与现有的证据相矛盾。<br />
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==Overview总览==<br />
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Gaian hypotheses suggest that organisms [[Co-evolution|co-evolve]] with their environment: that is, they "influence their [[abiotic]] environment, and that environment in turn influences the [[Biota (ecology)|biota]] by [[Darwinism|Darwinian process]]". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early [[Bacteria|thermo-acido-philic]] and [[methanogenic bacteria]] towards the oxygen-enriched [[atmosphere]] today that supports more [[Phanerozoic|complex life]].<br />
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Gaian hypotheses suggest that organisms co-evolve with their environment: that is, they "influence their abiotic environment, and that environment in turn influences the biota by Darwinian process". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early thermo-acido-philic and methanogenic bacteria towards the oxygen-enriched atmosphere today that supports more complex life.<br />
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盖亚假说认为,生物体与其环境共同进化。也就是说,生物“影响它们的非生物环境,而环境反过来又通过自然选择的过程影响生物群”。Lovelock(1995)在他的第二本书中提供了证据,展示了从早期嗜酸、产甲烷细菌的世界向今天支持更复杂生命的富氧大气的进化。<br />
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A reduced version of the hypothesis has been called "influential Gaia"<ref name=":02">{{Cite journal|last=Lapenis|first=Andrei G.|year=2002|title=Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?|url=|journal=The Professional Geographer|volume=54 |issue=3|pages=379–391|via=[Peer Reviewed Journal]|doi=10.1111/0033-0124.00337}}</ref> in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the [[Biota (ecology)|biota]] influence certain aspects of the abiotic world, e.g. [[temperature]] and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<ref name=":02" /> and biogeochemical processes. An example is how the activity of [[Photosynthesis|photosynthetic]] bacteria during Precambrian times completely modified the [[Earth's atmosphere|Earth atmosphere]] to turn it aerobic, and thus supports the evolution of life (in particular [[eukaryotic]] life).<br />
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A reduced version of the hypothesis has been called "influential Gaia" in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the biota influence certain aspects of the abiotic world, e.g. temperature and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<br />
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在《生物圈的定向进化: 生物地球化学选择还是盖亚? 》一书中,这一假说的简化版被称为“有影响力的盖亚”。安德烈·G·拉佩尼斯在这本书中指出生物影响着非生物世界的温度和大气等多个方面。这本书不是一个人的工作,而是一群俄罗斯科研人员的成果合并成这个通过同行评议的出版物。它通过“微观力量”阐述了生命与环境的共同进化。<br />
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Since barriers existed throughout the twentieth century between Russia and the rest of the world, it is only relatively recently that the early Russian scientists who introduced concepts overlapping the Gaia hypothesis have become better known to the Western scientific community.<ref name=":02" /> These scientists include [[Piotr Kropotkin|Piotr Alekseevich Kropotkin]] (1842–1921) (although he spent much of his professional life outside Russia), Vasil’evich Rizpolozhensky (1847–1918), [[Vladimir Ivanovich Vernadsky]] (1863–1945), and Vladimir Alexandrovich Kostitzin (1886–1963).<br />
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由于二十世纪苏联与西方国家存在隔阂,直到最近,在盖亚假说中引进重叠概念的早期苏联科学家才为西方科学界所熟知。<br />
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The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<br />
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盖亚假说认为,地球是一个自我调节的复杂系统,包括生物圈、大气层、水圈和土壤圈,作为一个进化的系统紧密结合在一起。这个假说认为,这个被称为盖亚的系统作为整体,寻求适合当代生命的物理和化学环境。<br />
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Biologists and Earth scientists usually view the factors that stabilize the characteristics of a period as an undirected [[emergent property]] or [[entelechy]] of the system; as each individual species pursues its own self-interest, for example, their combined actiYons may have counterbalancing effects on environmental change. Opponents of this view sometimes reference examples of events that resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth's atmosphere from a [[reducing environment]] to an [[oxygen]]-rich one at the end of the [[Archean|Archaean]] and the beginning of the [[Proterozoic]] periods.<br />
生物学家和地球科学家通常将平衡一个时期的特征的因素视为系统的无方向[[涌现属性]]或[[有目的行为]];例如,由于每个物种都追求自身利益,它们的联合行动可能对环境变化产生抵消作用。反对这一观点的人有时会举出一些导致了巨大变化而非平衡的事件作为反例,例如在[[太古宙|太古代]]末期和[[元古代]]时期开始时,地球大气从[[还原环境]]转变为富含[[氧气]]。 <br />
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Gaia evolves through a cybernetic feedback system operated unconsciously by the biota, leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially microorganisms, with inorganic elements. These processes establish a global control system that regulates Earth's surface temperature, atmosphere composition and ocean salinity, powered by the global thermodynamic disequilibrium state of the Earth system.<!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
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盖亚通过一个由生物群无意识操作的控制论反馈系统实现进化,在完全的内稳态中广泛获得稳定的可居住条件。地球表面的许多过程对生命的保障条件至关重要,这些过程依赖于生命形式,特别是微生物与无机元素的相互作用。这些过程建立了一个全球控制系统,由地球系统的全球热力学不平衡状态提供动力,调节地球表面温度、大气成分和海洋盐度。<br />
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Less accepted versions of the hypothesis claim that changes in the biosphere are brought about through the [[Superorganism|coordination of living organisms]] and maintain those conditions through [[homeostasis]]. In some versions of [[Gaia philosophy]], all lifeforms are considered part of one single living planetary being called ''Gaia''. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the [[Coevolution|coevolving]] diversity of living organisms.<br />
一种不太被接受的假说声称生物圈的变化是通过[[超级有机体|生物体的协调]]来实现的,并通过[[内稳态]]来维持这些条件。在一些版本的[[盖亚哲学]]中,所有的生命形式都是一个被称为“盖亚”的生命行星的一部分。在这种观点下,大气、海洋和地壳将是盖亚通过生物多样性进行干预的结果。 <br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of biogeochemistry, and it is being investigated also in other fields like Earth system science. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<br />
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以前在生物地球化学领域已经观察到受生命形式影响的行星内稳态的存在,而且地球系统科学等其他领域也在研究这一现象。盖亚假说的原创性依赖于这样一种观点: 即使地球或外部事件威胁到内稳态平衡,盖亚也会为了保持生命的最佳状态而积极追求这种平衡。<br />
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The Gaia hypothesis was an influence on the [[deep ecology]] movement.<ref>David Landis Barnhill, Roger S. Gottlieb (eds.), ''Deep Ecology and World Religions: New Essays on Sacred Ground'', SUNY Press, 2010, p. 32.</ref><br />
盖亚假说对[[深层生态学]]运动产生了影响 <br />
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==Details细节==<br />
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Rob Rohde's palaeotemperature graphs<br />
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罗布·罗德的古温度图<br />
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The Gaia hypothesis posits that the Earth is a self-regulating [[complex system]] involving the [[biosphere]], the [[Earth's atmosphere|atmosphere]], the [[hydrosphere]]s and the [[pedosphere]], tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<ref name="vanishing255">Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 255. {{ISBN|978-0-465-01549-8}}</ref><br />
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盖亚假说假设地球是一个自我调节的[[复杂系统]],包括[[生物圈]]、[[地球大气|大气]]、[[水圈]]和[[土壤圈]],作为一个进化系统紧密耦合。该假说认为,这个系统作为一个整体,称为盖亚,寻求一个最适合当代生活的物理和化学环境 <br />
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Since life started on Earth, the energy provided by the Sun has increased by 25% to 30%; however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on Titan. research has suggested that "oxygen shocks" and reduced methane levels led, during the Huronian, Sturtian and Marinoan/Varanger Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre Phanerozoic biosphere to fully self-regulate.<br />
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自从地球上有生命以来,太阳提供的能量增加了25%到30%;然而,地球表面温度一直保持在适宜居住的水平上,不曾突破上限或是下限。洛夫洛克还假设,产甲烷菌在早期大气中产生了较高水平的甲烷,这与在石化烟雾中发现的成分相似,在某些方面与土卫六上的大气相似。研究表明,在休伦期、斯图尔特期和马里诺/瓦朗格冰期,“氧冲击”和甲烷含量降低导致世界几乎变成了一个坚实的“雪球”。这些时代是前显生宙生物圈完全拥有自我调节能力的证据。<br />
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Gaia evolves through a [[Cybernetic#In biology|cybernetic]] [[feedback]] system operated unconsciously by the [[biota (ecology)|biota]], leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially [[microorganisms]], with inorganic elements. These processes establish a global control system that regulates Earth's [[Sea surface temperature|surface temperature]], [[atmosphere composition]] and [[ocean]] [[salinity]], powered by the global thermodynamic disequilibrium state of the Earth system.<ref>Kleidon, Axel. ''How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?''. Article submitted to the ''Philosophical Transactions of the Royal Society'' on Thu, 10 Mar 2011</ref><!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
盖亚通过一个[[控制论|生物学|控制论]][[反馈]]系统在[[生物群(生态学)|生物群]]的无意识运作中实现进化,导致在完全的内稳态中广泛存在稳定的可居住条件。地球表面对生命条件至关重要的许多过程都依赖于生物,特别是[微生物]与无机元素的相互作用。这些过程建立了一个全球控制系统,调节地球的[[海表温度|表面温度]]、[[大气组成]]和[[海洋]][[盐度]],其动力来自地球系统的全球热力学不平衡状态。<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
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温室气体CO<sub>2</sub>的处理在维持地球温度在可居住范围内起着关键作用(解释详见下文)。<br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of [[biogeochemistry]], and it is being investigated also in other fields like [[Earth system science]]. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 179. {{ISBN|978-0-465-01549-8}}</ref><br />
受生命形式影响的行星内稳态的存在,以前在[[生物地球化学]]领域就已被观察到,而且其他领域,如[[地球系统科学]]也在研究这种稳态。盖亚假说的独创性依赖于这样一种观点,即盖亚积极追求这种内平衡,以保持维护生命的最佳状态,即使是在地球或外部事件威胁它们的时候。<br />
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The CLAW hypothesis, inspired by the Gaia hypothesis, proposes a feedback loop that operates between ocean ecosystems and the Earth's climate. The hypothesis specifically proposes that particular phytoplankton that produce dimethyl sulfide are responsive to variations in climate forcing, and that these responses lead to a negative feedback loop that acts to stabilise the temperature of the Earth's atmosphere.<br />
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受盖亚假说的启发,CLAW 假说提出了一个在海洋生态系统和地球气候之间运行的反馈回路。该假说特别提出,产生二甲硫醚的浮游植物对气候变化有反应,这些反应导致了一个负反馈循环,稳定了地球大气的温度。<br />
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===Regulation of global surface temperature地球表面温度的调控===<br />
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[[File:All palaeotemps.png|thumb|480px|Rob Rohde's palaeotemperature graphs]]<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of greenhouse gases may cause negative feedbacks in the environment to become positive feedback. Lovelock has stated that this could bring an extremely accelerated global warming, but he has since stated the effects will likely occur more slowly.<br />
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目前,人口的增加及其活动对环境的影响,例如温室气体的增加,可能导致环境中的负反馈成为正反馈。洛夫洛克表示,这可能会极大地加速全球变暖,但他后来又表示,这种影响也可能发生得更慢。<br />
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{{See also|Paleoclimatology}}<br />
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Since life started on Earth, the energy provided by the [[Sun]] has increased by 25% to 30%;<ref name="Owen1979">{{cite journal | author = Owen, T. | author2 = Cess, R.D. | author3 = Ramanathan, V. | date = 1979 | title = Earth: An enhanced carbon dioxide greenhouse to compensate for reduced solar luminosity | journal = [[Nature (journal)|Nature]] | volume = 277 | pages = 640–2 | doi = 10.1038/277640a0 | issue=5698 | bibcode = 1979Natur.277..640O | ref = harv }}</ref> however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on [[Titan (moon)|Titan]].<ref name="agesofgaia"/> This, he suggests tended to screen out ultraviolet until the formation of the ozone screen, maintaining a degree of homeostasis. However, the [[Snowball Earth]]<ref>Hoffman, P.F. 2001. [http://www.snowballearth.org ''Snowball Earth theory'']</ref> research has suggested that "oxygen shocks" and reduced methane levels led, during the [[Huronian]], [[Sturtian]] and [[Marinoan]]/[[Cryogenian|Varanger]] Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre [[Phanerozoic]] biosphere to fully self-regulate.<br />
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Plots from a standard black and white [[Daisyworld simulation]]<br />
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从一个标准的黑白图[[雏菊世界模拟]]<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
说明了在温室气体维持低于临界温度的过程中,CO2起着至关重要的作用。 <br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic group selection and cooperation between organisms, James Lovelock and Andrew Watson developed a mathematical model, Daisyworld, in which ecological competition underpinned planetary temperature regulation.<br />
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有人批评盖亚假说似乎需要有机体之间不切实际的群体选择与合作,为了回应这种批评,James Lovelock 和 Andrew Watson建立了一个数学模型---- 雏菊世界,其中生态竞争支撑着地。<br />
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The [[CLAW hypothesis]], inspired by the Gaia hypothesis, proposes a [[feedback|feedback loop]] that operates between [[ocean]] [[ecosystem]]s and the [[Earth]]'s [[climate]].<ref name="CLAW87">{{cite journal |doi=10.1038/326655a0 |author=[[Robert Jay Charlson|Charlson, R. J.]], [[James Lovelock|Lovelock, J. E]], Andreae, M. O. and Warren, S. G. |title=Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate |journal=Nature |volume=326 |issue=6114 |pages=655–661 |date=1987 |bibcode=1987Natur.326..655C |ref=harv }}</ref> The [[hypothesis]] specifically proposes that particular [[phytoplankton]] that produce [[dimethyl sulfide]] are responsive to variations in [[climate forcing]], and that these responses lead to a [[negative feedback|negative feedback loop]] that acts to stabilise the [[temperature]] of the [[Earth's atmosphere]].<br />
受到盖亚假说启发的[[爪假说]]提出了一个在[[海洋]][[生态系统]]和[[地球]]的[[气候]]之间运行的[[反馈|反馈回路]]。<br />
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Daisyworld examines the energy budget of a planet populated by two different types of plants, black daisies and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the albedo of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
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《雏菊世界》调查了一个星球的能量预算,这个星球上生长着两种不同的植物,黑色雏菊和白色雏菊,这两种植物占据了星球表面的很大一部分。雏菊的颜色影响了地球的反照率,黑色的雏菊吸收更多的光线,使地球变暖,而白色的雏菊则反射更多的光线,使地球变冷。人们认为黑色雏菊在较低的温度下生长和繁殖最好,而白色雏菊则被认为在较高的温度下生长最好。当温度上升到接近白色雏菊所喜欢的温度时,白色雏菊繁殖率高于黑色雏菊,导致更大比例的白色表面,更多的阳光被反射,减少热量输入,最终使地球降温。相反,随着气温的下降,黑色雏菊繁殖率高于白色雏菊,吸收了更多的阳光,使地球变暖。因此,温度会收敛于两种植物繁殖率相等时对应温度的值。<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of [[greenhouse gases]] may cause [[negative feedback]]s in the environment to become [[positive feedback]]. Lovelock has stated that this could bring an [[James Lovelock#The revenge of Gaia|extremely accelerated global warming]],<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, {{ISBN|978-0-465-01549-8}}</ref> but he has since stated the effects will likely occur more slowly.<ref>Lovelock J., NBC News. [http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite Link] Published 23 April 2012, accessed 22 August 2012. {{Webarchive|url=https://web.archive.org/web/20120913163635/http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite |date=13 September 2012 }}</ref><br />
目前,人口的增加及其活动对环境的影响,如[[温室气体]]的倍增,可能导致环境中的[[负反馈]]变成[[正反馈]]。洛夫洛克曾表示,这可能会带来一场【【James Loveloc【《盖亚的复仇』极度加速的全球变暖】】 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this negative feedback due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
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洛夫洛克和沃森指出,在有限的条件下,如果太阳的能量输出发生变化,由于竞争产生的负反馈可以将地球温度稳定在支持生命存在的范围内,而没有生命的地球则会表现出巨大的温度波动。白色和黑色雏菊的百分比会不断变化,以保持植物繁殖率相等的温度值,使两种生命形式都能茁壮成长。<br />
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====Daisyworld simulations雏菊世界模拟====<br />
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[[File:StandardDaisyWorldRun2color.gif|thumb|280px|Plots from a standard black and white [[Daisyworld]] simulation]]<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<br />
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有人认为,这些结果是可以预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的答案。<br />
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{{Main|Daisyworld}}<br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic [[group selection]] and [[Cooperation (evolution)|cooperation]] between organisms, James Lovelock and [[Andrew Watson (scientist)|Andrew Watson]] developed a mathematical model, [[Daisyworld]], in which [[Competition (biology)|ecological competition]] underpinned planetary temperature regulation.<ref name="daisyworld">{{cite journal<br />
有人批评盖亚假说似乎需要有机体之间不切实际的[[群体选择]]和[[合作(进化)|合作]],詹姆斯·洛夫洛克和[[安德鲁·沃森(科学家)|安德鲁·沃森]]开发了一个数学模型,[[雏菊世界]],其中[[竞争(生物学)|生态竞争]]为基础行星温度调节。 <br />
|date = 1983<br />
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Ocean salinity has been constant at about 3.5% for a very long time. Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested that salinity may also be strongly influenced by seawater circulation through hot basaltic rocks, and emerging as hot water vents on mid-ocean ridges. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<br />
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长期以来,海洋盐度一直保持在3.5% 左右。海洋环境中盐度的稳定性很重要,因为大多数细胞需要相当恒定的盐度,一般不能耐受超过5% 的盐度值。海洋盐度为何恒定是一个长期的奥秘,因为没有任何方法可以抵消来自河流的流入盐。最近有人提出,盐分也会洋中脊的热水喷口排出,因此盐度可能受到穿过炽热玄武岩的海水循环的强烈影响。然而,海水的组成离平衡还很远,如果没有有机过程的影响,很难解释这一事实。有一种解释认为,地球历史上盐滩的形成是盐度平衡的原因之一。据推测,这些盐滩是由细菌菌落产生的,它们在生命过程中固定离子和重金属。<br />
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|title = Biological homeostasis of the global environment: the parable of Daisyworld<br />
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|journal = Tellus<br />
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|volume = 35B<br />
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Vostok, Antarctica research station. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
沃斯托克,南极洲研究站。当前期间在左边。<!--基于此图表的GIMP-FX版本的非源材料。现在的版本是正确的,原版的。必须删除这句话:请注意,当前CO2水平超过390ppm,远高于过去40万年来的任何时候-->] <br />
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|pages = 286–9<br />
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|bibcode = 1983TellB..35..284W<br />
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|doi = 10.1111/j.1600-0889.1983.tb00031.x<br />
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The Gaia hypothesis states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organisms or processed by them.<br />
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盖亚假说认为,地球的大气组成是由于生命的存在而保持在动态稳定的状态。大气成分提供了支持现代生命的条件。大气中除惰性气体以外的所有大气气体,要么是由生物体产生的,要么是由生物体加工的。<br />
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|last1 = Watson | first1= A.J. | last2= Lovelock | first2= J.E<br />
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|issue = 4<br />
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The stability of the atmosphere in Earth is not a consequence of chemical equilibrium. Oxygen is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the Great Oxygenation Event. Since the start of the Cambrian period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume. Traces of methane (at an amount of 100,000 tonnes produced per year) should not exist, as methane is combustible in an oxygen atmosphere.<br />
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地球大气层的稳定性不是化学平衡的结果。氧是一种活性化合物,最终会与地球大气层和地壳中的气体和矿物质结合。在大氧化事件开始之前,大约5000万年前,氧气才开始在大气中持续少量存在。自寒武纪以来,大气中氧浓度一直在大气体积的15% 至35% 之间波动。微量的甲烷(每年产生100,000吨)不适合存在,因为甲烷在氧气氛中是可燃的。<br />
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|ref = harv<br />
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}}</ref><br />
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Dry air in the atmosphere of Earth contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases including methane. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. <br />
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地球大气层中的干燥空气大致(按体积计算)含有78.09% 的氮气、20.95% 的氧气、0.93% 的氩气、0.039% 的二氧化碳以及少量的其他气体,包括甲烷。洛夫洛克最初推测,高于25% 的氧气浓度会增加森林大火和森林大火的发生频率。石炭纪和白垩纪煤系地质时期O2浓度确实超过了25%时,正是这一时期形成了火成木炭。这一结果支持了 Lovelock 的论点。<br />
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Daisyworld examines the [[Earth's energy budget|energy budget]] of a [[planet]] populated by two different types of plants, black [[Asteraceae|daisies]] and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the [[albedo]] of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
Daisyworld研究了居住着两种不同类型的植物的[[地球的能源预算|能源预算]],这两种植物是黑色的[[菊科的雏菊]]和白色的雏菊,这两种植物被认为占据了地表的很大一部分。雏菊的颜色影响着这个星球的[反照率],因此黑色雏菊吸收更多的光并温暖地球,而白色雏菊则反射更多的光并使地球降温。黑雏菊在较低温度下生长繁殖最好,而白雏菊在较高温度下生长繁殖最好。当温度上升到接近白色雏菊的最适生长温度时,白色雏菊的繁殖能力超过了黑色雏菊,导致白色表面的比例增大,更多的阳光被反射,减少了热量输入,最终使地球变冷。相反,随着温度的下降,黑雏菊的繁殖能力超过了白雏菊,吸收了更多的阳光,使地球变暖。因此,温度将收敛到两种植物繁殖率相等对应的温度值。 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this [[negative feedback]] due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
Lovelock和Watson表明,在有限的条件范围内,如果太阳的能量输出发生变化,由于竞争而产生的[[负反馈]]可以将地球的温度稳定在支持生命的值上,而没有生命的行星则会出现大范围的温度波动。白雏菊和黑雏菊的比例会不断变化,以使温度保持在植物繁殖率相等的值,从而使两种生命形式都能茁壮成长。 <br />
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Gaia scientists see the participation of living organisms in the carbon cycle as one of the complex processes that maintain conditions suitable for life. The only significant natural source of atmospheric carbon dioxide (CO<sub>2</sub>) is volcanic activity, while the only significant removal is through the precipitation of carbonate rocks. Carbon precipitation, solution and fixation are influenced by the bacteria and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
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盖亚假说的科学家们把生物体参与碳循环看作是维持适合生命条件的复杂过程之一。火山活动是大气中二氧化碳的最重要的自然来源,而碳酸盐岩的沉淀是大气中二氧化碳最重要的去除途径。碳沉淀、溶解和固定受到土壤中细菌和植物根系的影响,这些细菌和植物根系可以改善气体循环,或者在珊瑚礁中,碳酸钙以固体的形式沉积在海底。碳酸钙被活的有机体用来制造含碳的结构和外壳。一旦死亡,生物体的外壳就会沉到海底,在那里它们产生白垩和石灰石的沉淀物。<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<ref>{{cite journal | doi = 10.1023/A:1023494111532 | date = 2003 | last1 = Kirchner | first1 = James W. | journal = Climatic Change | volume = 58 |issue=1–2| pages = 21–45 |title=The Gaia Hypothesis: Conjectures and Refutations | ref = harv}}</ref><br />
有人认为,结果是可预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的反应。 <br />
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One of these organisms is Emiliania huxleyi, an abundant coccolithophore algae which also has a role in the formation of clouds. CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants. Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean algal blooms are also increasing.<br />
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其中一种是赫氏圆石藻,这是一种数量丰富的颗石藻类,也参与了云的形成。通过增加球石氟化物的寿命来补偿过量的CO < sub > 2 </sub > ,增加了锁定在海底的 CO < sub > 2 </sub > 的数量。球石粉会增加云量,从而控制地表温度,有助于降低整个地球的温度,有利于地球上植物所必需的降水。近年来,大气中 CO < < sub > 2 </sub > 浓度有所增加,有证据表明,海洋藻华的浓度也在增加。<br />
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===Regulation of oceanic salinity海洋盐度调节 ===<br />
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Lichen and other organisms accelerate the weathering of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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地衣和其他生物加速了岩石表面的风化,而岩石在土壤中的分解也加快了,这要归功于根、真菌、细菌和地下动物的活动。因此,二氧化碳从大气层流向土壤的过程是在生物的帮助下调节的。当大气中 CO2水平升高时,温度升高,植物生长。这种生长会增加植物对二氧化碳的消耗,植物会将二氧化碳处理到土壤中,从大气中排出。<br />
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Ocean [[salinity]] has been constant at about 3.5% for a very long time.<ref name=":0">{{Cite book|title=The Introduction to Ocean Sciences|last=Segar|first=Douglas|publisher=Library of Congress|year=2012|isbn=978-0-9857859-0-1|location=http://www.reefimages.com/oceans/SegarOcean3Chap05.pdf|pages=Chapter 5 3rd Edition|quote=|via=}}</ref> Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested<ref name="Gorham19912">{{cite journal|last=Gorham|first=Eville|date=1 January 1991|title=Biogeochemistry: its origins and development|journal=Biogeochemistry|publisher=Kluwer Academic|volume=13|issue=3|pages=199–239|doi=10.1007/BF00002942|issn=1573-515X|ref=harv}}</ref> that salinity may also be strongly influenced by [[seawater]] circulation through hot [[basalt]]ic rocks, and emerging as hot water vents on [[mid-ocean ridge]]s. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<ref name=":0" /><br />
在很长一段时间内,海洋盐度一直保持在3.5%左右。[23]海洋环境中的盐度稳定性非常重要,因为大多数细胞需要相当恒定的盐度,并且通常不能耐受超过5%的盐度值。恒定的海洋盐度是一个长期存在的谜团,因为没有任何过程可以抵消河流中的盐流入。大洋中脊上的热水喷口会排出盐分,有人认为[24]这说明盐分也会受到海水循环的强烈影响。然而,海水的组成远未达到平衡,如果没有有机过程的影响,很难解释这一事实。地球历史中盐滩的形成是一个常用的证据。据推测,这些盐滩是由在生命过程中固定离子和重金属的菌落产生的<br />
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In the biogeochemical processes of Earth, sources and sinks are the movement of elements. The composition of salt ions within our oceans and seas is: sodium (Na<sup>+</sup>), chlorine (Cl<sup>−</sup>), sulfate (SO<sub>4</sub><sup>2−</sup>), magnesium (Mg<sup>2+</sup>), calcium (Ca<sup>2+</sup>) and potassium (K<sup>+</sup>). The elements that comprise salinity do not readily change and are a conservative property of seawater.<ref name=":0" /> There are many mechanisms that change salinity from a particulate form to a dissolved form and back. The known sources of sodium i.e. salts are when weathering, erosion, and dissolution of rocks are transported into rivers and deposited into the oceans.<br />
在地球的生物地球化学过程中,源和汇是元素的运动。我们海洋中盐离子的组成是:钠(Na+)、氯(Cl-)、硫酸盐(SO42-)、镁(Mg2+)、钙(Ca2+)和钾(K+)。构成盐度的元素不易变化,是海水的一种保守属性。[23]有许多机制可以将盐度从颗粒形态改变为溶解形态,然后再返回。已知的钠(即盐)因为岩石的风化、侵蚀和溶解作用被输送到河流中并沉积到海洋中。 <br />
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The [[Mediterranean Sea]] as being Gaia's kidney is found ([http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/ here]) by Kenneth J. Hsue, a correspondence author in 2001. The "[[desiccation]]" of the Mediterranean is the evidence of a functioning kidney. Earlier "kidney functions" were performed during the "[[Deposition (geology)|deposition]] of the [[Cretaceous]] ([[Atlantic Ocean|South Atlantic]]), [[Jurassic]] ([[Gulf of Mexico]]), [[Permian–Triassic extinction event|Permo-Triassic]] ([[Europe]]), [[Devonian]] ([[Canada]]), [[Cambrian]]/[[Precambrian]] ([[Gondwana]]) saline giants."<ref>{{Cite web|url=http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/|title=Scientia Marina: List of Issues|last=http://www.webviva.com|first=Justino Martinez. Web Viva 2007|website=scimar.icm.csic.es|language=English|access-date=2017-02-04}}</ref><br />
地中海是盖亚的肾脏,由肯尼斯·J·休伊(KennethJ.Hsue)在2001年发现的。地中海的“干涸”是肾功能正常的证据。早期的“肾功能”是在“白垩纪(南大西洋)、侏罗纪(墨西哥湾)、二叠纪-三叠纪(欧洲)、泥盆纪(加拿大)、寒武纪/前寒武纪(冈瓦纳)盐沼沉积时期进行的。” <br />
[[Earthrise taken from Apollo 8 on December 24, 1968]]<br />
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[1968年12月24日阿波罗8号拍摄的地出]<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = <br />
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地球是一个完整的整体,一个有生命的存在,这个观念有着悠久的传统。神话中的盖亚是拟人化地球的原始希腊女神,是希腊版本的“自然母亲”(来自 Ge = 地球,和 Aia = <br />
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===Regulation of oxygen in the atmosphere大气层的氧气调节===<br />
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PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a suggestion from the novelist William Golding, who was living in the same village as Lovelock at the time (Bowerchalke, Wiltshire, UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of living organisms, climate, and Earth's crust. His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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派祖母,或地球母亲。詹姆斯·洛夫洛克根据小说家威廉·戈尔丁的建议给他的假设起了这个名字,他当时和洛夫洛克住在同一个村子里(英国威尔特郡鲍尔查尔克)。戈尔丁的建议是以Gea为基础的,Gea是希腊女神名字的另一种拼写,在地质学、地球物理和地球化学中,Gea是前缀。后来,博物学家和探险家亚历山大·冯·洪堡认识到生物、气候和地壳的共同进化。他的远见卓识的声明在西方没有被广泛接受,几十年后,盖亚假说刚提出时同样受到了科学界的抵制。<br />
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[[File:Vostok 420ky 4curves insolation.jpg|thumb|280px|Levels of gases in the atmosphere in 420,000 years of ice core data from [[Vostok Station|Vostok, Antarctica research station]]. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
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{{See also|Geological history of oxygen}}<br />
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Also in the turn to the 20th century Aldo Leopold, pioneer in the development of modern environmental ethics and in the movement for wilderness conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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同样在20世纪之交,现代环境伦理学发展的先驱、荒野保护运动的先驱奥尔多 · 利奥波德在他的生物中心或整体的土地伦理学中提出了一个有生命的地球。<br />
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The Gaia hypothesis states that the Earth's [[Atmospheric chemistry#Atmospheric composition|atmospheric composition]] is kept at a dynamically steady state by the presence of life.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 163. {{ISBN|978-0-465-01549-8}}</ref> The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than [[noble gas]]es present in the atmosphere are either made by organisms or processed by them.<br />
盖亚假说指出,地球的大气成分由于生命的存在而保持在动态稳定的状态。大气中除惰性气体以外的所有大气气体都是由生物体制造或加工而成。<br />
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The stability of the atmosphere in Earth is not a consequence of [[chemical equilibrium]]. [[Oxygen]] is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the [[Great Oxygenation Event]].<ref name=Anabar2007>{{Cite journal| last4 = Arnold| last6 = Creaser| last3 = Lyons| first1 = A. | first2 = Y.| last9 = Scott| last2 = Duan | first3 = T. | first4 = G.| last8 = Gordon | first5 = B. | first10 = J. | first6 = R.| last10 = Garvin | first7 = A.| last11 = Buick | first8 = G. | first11 = R. | first9 = C.| title = A whiff of oxygen before the great oxidation event?| journal = Science| volume = 317| issue = 5846| year = 2007| last7 = Kaufman| pages = 1903–1906| last5 = Kendall| pmid = 17901330| last1 = Anbar | doi = 10.1126/science.1140325|bibcode = 2007Sci...317.1903A }}</ref> Since the start of the [[Cambrian]] period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume.<ref name=Berner1999>{{Cite journal<br />
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Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut William Anders in 1968 during the Apollo 8 mission became, through the Overview Effect an early symbol for the global ecology movement.<br />
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盖亚假说和环境运动的另一个影响来自于苏联和美利坚合众国之间太空竞赛。在20世纪60年代,第一批进入太空的人类可以看到地球作为一个整体的样子。1968年,宇航员威廉 · 安德斯在阿波罗8号任务期间拍摄的地出照片,通过总体效应成为全球生态运动的早期象征。<br />
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| pmid = 10500106<br />
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| date=Sep 1999 | last1 = Berner | first1 = R. A.<br />
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| title = Atmospheric oxygen over Phanerozoic time<br />
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[[James Lovelock, 2005]]<br />
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[ James Lovelock,2005]<br />
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| volume = 96<br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the Jet Propulsion Laboratory in California on methods of detecting life on Mars. The first paper to mention it was Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life, co-authored with C.E. Giffin. A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the Pic du Midi observatory, planets like Mars or Venus had atmospheres in chemical equilibrium. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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65年9月,洛夫洛克在加利福尼亚喷气推进实验室研究探测火星生命的方法时,开始定义由生物群落控制的自我调节地球的概念。第一篇提到它的论文是行星大气:与C.E.Giffin合著的与生命存在有关的成分和其他变化。一个主要的概念是,通过大气的化学成分可以在行星尺度上探测到生命。根据picdumidi天文台收集的数据,像火星或金星这样的行星,其大气层处于化学平衡状态。这种与地球大气的差异被认为是这些行星上没有生命的证据。 <br />
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Lovelock formulated the Gaia Hypothesis in journal articles in 1972 and 1974, and a popular book length version of the hypothesis, published in 1979 as The Quest for Gaia, began to attract scientific and critical attention.<br />
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洛夫洛克在1972年和1974年的期刊文章中提出了盖亚假说,并在1979年出版了一本畅销书,名为《寻找盖亚》 ,开始引起科学界和批判界的关注。<br />
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| journal = Proceedings of the National Academy of Sciences of the United States of America<br />
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Lovelock called it first the Earth feedback hypothesis, and it was a way to explain the fact that combinations of chemicals including oxygen and methane persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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洛夫洛克首先将其称为地球反馈假说,解释氧气和甲烷等化学物质在地球大气中如何保持稳定浓度。洛夫洛克认为,在其他行星的大气层中探测这种组合,是一种相对便宜可靠的探测生命的方法。<br />
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| doi = 10.1073/pnas.96.20.10955<br />
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[[Lynn Margulis]]<br />
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[琳 · 玛格丽丝]<br />
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|bibcode = 1999PNAS...9610955B }}</ref> Traces of [[Atmospheric methane|methane]] (at an amount of 100,000 tonnes produced per year)<ref name="Cicerone1988">{{cite journal |last1=Cicerone |first1=R.J. |last2=Oremland |first2=R.S. |date=1988 |title=Biogeochemical aspects of atmospheric methane |journal=Global Biogeochemical Cycles |volume=2 |issue=4 |pages=299–327 |url=//webfiles.uci.edu/setrumbo/public/Methane_papers/Cicerone_Global%20Biogeochem%20Cy_1988.pdf |doi=10.1029/GB002i004p00299 |bibcode=1988GBioC...2..299C}}</ref> should not exist, as methane is combustible in an oxygen atmosphere.<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<br />
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后来出现了其他关系,例如海洋生物产生的硫和碘的数量与陆地生物所需的数量大致相同,这些都支持了这一假说。<br />
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Dry air in the [[atmosphere of Earth]] contains roughly (by volume) 78.09% [[nitrogen]], 20.95% oxygen, 0.93% [[argon]], 0.039% [[Carbon dioxide in the Earth's atmosphere|carbon dioxide]], and small amounts of other gases including [[methane]]. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. {{citation needed|date=June 2012}}<br />
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[[地球大气]]中的干空气大约(按体积)包含78.09%[[氮]],20.95%的氧,0.93%[[氩]],0.039%[地球大气中的二氧化碳|二氧化碳]],以及少量其他气体,包括[[甲烷]]。洛夫洛克最初推测,氧气浓度超过25%会增加森林火灾和火灾的发生率。最近在石炭纪和白垩纪煤系中火成木炭的研究(这两个地质时期O<sub>2</sub>浓度超过25%)支持了Lovelock的观点 <br />
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In 1971 microbiologist Dr. Lynn Margulis joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet. The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of eukaryotic organelles and her contributions to the endosymbiotic theory, nowadays accepted. Margulis dedicated the last of eight chapters in her book, The Symbiotic Planet, to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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1971年,微生物学家 Lynn Margulis 博士加入了 Lovelock 的行列,努力将最初的假设充实为科学证明的概念。Margulis 贡献了她关于微生物如何影响大气层和地球表面不同层次的知识。这位美国生物学家也唤受到科学界的批评,因为她倡导真核细胞器起源的理论,以及她对美国共生发源学会的贡献——现在被接受了。玛格丽丝在她的书《共生星球》中将最后八章用于描述盖亚。然而,她反对对盖亚的广泛拟人化,并强调盖亚“不是一个有机体” ,而是“有机体之间相互作用的一个新兴属性”。她将盖亚定义为“组成地球表面一个巨大生态系统的一系列相互作用的生态系统”。句号”。这本书最令人难忘的“口号”实际上是由马古利斯的一个学生打趣说的: “从太空看,盖亚只是共生而已。”。<br />
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===Processing of CO<sub>2</sub>二氧化碳处理===<br />
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{{See also|Carbon cycle}}<br />
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James Lovelock called his first proposal the Gaia hypothesis but has also used the term Gaia theory. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments and provided a number of useful predictions. In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating. The principal sponsor was the National Audubon Society. Speakers included James Lovelock, George Wald, Mary Catherine Bateson, Lewis Thomas, John Todd, Donald Michael, Christopher Bird, Thomas Berry, David Abram, Michael Cohen, and William Fields. Some 500 people attended.<br />
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詹姆斯 · 洛夫洛克称他的第一个提议为盖亚假说,但也使用了盖亚理论这个术语。洛夫洛克说,最初的提法是基于观察,但仍然缺乏科学的解释。盖亚假说从那以后得到了一些科学实验的支持,并提供了一些有用的预测。事实上,更广泛的研究证明了最初的假设是错误的,在这个意义上,不是生命本身,而是整个地球系统在调节。主要赞助者是奥杜邦学会。讲者包括 James Lovelock、 George Wald、 Mary Catherine Bateson、 Lewis Thomas、 John Todd、 Donald Michael、 Christopher Bird、 Thomas Berry、 David Abram、 Michael Cohen 和 William Fields。大约有500人参加。<br />
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Gaia scientists see the participation of living organisms in the [[carbon cycle]] as one of the complex processes that maintain conditions suitable for life. The only significant natural source of [[Carbon dioxide in Earth's atmosphere|atmospheric carbon dioxide]] ([[Carbon dioxide|CO<sub>2</sub>]]) is [[volcanic activity]], while the only significant removal is through the precipitation of [[carbonate rocks]].<ref name="Karhu1996">{{cite journal | author = Karhu, J.A. | author2 = Holland, H.D. | date = 1 October 1996 | title = Carbon isotopes and the rise of atmospheric oxygen | journal = [[Geology (journal)|Geology]] | volume = 24 | issue = 10 | pages = 867–870 | doi = 10.1130/0091-7613(1996)024<0867:CIATRO>2.3.CO;2|bibcode = 1996Geo....24..867K | ref = harv}}</ref> Carbon precipitation, solution and [[Carbon fixation|fixation]] are influenced by the [[bacteria]] and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
盖亚的科学家认为,生物参与[[碳循环]是维持适宜生命条件的复杂过程之一。[[地球大气中的二氧化碳|大气二氧化碳]]([[二氧化碳| CO2]])最重要的自然来源是[[火山活动]],而最重要的去除过程是[[碳酸盐岩]]的沉淀,溶液和[[固碳|固碳]]受土壤中的[[细菌]]和植物根系的影响,它们改善了气体循环,珊瑚礁中碳酸钙以固体形式沉积在海底。碳酸钙被生物用来制造含碳结构和贝壳。一旦死亡,这些生物的壳就会落到海底,在那里它们会产生白垩和石灰岩的沉积物。 <br />
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One of these organisms is ''[[Emiliania huxleyi]]'', an abundant [[coccolithophore]] [[algae]] which also has a role in the formation of [[cloud]]s.<ref name="Harding2006">{{cite book |author=Harding, Stephan |title=Animate Earth |publisher=Chelsea Green Publishing |date=2006 |pages=65 |isbn=978-1-933392-29-5 }}</ref> CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants.{{citation needed|date=July 2015}} Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean [[algal bloom]]s are also increasing.<ref>{{Cite web | date = 12 September 2007 | title = Interagency Report Says Harmful Algal Blooms Increasing | url = http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | url-status = dead | archiveurl = https://web.archive.org/web/20080209234239/http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | archivedate = 9 February 2008 }}</ref><br />
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In 1988, climatologist Stephen Schneider organised a conference of the American Geophysical Union. The first Chapman Conference on Gaia,<br />
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在1988年,气候学家史蒂芬·史奈德组织了一次美国美国地球物理联盟协会的会议。关于盖亚假说的第一次查普曼会议,<br />
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[[Lichen]] and other organisms accelerate the [[weathering]] of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the Daisyworld Model (and its modifications, above) as evidence against most of these criticisms.<br />
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然而,洛夫洛克和其他支持盖亚理论的科学家确实试图反驳这样一种说法,即这种假设不科学,因为不可能通过控制实验来检验它。例如,针对盖亚假说是目的论的指责,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修正,上文)反驳这些批评。<br />
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==History历史==<br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of teleologism ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,这一版本中盖亚并不是有意地在她的环境中维持生命赖以生存的复杂平衡。看起来,盖亚假说“故意”行为的说法只是他那本广受欢迎的书中的一个比喻性陈述,并不是字面意义上的理解。这种对盖亚假说的新陈述更能为科学界所接受。在这次会议之后,大多数关于目的论的指责都停止了。<br />
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===Precedents先例===<br />
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[[File:NASA-Apollo8-Dec24-Earthrise.jpg|thumb|''[[Earthrise]]'' taken from [[Apollo 8]] on December 24, 1968]]<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000, the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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到2000年6月23日在西班牙巴伦西亚举行关于盖亚假说的第二次查普曼会议时,情况发生了重大变化。与其讨论盖亚假说的目的论观点,或盖亚假说的“类型” ,不如将重点放在具体的机制上,通过这些机制,短期内基本稳态在重要的进化长期结构变化的框架内得以维持。<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The [[Gaia (mythology)|mythical Gaia]] was the primal Greek goddess personifying the [[Earth]], the Greek version of "[[Mother Nature]]" (from Ge = Earth, and Aia = <br />
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[[PIE]] grandmother), or the [[Earth Mother]]. James Lovelock gave this name to his hypothesis after a suggestion from the novelist [[William Golding]], who was living in the same village as Lovelock at the time ([[Bowerchalke]], [[Wiltshire]], UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry.<ref name=vanish09 /> Golding later made reference to Gaia in his [[Nobel prize]] acceptance speech.<br />
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The major questions were:<br />
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主要的问题是:<br />
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In the eighteenth century, as [[geology]] consolidated as a modern science, [[James Hutton]] maintained that geological and biological processes are interlinked.<ref name=CapraWeb>{{cite book |author=Capra, Fritjof |title=The web of life: a new scientific understanding of living systems |publisher=Anchor Books |location=Garden City, N.Y |date=1996 |page=[https://archive.org/details/weboflifenewscie00capr/page/23 23] |isbn=978-0-385-47675-1 |url=https://archive.org/details/weboflifenewscie00capr/page/23 }}</ref> Later, the [[naturalist]] and explorer [[Alexander von Humboldt]] recognized the coevolution of living organisms, climate, and Earth's crust.<ref name=CapraWeb /> In the twentieth century, [[Vladimir Vernadsky]] formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian [[geochemist]] and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological processes. During the 1920s he published works arguing that living organisms could reshape the planet as surely as any physical force. Vernadsky was a pioneer of the scientific bases for the environmental sciences.<ref>S.R. Weart, 2003, ''The Discovery of Global Warming'', Cambridge, Harvard Press</ref> His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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"How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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“被称为盖亚的全球生物地球化学/气候系统是如何及时发生变化的?它的历史是什么?盖亚假说能够在一个时间尺度上保持系统的稳定性,但是在更长的时间尺度上仍然经历矢量变化吗?如何利用地质记录来检验这些问题? ”<br />
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"What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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“盖亚假说的结构是什么?这些反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由在任何特定时间进行的学科研究务实地决定的,还是有一些部分应该被认为是最真实的,以了解盖亚假说随着时间的推移包含进化中的生物体?盖亚系统这些不同部分之间的反馈是什么? 对盖亚假说作为全球生态系统的结构和生命的生产力来说,物质的近乎封闭意味着什么? ”<br />
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Also in the turn to the 20th century [[Aldo Leopold]], pioneer in the development of modern [[environmental ethics]] and in the movement for [[wilderness]] conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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"How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
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“盖亚假说过程和现象的模型如何与现实相关,它们如何帮助解决和理解盖亚?雏菊世界的成果如何转移到现实世界?什么是“雏菊”的主要候选人?我们发现雏菊与否对盖亚理论重要吗?我们应该怎样寻找雏菊,我们应该加紧寻找吗?如何利用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制? ”<br />
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{{quotation|It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated functions, but possibly also that process of consumption as replacement which in biology we call metabolism, or growth. In such case we would have all the visible attributes of a living thing, which we do not realize to be such because it is too big, and its life processes too slow.| Stephan Harding | ''Animate Earth''.<ref>Harding, Stephan. ''Animate Earth Science, Intuition and Gaia''. Chelsea Green Publishing, 2006, p. 44. {{ISBN|1-933392-29-0}}</ref>}}<br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise entropy production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
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1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是一种向远离平衡的稳态演化的结果,这种平衡状态使熵产生最大化,克莱顿(2004)同意这样的说法:“自稳态行为可以从与行星反照率相关的MEP状态中产生”;“……一个如盖亚假说所述,处于MEP状态的生物地球很可能导致地球系统在长时间尺度上的近稳态行为。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。<br />
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Another influence for the Gaia hypothesis and the [[environmental movement]] in general came as a side effect of the [[Space Race]] between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph ''[[Earthrise]]'' taken by astronaut [[William Anders]] in 1968 during the [[Apollo 8]] mission became, through the [[Overview Effect]] an early symbol for the global ecology movement.<ref>[http://digitaljournalist.org/issue0309/lm11.html 100 Photographs that Changed the World by Life - The Digital Journalist]</ref><br />
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盖亚假说和[[环境运动]]的另一个总体影响来自苏联和美利坚合众国之间[[太空竞赛]]的副作用。在20世纪60年代,第一批进入太空的人类可以看到地球的整体面貌。1968年宇航员[[William Anders]]在[[Apollo 8]]任务期间拍摄的照片“[[地球升起]”,通过[[概述效果]]成为全球生态运动的早期标志<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<br />
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第四次关于盖亚假说的国际会议,由北弗吉尼亚地区公园管理局和其他机构主办,于2006年10月在弗吉尼亚州乔治梅森大学的阿灵顿校区举行。<br />
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===Formulation of the hypothesis假说形成===<br />
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[[File:James Lovelock in 2005.jpg|thumb|[[James Lovelock]], 2005]]<br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
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马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。Lynn Margulis是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the [[Jet Propulsion Laboratory]] in California on methods of detecting [[life on Mars (planet)|life on Mars]].<ref name="Lovelock1965">{{cite journal | author = Lovelock, J.E. | date = 1965 | title = A physical basis for life detection experiments | journal = [[Nature (journal)|Nature]] | volume = 207 | issue = 7 | pages = 568–570 | doi = 10.1038/207568a0 | pmid=5883628|bibcode = 1965Natur.207..568L | ref = harv}}</ref><ref>{{Cite web |url=http://www.jameslovelock.org/page4.html |title=Geophysiology |access-date=2007-05-05 |archive-url=https://web.archive.org/web/20070506073502/http://www.jameslovelock.org/page4.html |archive-date=2007-05-06 |url-status=dead }}</ref> The first paper to mention it was ''Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life'', co-authored with C.E. Giffin.<ref>{{cite journal | author1 = Lovelock, J.E. | author2 = Giffin, C.E. | date = 1969 | title = Planetary Atmospheres: Compositional and other changes associated with the presence of Life | journal = Advances in the Astronautical Sciences | volume = 25 | pages = 179–193 | isbn = 978-0-87703-028-7 | ref = harv}}</ref> A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the [[Pic du Midi de Bigorre|Pic du Midi observatory]], planets like Mars or Venus had atmospheres in [[chemical equilibrium]]. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
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这次会议将盖亚假说作为一种科学和隐喻的手段,来理解我们如何开始解决21世纪的问题,如气候变化和持续的环境破坏。<br />
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Lovelock formulated the ''Gaia Hypothesis'' in journal articles in 1972<ref name="J1972">{{cite journal | author = J. E. Lovelock | title = Gaia as seen through the atmosphere | date = 1972 | journal = [[Atmospheric Environment]] | volume = 6 | issue = 8 | pages = 579–580 | doi = 10.1016/0004-6981(72)90076-5 | ref = harv|bibcode = 1972AtmEn...6..579L }}</ref> and 1974,<ref name="lovelock1974" /> followed by a popularizing 1979 book ''Gaia: A new look at life on Earth''. An article in the ''[[New Scientist]]'' of February 6, 1975,<ref>Lovelock, John and Sidney Epton, (February 8, 1975). "The quest for Gaia". [https://books.google.com/books?id=pnV6UYEkU4YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false New Scientist], p. 304.</ref> and a popular book length version of the hypothesis, published in 1979 as ''The Quest for Gaia'', began to attract scientific and critical attention.<br />
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Lovelock called it first the Earth feedback hypothesis,<ref name="Lovelock01">{{harvnb|Lovelock, James|2001}}</ref> and it was a way to explain the fact that combinations of chemicals including [[oxygen]] and [[methane]] persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as Ford Doolittle, Richard Dawkins and Stephen Jay Gould. Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists, He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoietic or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole. With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<br />
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在最初几乎没有引起科学家的注意之后(从1969年到1977年) ,有一段时间,最初的盖亚假说受到了一些科学家的批评,如福特杜利特,理查德道金斯和史蒂芬·古尔德。洛夫洛克说,因为他的假说是以一位希腊女神的名字命名的,并得到许多非科学家的拥护,他想知道实现自我调节体内平衡的实际机制。在为盖亚辩护时,戴维•阿布拉姆认为,古尔德忽视了一个事实,即“机制”本身就是一个隐喻——尽管这个隐喻极其常见,而且往往不为人所知——这个隐喻让我们把自然和生命系统看作是由外部组织和建造的机器(而不是自动生成或自组织现象)。根据阿布拉姆的说法,机械隐喻使我们忽略了生命实体的活跃性或代表性,而盖亚假说的有机隐喻强调了生物群和整个生物圈的活跃性。关于盖亚的因果关系,洛夫洛克认为没有单一的机制是负责任的,各种已知机制之间的联系可能永远不会被人知道,这在生物学和生态学的其他领域是理所当然地被接受的,并且由于其他原因,特定的敌意是保留给他自己的假设的。<br />
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[[File:Lynn Margulis.jpg|thumb|left|[[Lynn Margulis]]]]<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of greedy reductionism in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<br />
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除了澄清他的语言和理解什么是生命形式,洛夫洛克自己把大部分的批评归因于他的批评者缺乏对非线性数学的理解,以及贪婪还原主义的线性化形式,在这种形式中,所有事件都必须立即归因于事件发生之前的特定原因。他还表示,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,以及一些自我调节现象可能无法在数学上解释。<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<ref>{{cite journal | first1=W.D. | last1=Hamilton | first2=T.M. | last2=Lenton | title=Spora and Gaia: how microbes fly with their clouds | journal=Ethology Ecology & Evolution | volume=10 | pages=1–16 | date=1998 | issue=1 | url=http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | format=PDF | doi=10.1080/08927014.1998.9522867 | ref=harv | url-status=dead | archiveurl=https://web.archive.org/web/20110723055017/http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | archivedate=2011-07-23 }}</ref><br />
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Evolutionary biologist W. D. Hamilton called the concept of Gaia Copernican, adding that it would take another Newton to explain how Gaian self-regulation takes place through Darwinian natural selection. More recently Ford Doolittle building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis. <br />
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进化生物学家W.D.Hamilton称盖亚假说为哥白尼式的概念,并补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。最近,Ford Doolittle在他和Inkpen的ITSNTS(这是歌手而不是歌曲)的建议中提出,差异持续性可以在自然选择进化中起到与差异生殖相似的作用,从而为自然选择理论和盖亚假说之间提供了一种可能的调和。 <br />
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In 1971 [[microbiologist]] Dr. [[Lynn Margulis]] joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet.<ref name="Turney, Jon 2003">{{cite book |author=Turney, Jon |title=Lovelock and Gaia: Signs of Life |publisher=Icon Books |location=UK |date=2003 |isbn=978-1-84046-458-0 |url-access=registration |url=https://archive.org/details/lovelockgaiasign0000turn }}</ref> The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of [[eukaryote|eukaryotic]] [[organelle]]s and her contributions to the [[endosymbiotic theory]], nowadays accepted. Margulis dedicated the last of eight chapters in her book, ''The Symbiotic Planet'', to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal Climatic Change in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it. to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background" The CLAW hypothesis, In 2009 the Medea hypothesis was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<br />
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盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论据是,生命对环境产生了有害或不稳定的影响,而不是采取行动加以调节。为了“令人不安地徘徊在污点隐喻、事实和虚假科学之间,我宁愿把盖亚假说牢牢地放在背景下。”爪假说,2009年提出的美狄亚假说:生命对行星条件有高度有害的(生物杀灭)影响,与盖亚假说直接相反。 <br />
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James Lovelock called his first proposal the ''Gaia hypothesis'' but has also used the term ''Gaia theory''. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments<ref name="J1990">{{cite journal | author = J. E. Lovelock | title = Hands up for the Gaia hypothesis | date = 1990 | journal = [[Nature (journal)|Nature]] | volume = 344 | issue = 6262 | pages = 100–2 | doi = 10.1038/344100a0|bibcode = 1990Natur.344..100L | ref = harv}}</ref> and provided a number of useful predictions.<ref name="Volk2003">{{cite book |author=Volk, Tyler |title=Gaia's Body: Toward a Physiology of Earth |publisher=[[MIT Press]] |location=Cambridge, Massachusetts |date=2003 |isbn=978-0-262-72042-7 }}</ref> In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating.<ref name="vanishing255"/><br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it". Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works". This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<br />
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2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新想法,并倡导一种整体的方法来研究地球”。在其他地方,他提出了自己的结论:“盖亚假说并不是我们这个世界如何运转的精确图像”。这种说法需要被理解为是指盖亚假说的“强”和“中”形式,生物群遵循的原则是使地球成为最佳(强度5)或有利于生命(强度4),或是作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化的盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释。<br />
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===First Gaia conference第一次盖亚会议===<br />
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In 1985, the first public symposium on the Gaia hypothesis, ''Is The Earth A Living Organism?'' was held at [[University of Massachusetts Amherst]], August 1–6.<ref>{{cite news |last=Joseph |first=Lawrence E. |title=Britain's Whole Earth Guru |work=The New York Times Magazine |date=November 23, 1986 |url=https://www.nytimes.com/1986/11/23/magazine/britain-s-whole-earth-guru.html |accessdate=1 December 2013}}</ref> The principal sponsor was the [[National Audubon Society]]. Speakers included James Lovelock, [[George Wald]], [[Mary Catherine Bateson]], [[Lewis Thomas]], [[John Todd (Canadian biologist)|John Todd]], Donald Michael, [[Christopher Bird]], [[Thomas Berry]], [[David Abram]], [[Michael A. Cohen|Michael Cohen]], and William Fields. Some 500 people attended.<ref>Bunyard, Peter (1996), "Gaia in Action: Science of the Living Earth" (Floris Books)</ref><br />
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1985年,关于盖亚假说的第一次公开研讨会,“地球是一个活的有机体吗?”在马萨诸塞大学阿默斯特举行 <br />
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===Second Gaia conference第二次盖亚会议===<br />
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In 1988, [[climatology|climatologist]] [[Stephen Schneider]] organised a conference of the [[American Geophysical Union]]. The first Chapman Conference on Gaia,<ref name="ReferenceB"/> was held in San Diego, California on March 7, 1988.<br />
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1988年,climatology和Stephen Schneider组织了一次美国地球物理联合会会议。关于盖亚假说的第一次查普曼会议 <br />
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During the "philosophical foundations" session of the conference, [[David Abram]] spoke on the influence of metaphor in science, and of the Gaia hypothesis as offering a new and potentially game-changing metaphorics, while [[James Kirchner]] criticised the Gaia hypothesis for its imprecision. Kirchner claimed that Lovelock and Margulis had not presented one Gaia hypothesis, but four -<br />
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在会议的“哲学基础”会议上,David Abram谈到了隐喻在科学中的影响,盖亚假说提供了一种新的、可能改变游戏规则的隐喻,而James Kirchner则批评盖亚假说的不精确性。基什纳声称,洛夫洛克和马古利斯提出的盖亚假说不是一个,而是四个- <br />
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* [[Coevolution|CoEvolutionary]] Gaia: that life and the environment had evolved in a coupled way. Kirchner claimed that this was already accepted scientifically and was not new.<br />
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* [[Homeostatic]] Gaia: that life maintained the stability of the natural environment, and that this stability enabled life to continue to exist.<br />
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* [[Geophysics|Geophysical]] Gaia: that the Gaia hypothesis generated interest in geophysical cycles and therefore led to interesting new research in terrestrial geophysical dynamics.<br />
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* Optimising Gaia: that Gaia shaped the planet in a way that made it an optimal environment for life as a whole. Kirchner claimed that this was not testable and therefore was not scientific.<br />
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盖亚:生命和环境是以耦合的方式进化的。基什内尔声称,这已经被科学界接受,并不是什么新鲜事。 <br />
盖亚:生命维持着自然环境的稳定,这种稳定性使生命得以继续存在。 <br />
盖亚:盖亚假说引起了人们对地球物理周期的兴趣,因此导致了地球物理动力学中有趣的新研究。 <br />
优化盖亚:盖亚塑造了地球,使之成为整个生命的最佳环境。基什内尔声称,这是不可测试的,因此是不科学的。 <br />
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Of Homeostatic Gaia, Kirchner recognised two alternatives. "Weak Gaia" asserted that life tends to make the environment stable for the flourishing of all life. "Strong Gaia" according to Kirchner, asserted that life tends to make the environment stable, ''to enable'' the flourishing of all life. Strong Gaia, Kirchner claimed, was untestable and therefore not scientific.<ref>{{cite journal | bibcode=1989RvGeo..27..223K | doi = 10.1029/RG027i002p00223 | title=The Gaia hypothesis: Can it be tested? | date=1989 | last1=Kirchner | first1=James W. | journal=Reviews of Geophysics | volume=27 | issue=2 | pages=223 | ref=harv}}</ref><br />
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基什内尔发现了两种选择“软弱的盖亚”断言,为了所有生命的繁衍,生命往往会使环境变得稳定根据基什内尔的说法,“强大的盖亚”断言,生命趋向于使环境稳定,“使”所有生命繁荣昌盛。基什内尔声称,强大的盖亚是不稳定的,因此不科学。 <br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the [[Daisyworld]] Model (and its modifications, above) as evidence against most of these criticisms.<ref name="daisyworld"/> Lovelock said that the Daisyworld model "demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways".<ref>{{cite journal | pmid=10968941 | date=2000 | last1=Lenton | first1=TM | last2=Lovelock | first2=JE | s2cid=5486128 | title=Daisyworld is Darwinian: Constraints on adaptation are important for planetary self-regulation | volume=206 | issue=1 | pages=109–14 | doi=10.1006/jtbi.2000.2105 | journal=Journal of Theoretical Biology | ref=harv}}</ref><br />
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然而,洛夫洛克和其他支持盖亚假说的科学家,确实试图反驳这种说法,即这个假设是不科学的,因为不可能通过受控实验来检验它。例如,针对盖亚假说是目的论的指控,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修改,洛夫洛克说,雏菊世界模型“证明了全球环境的自我调节可以通过不同方式改变当地环境的生活类型之间的竞争产生”。 <br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of [[teleology|teleologism]] ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,没有声称盖亚有意或有意识地维持着生命生存所需的复杂平衡。看来盖亚假说“故意”的行为是他最受欢迎的第一本书中的隐喻性陈述,并不是字面意思。盖亚假说的这一新说法更为科学界所接受。在这次会议之后,[[目的论|目的论]]的大多数指控都停止了。<br />
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===Third Gaia conference第三次盖亚会议===<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000,<ref>{{cite news|last=Simón|first=Federico|title=GEOLOGÍA Enfoque multidisciplinar La hipótesis Gaia madura en Valencia con los últimos avances científicos|journal=El País|date=21 June 2000|url=http://elpais.com/diario/2000/06/21/futuro/961538404_850215.html|accessdate=1 December 2013|language=spanish}}</ref> the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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The major questions were:<ref>{{cite web|title=General Information Chapman Conference on the Gaia Hypothesis University of Valencia Valencia, Spain June 19-23, 2000 (Monday through Friday) |url=http://www.agu.org/meetings/chapman/chapman_archive/cc00bcall.html |work=AGU Meetings |accessdate=7 January 2017 |author=American Geophysical Union }}</ref><br />
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# "How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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# "What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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# "How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
“被称为盖亚的全球生物地球化学/气候系统是如何随时间变化的?它的历史是什么?盖亚能在一个时间尺度上保持系统的稳定性,但在较长的时间尺度上仍能经历向量变化吗?如何利用地质记录来检验这些问题?” <br />
“盖亚假说的结构是什么?反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由任何给定时间正在进行的任何学科研究实际确定的,还是有一组应该被视为最真实的部分来理解盖亚假说,即随着时间的推移包含进化中的有机体?盖亚系统的这些不同部分之间的反馈是什么?物质的接近封闭对盖亚作为全球生态系统的结构和生命的生产力意味着什么?” <br />
“盖亚假说过程和现象的模型如何与现实联系起来,它们如何帮助解决和理解盖亚假说?雏菊世界的结果如何传递到真实世界?“雏菊”的主要候选对象是什么?我们是否找到雏菊对盖亚理论有意义吗?我们应该如何寻找雏菊,我们应该加强搜索?如何使用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制?” <br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise [[entropy]] production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是朝着使熵产量最大化的远非平衡的状态演化的结果,克莱顿(2004)同意这样的说法:“自稳行为可以从与行星反照率相关的MEP状态中产生”;“……生物地球在MEP状态下的行为很可能导致地球系统在长时间尺度上的近稳态行为,正如盖亚假说所述”。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。 <br />
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===Fourth Gaia conference第四次盖亚会议===<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<ref>{{cite web|title=Gaia Theory Conference at George Mason University Law School|url=http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|accessdate=1 December 2013|author=Official Site of Arlington County Virginia|archive-url=https://web.archive.org/web/20131203043657/http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|archive-date=2013-12-03|url-status=dead}}</ref><br />
第四届盖亚假说国际会议于2006年10月在乔治梅森大学阿灵顿分校举行,会议由北弗吉尼亚州公园管理局和其他机构赞助。 <br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。林恩 马古拉斯是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
这次会议将盖亚假说作为一种科学和隐喻来探讨,以此来理解我们如何着手解决21世纪的问题,如气候变化和持续的环境破坏<br />
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==Criticism批评==<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as [[Ford Doolittle]],<ref name=":1">{{Cite journal|last=Doolittle|first=W. F.|year=1981|title=Is Nature Really Motherly|url=|journal=The Coevolution Quarterly|volume=Spring|pages=58–63|via=}}</ref> [[Richard Dawkins]]<ref name=":2">{{Cite book|title=The Extended Phenotype: the Long Reach of the Gene|last=Dawkins|first=Richard|publisher=Oxford University Press|year=1982|isbn=978-0-19-286088-0|location=|pages=}}</ref> and [[Stephen Jay Gould]].<ref name="ReferenceB">Turney, Jon. "Lovelock and Gaia: Signs of Life" (Revolutions in Science)</ref> Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists,<ref name="Lovelock01"/> the Gaia hypothesis was interpreted as a [[neo-Pagan]] [[religion]]. Many scientists in particular also criticised the approach taken in his popular book ''Gaia, a New Look at Life on Earth'' for being [[teleology|teleological]]—a belief that things are purposeful and aimed towards a goal. Responding to this critique in 1990, Lovelock stated, "Nowhere in our writings do we express the idea that planetary self-regulation is purposeful, or involves foresight or planning by the [[biota (ecology)|biota]]".<br />
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最初很少受到科学家的关注(从1969年到1977年),此后的一段时间里,最初的盖亚假说受到了许多科学家的批评,比如福特·杜利特,理查德·道金斯和斯蒂芬·杰伊·古尔德洛夫洛克曾说过,因为他的假设是以希腊女神的名字命名的,新盖亚假说被许多非教派的科学家解释为。特别是许多科学家还批评了他的畅销书《盖亚》中采用的方法,认为地球上的生命是目的论的,认为事物是有目的的,是有目的的。洛夫洛克在1990年回应这一批评时说:“在我们的著作中我们没有任何地方表达行星自我调节是有目的的,或涉及生物群的远见或计划。”<br />
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[[Stephen Jay Gould]] criticised Gaia as being "a metaphor, not a mechanism."<ref name="Gould 1997">{{cite journal |author=Gould S.J. |title=Kropotkin was no crackpot |journal=Natural History |volume=106 |pages=12–21 |date=June 1997 |url=http://libcom.org/library/kropotkin-was-no-crackpot |ref=harv}}</ref> He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as [[autopoiesis|autopoietic]] or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole.<ref>Abram, D. (1988) "The Mechanical and the Organic: On the Impact of Metaphor in Science" in Scientists on Gaia, edited by Stephen Schneider and Penelope Boston, Cambridge, Massachusetts: MIT Press, 1991</ref><ref>{{cite web|url=http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |title=The Mechanical and the Organic |accessdate=August 27, 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120223165936/http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |archivedate=February 23, 2012 }}</ref> With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<ref name="Lovelock, James 2001">Lovelock, James (2001), ''Homage to Gaia: The Life of an Independent Scientist'' (Oxford University Press)</ref><br />
史蒂芬·杰伊·古尔德批评盖亚假说是“一种隐喻,而不是一种机制。”他想知道实现自我调节内稳态的实际机制。在为盖亚假说辩护时,大卫·艾布拉姆认为古尔德忽略了一个事实,即“机制”本身就是一个隐喻——尽管这是一个非常常见且常常未被人认识的隐喻——它使我们把自然和生命系统看作是从外部组织和建造的机器(而不是自动或自组织的)现象)。艾布拉姆认为,机械隐喻使我们忽视了生命实体的活动性或能动性,而盖亚假说的有机体隐喻强调了生物群和生物圈作为一个整体的能动性。关于盖亚假说的因果关系,洛夫洛克认为没有单一的机制负责各种已知机制之间的联系可能永远不为人所知,这一点在其他生物学和生态学领域都是理所当然的,而具体的敌意是出于其他原因留给他自己的假设的<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of [[greedy reductionism]] in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<ref name="Lovelock, James 2001"/><br />
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除了澄清自己的语言和对生命形式的理解之外,洛夫洛克自己将大部分批评归咎于批评家对非线性数学缺乏理解,以及贪婪还原论的线性化形式,在这种形式中,所有事件都必须在事实发生之前立即归因于特定的原因。他还指出,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,有些自我调节的现象可能无法用数学解释 <br />
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===Natural selection and evolution自然选择和进化===<br />
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Lovelock has suggested that global biological feedback mechanisms could evolve by [[natural selection]], stating that organisms that improve their environment for their survival do better than those that damage their environment. However, in the early 1980s, [[Ford Doolittle|W. Ford Doolittle]] and [[Richard Dawkins]] separately argued against this aspect of Gaia. Doolittle argued that nothing in the [[genome]] of individual organisms could provide the feedback mechanisms proposed by Lovelock, and therefore the Gaia hypothesis proposed no plausible mechanism and was unscientific.<ref name=":1" /> Dawkins meanwhile stated that for organisms to act in concert would require foresight and planning, which is contrary to the current scientific understanding of evolution.<ref name=":2" /> Like Doolittle, he also rejected the possibility that feedback loops could stabilize the system.<br />
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洛夫洛克提出,全球生物反馈机制可以通过自然选择而进化,他指出,为生存而改善环境的生物比那些破坏环境的生物做得更好。然而,在20世纪80年代早期,W·福特·杜立德和理查德·道金斯分别反对盖亚假说的这一方面。杜立德认为,单个生物体的基因组中没有任何东西能够提供洛夫洛克提出的反馈机制,因此盖亚假说没有提出任何合理的机制,是不科学的。道金斯同时指出,要使有机体协同行动,就需要有远见和计划,这与当前科学界对进化论的理解相悖和杜立德一样,他也拒绝了反馈回路可以稳定系统的可能性。<br />
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[[Lynn Margulis]], a microbiologist who collaborated with Lovelock in supporting the Gaia hypothesis, argued in 1999, that "[[Charles Darwin|Darwin]]'s grand vision was not wrong, only incomplete. In accentuating the direct competition between individuals for resources as the primary selection mechanism, Darwin (and especially his followers) created the impression that the environment was simply a static arena". She wrote that the composition of the Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in [[homeostasis]], but those set points change with time.<ref name="ReferenceA">Margulis, Lynn. Symbiotic Planet: A New Look At Evolution. Houston: Basic Book 1999</ref><br />
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Lynn Margulis,一位与Lovelock合作支持盖亚假说的微生物学家,在1999年指出,“达尔文的宏伟愿景没有错,只是不完整。达尔文(特别是他的追随者)强调个人之间对资源的直接竞争是主要的选择机制,他给人的印象是环境只是一个静态的竞技场”。她写道,地球大气、水圈和岩石圈的组成都是围绕着“设定点”来调节的,就像在体内平衡中一样,但是这些设定点会随着时间的推移而变化 <br />
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Evolutionary biologist [[W. D. Hamilton]] called the concept of Gaia [[Nicolaus Copernicus|Copernican]], adding that it would take another [[Isaac Newton|Newton]] to explain how Gaian self-regulation takes place through Darwinian [[natural selection]].<ref name=vanish09>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, pp. 195-197. {{ISBN|978-0-465-01549-8}}</ref>{{better source|date=September 2012|reason=it should be possible to find the original place where Hamilton said this}} More recently [[Ford Doolittle]] building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal<ref name="ITSNTS">Doolittle WF, Inkpen SA. Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking. [https://www.pnas.org/content/115/16/4006 PNAS April 17, 2018 115 (16)] 4006-4014 </ref> proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis<ref name="Darwinizing Gaia">Doolittle WF. Darwinizing Gaia. [https://doi.org/10.1016/j.jtbi.2017.02.015 Journal of Theoretical BiologyVolume 434], 7 December 2017, Pages 11-19 </ref>. <br />
进化生物学家汉密尔顿称盖亚哥白尼为盖亚的概念,他补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。通过自然选择在进化过程中的繁殖,从而为自然选择理论和盖亚假说提供了可能的调和。 <br />
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===Criticism in the 21st century21世纪的批评===<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal ''Climatic Change'' in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it.<ref name="kirchner2002"/><ref name="volk2002"/> Several recent books have criticised the Gaia hypothesis, expressing views ranging from "... the Gaia hypothesis lacks unambiguous observational support and has significant theoretical difficulties"<ref>{{cite book |last=Waltham |first=David |authorlink=David Waltham |date=2014 |title=Lucky Planet: Why Earth is Exceptional – and What that Means for Life in the Universe |url=https://archive.org/details/luckyplanetwhyea0000walt |location= |publisher=Icon Books |page= |isbn=9781848316560 |accessdate= |url-access=registration }}</ref> to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background"<ref name="beerling2007"/> to "The Gaia hypothesis is supported neither by evolutionary theory nor by the empirical evidence of the geological record".<ref>{{cite book |last1=Cockell |first1=Charles |authorlink1=Charles Cockell |last2=Corfield |first2=Richard |last3=Dise |first3= Nancy |last4=Edwards |first4=Neil |last5=Harris |first5=Nigel |date=2008 |title= An Introduction to the Earth-Life System |url= http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/palaeontology-and-life-history/introduction-earth-life-system |location=Cambridge (UK) |publisher= Cambridge University Press |page= |isbn= 9780521729536 |accessdate= }}</ref> The [[CLAW hypothesis]],<ref name="CLAW87" /> initially suggested as a potential example of direct Gaian feedback, has subsequently been found to be less credible as understanding of [[cloud condensation nuclei]] has improved.<ref>{{Citation |last1= Quinn |first1=P.K. |last2= Bates |first2=T.S. |title =The case against climate regulation via oceanic phytoplankton sulphur emissions |journal =Nature |volume=480 |issue=7375 |pages =51–56 |date = 2011 |doi=10.1038/nature10580|bibcode = 2011Natur.480...51Q |pmid=22129724|url=https://zenodo.org/record/1233319 }}</ref> In 2009 the [[Medea hypothesis]] was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<ref>Peter Ward (2009), ''The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?'', {{ISBN|0-691-13075-2}}</ref><br />
盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论点是在许多例子中,生命对环境产生了有害或不稳定的影响,而不是采取行动来调节它。最近几本书批评了盖亚假说,譬如“盖亚假说缺乏明确的观察支持,并且有重大的理论困难”“(盖亚假说)令人不安地徘徊在污点、隐喻、事实和虚假科学之间,我宁愿把盖亚牢牢地放在原有的背景中”“盖亚假说既没有进化论的支持,也没有地质记录的经验证据的支持。爪假说最初被认为是盖亚直接反馈的一个潜在例子,后来被发现对云的理解不那么可信凝聚核已经得到了改善。2009年,美狄亚假说提出:生命对行星的状况非常有害,这与盖亚假说直接相反。 <br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it".<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=209 |isbn=9780691121581 |accessdate= }}</ref> Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works".<ref>{{Citation |last= Tyrrell |first = Toby |title =Gaia: the verdict is… |journal = New Scientist |volume = 220 |issue = 2940 |pages = 30–31 |date= 26 October 2013 |doi=10.1016/s0262-4079(13)62532-4}}</ref> This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=208 |isbn=9780691121581 |accessdate= }}</ref><br />
2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新思想,并倡导一种研究地球的整体方法。”在其他地方,他提出了自己的结论:“盖亚假说并不是一个关于如何进行的精确描述我们的世界在运转。”这种说法需要被理解为是指盖亚假说的“强大”和“温和”形式,生物群遵循的原则是使地球处于最佳状态(强度5)或有利于生命(强度4),或者它作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化德盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释 <br />
Category:Cybernetics<br />
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类别: 控制论<br />
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Category:Ecological theories<br />
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范畴: 生态学理论<br />
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==See also==<br />
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Category:Superorganisms<br />
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类别: 超级有机体<br />
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{{Portal|Environment|Earth sciences|Geography}}<br />
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Category:Climate change feedbacks<br />
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类别: 气候变化反馈<br />
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Category:1965 introductions<br />
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类别: 1965年引言<br />
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* {{annotated link|Biocoenosis}}<br />
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Category:Biogeochemistry<br />
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类别: 生物地球化学<br />
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* {{annotated link|Earth science}}<br />
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Category:Earth<br />
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类别: 地球<br />
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* {{annotated link|Environmentalism}}<br />
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Category:Biological hypotheses<br />
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类别: 生物学假说<br />
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* {{annotated link|Gaianism}}<br />
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Category:Astronomical hypotheses<br />
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类别: 天文学假设<br />
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* {{annotated link|Holism}}<br />
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Category:Meteorological hypotheses<br />
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类别: 气象假说<br />
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<small>This page was moved from [[wikipedia:en:Gaia hypothesis]]. Its edit history can be viewed at [[盖亚假说/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%96%E4%BA%9A%E5%81%87%E8%AF%B4&diff=21547盖亚假说2021-02-04T02:46:25Z<p>Vicky:</p>
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<div>此词条由Henry第一次翻译。<br />
已由三奇同学完成校对。<br />
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{{short description|Hypothesis that living organisms interact with their surroundings in a self-regulating system}}<br />
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[[File:The Earth seen from Apollo 17.jpg|thumb|The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth]]'s conditions, as the Earth is the only planet currently known to harbour life (''[[The Blue Marble]]'', 1972 [[Apollo 17]] photograph)]]<br />
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The study of planetary habitability is partly based upon extrapolation from knowledge of the [[Earth's conditions, as the Earth is the only planet currently known to harbour life (The Blue Marble, 1972 Apollo 17 photograph)]]<br />
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对行星可居住性的研究主要基于对[[地球条件]的了解进行推断,因为地球是目前已知的唯一一颗拥有生命的行星 <br />
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The '''Gaia hypothesis''' {{IPAc-en|ˈ|ɡ|aɪ|.|ə}}, also known as the '''Gaia theory''' or the '''Gaia principle''', proposes that living [[organism]]s interact with their [[Inorganic compound|inorganic]] surroundings on [[Earth]] to form a [[Synergy|synergistic]] and [[Homeostasis|self-regulating]], [[complex system]] that helps to maintain and perpetuate the conditions for [[life]] on the planet.<br />
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The Gaia hypothesis , also known as the Gaia theory or the Gaia principle, proposes that living organisms interact with their inorganic surroundings on Earth to form a synergistic and self-regulating, complex system that helps to maintain and perpetuate the conditions for life on the planet.<br />
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盖亚假说(又称盖亚理论或盖亚原理)认为,生物体与地球上的无机环境相互作用,形成一个协同和自我调节的复杂系统,有助于维持和延续地球上的生命条件。<br />
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The hypothesis was formulated by the chemist [[James Lovelock]]<ref name="J1972" /> and co-developed by the microbiologist [[Lynn Margulis]] in the 1970s.<ref name="lovelock1974">{{cite journal|last1=Lovelock|first1=J.E.|last2=Margulis|first2=L.|title=Atmospheric homeostasis by and for the biosphere: the Gaia hypothesis|journal=Tellus|date=1974|volume=26|series=Series A|issue=1–2|pages=2–10|doi=10.1111/j.2153-3490.1974.tb01946.x|publisher=International Meteorological Institute|location=Stockholm|issn=1600-0870|ref=harv|bibcode=1974Tell...26....2L}}</ref> Lovelock named the idea after [[Gaia]], the primordial goddess who personified the Earth in [[Greek mythology]]. In 2006, the [[Geological Society of London]] awarded Lovelock the [[Wollaston Medal]] in part for his work on the Gaia hypothesis.<ref>{{cite web|title=Wollaston Award Lovelock|url=https://www.geolsoc.org.uk/About/History/Awards-Citations-Replies-2001-Onwards/2006-Awards-Citations-Replies|accessdate=19 October 2015}}</ref><br />
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The hypothesis was formulated by the chemist James Lovelock Lovelock named the idea after Gaia, the primordial goddess who personified the Earth in Greek mythology. In 2006, the Geological Society of London awarded Lovelock the Wollaston Medal in part for his work on the Gaia hypothesis.<br />
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这个假设是由化学家詹姆斯·洛夫洛克提出的,他以希腊神话中地球的化身盖亚的名字命名了这个想法。2006年,伦敦地质学会授予洛夫洛克沃拉斯顿勋章,以表彰他在<font color="#ff8000"> 盖亚假说Gaia hypothesis</font>方面的工作。 <br />
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Topics related to the hypothesis include how the [[biosphere]] and the [[evolution]] of organisms affect the stability of [[global temperature]], [[salinity]] of [[seawater]], [[atmospheric oxygen]] levels, the maintenance of a [[hydrosphere]] of liquid water and other environmental variables that affect the [[habitability of Earth]].<br />
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Topics related to the hypothesis include how the biosphere and the evolution of organisms affect the stability of global temperature, salinity of seawater, atmospheric oxygen levels, the maintenance of a hydrosphere of liquid water and other environmental variables that affect the habitability of Earth.<br />
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与该假设有关的主题包括生物圈和生物体的进化如何影响全球温度的稳定性、海水的盐度、大气中的氧含量、液态水水圈的维持以及其他影响地球宜居性的环境变量。<br />
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The Gaia hypothesis was initially criticized for being [[teleological]] and against the principles of [[natural selection]], but later refinements aligned the Gaia hypothesis with ideas from fields such as [[Earth system science]], [[biogeochemistry]] and [[systems ecology]].<ref name="Turney, Jon 2003"/><ref name="Schwartzman2002">{{cite book |author=Schwartzman, David |title=Life, Temperature, and the Earth: The Self-Organizing Biosphere |publisher=Columbia University Press |date=2002 |isbn=978-0-231-10213-1 }}</ref><ref>Gribbin, John (1990), "Hothouse earth: The greenhouse effect and Gaia" (Weidenfeld & Nicolson)</ref> Lovelock also once described the "geophysiology" of the Earth.<ref name="agesofgaia">Lovelock, James, (1995) "The Ages of Gaia: A Biography of Our Living Earth" (W.W.Norton & Co)</ref>{{Explain|date=December 2017}} Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<ref name="kirchner2002">{{Citation |last= Kirchner |first = James W. |title =Toward a future for Gaia theory |journal=[[Climatic Change (journal)|Climatic Change]] |volume = 52 |issue = 4 |pages = 391–408 |date = 2002 | doi = 10.1023/a:1014237331082 }}</ref><ref name="volk2002">{{Citation |last= Volk |first = Tyler |title =The Gaia hypothesis: fact, theory, and wishful thinking |journal = Climatic Change |volume = 52 |issue = 4 |pages = 423–430 |date = 2002 | doi = 10.1023/a:1014218227825 }}</ref><ref name="beerling2007">{{cite book |last=Beerling |first=David |authorlink=David Beerling|date=2007 |title=The Emerald Planet: How plants changed Earth's history |url=http://ukcatalogue.oup.com/product/9780192806024.do |location=Oxford|publisher=Oxford University Press |page= |isbn= 978-0-19-280602-4 |accessdate= }}</ref><br />
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The Gaia hypothesis was initially criticized for being teleological and against the principles of natural selection, but later refinements aligned the Gaia hypothesis with ideas from fields such as Earth system science, biogeochemistry and systems ecology. Lovelock also once described the "geophysiology" of the Earth. Even so, the Gaia hypothesis continues to attract criticism, and today many scientists consider it to be only weakly supported by, or at odds with, the available evidence.<br />
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盖亚假说最初被诟病为目的论、反对自然选择的原则,但后来的改进使盖亚假说与来自地球系统科学、生物地球化学和系统生态学等领域的观点相一致。洛夫洛克还曾经描述过地球的“地球物理学”。即便如此,盖亚假说仍然受到一些批评,今天许多科学家认为只有少数证据支持这一理论,或与现有的证据相矛盾。<br />
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==Overview总览==<br />
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Gaian hypotheses suggest that organisms [[Co-evolution|co-evolve]] with their environment: that is, they "influence their [[abiotic]] environment, and that environment in turn influences the [[Biota (ecology)|biota]] by [[Darwinism|Darwinian process]]". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early [[Bacteria|thermo-acido-philic]] and [[methanogenic bacteria]] towards the oxygen-enriched [[atmosphere]] today that supports more [[Phanerozoic|complex life]].<br />
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Gaian hypotheses suggest that organisms co-evolve with their environment: that is, they "influence their abiotic environment, and that environment in turn influences the biota by Darwinian process". Lovelock (1995) gave evidence of this in his second book, showing the evolution from the world of the early thermo-acido-philic and methanogenic bacteria towards the oxygen-enriched atmosphere today that supports more complex life.<br />
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盖亚假说认为,生物体与其环境共同进化。也就是说,生物“影响它们的非生物环境,而环境反过来又通过自然选择的过程影响生物群”。Lovelock(1995)在他的第二本书中提供了证据,展示了从早期嗜酸、产甲烷细菌的世界向今天支持更复杂生命的富氧大气的进化。<br />
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A reduced version of the hypothesis has been called "influential Gaia"<ref name=":02">{{Cite journal|last=Lapenis|first=Andrei G.|year=2002|title=Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?|url=|journal=The Professional Geographer|volume=54 |issue=3|pages=379–391|via=[Peer Reviewed Journal]|doi=10.1111/0033-0124.00337}}</ref> in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the [[Biota (ecology)|biota]] influence certain aspects of the abiotic world, e.g. [[temperature]] and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<ref name=":02" /> and biogeochemical processes. An example is how the activity of [[Photosynthesis|photosynthetic]] bacteria during Precambrian times completely modified the [[Earth's atmosphere|Earth atmosphere]] to turn it aerobic, and thus supports the evolution of life (in particular [[eukaryotic]] life).<br />
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A reduced version of the hypothesis has been called "influential Gaia" in "Directed Evolution of the Biosphere: Biogeochemical Selection or Gaia?" by Andrei G. Lapenis, which states the biota influence certain aspects of the abiotic world, e.g. temperature and atmosphere. This is not the work of an individual but a collective of Russian scientific research that was combined into this peer reviewed publication. It states the coevolution of life and the environment through “micro-forces”<br />
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在《生物圈的定向进化: 生物地球化学选择还是盖亚? 》一书中,这一假说的简化版被称为“有影响力的盖亚”。安德烈·G·拉佩尼斯在这本书中指出生物影响着非生物世界的温度和大气等多个方面。这本书不是一个人的工作,而是一群俄罗斯科研人员的成果合并成这个通过同行评议的出版物。它通过“微观力量”阐述了生命与环境的共同进化。<br />
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Since barriers existed throughout the twentieth century between Russia and the rest of the world, it is only relatively recently that the early Russian scientists who introduced concepts overlapping the Gaia hypothesis have become better known to the Western scientific community.<ref name=":02" /> These scientists include [[Piotr Kropotkin|Piotr Alekseevich Kropotkin]] (1842–1921) (although he spent much of his professional life outside Russia), Vasil’evich Rizpolozhensky (1847–1918), [[Vladimir Ivanovich Vernadsky]] (1863–1945), and Vladimir Alexandrovich Kostitzin (1886–1963).<br />
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由于二十世纪苏联与西方国家存在隔阂,直到最近,在盖亚假说中引进重叠概念的早期苏联科学家才为西方科学界所熟知。<br />
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The Gaia hypothesis posits that the Earth is a self-regulating complex system involving the biosphere, the atmosphere, the hydrospheres and the pedosphere, tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<br />
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盖亚假说认为,地球是一个自我调节的复杂系统,包括生物圈、大气层、水圈和土壤圈,作为一个进化的系统紧密结合在一起。这个假说认为,这个被称为盖亚的系统作为整体,寻求适合当代生命的物理和化学环境。<br />
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Biologists and Earth scientists usually view the factors that stabilize the characteristics of a period as an undirected [[emergent property]] or [[entelechy]] of the system; as each individual species pursues its own self-interest, for example, their combined actiYons may have counterbalancing effects on environmental change. Opponents of this view sometimes reference examples of events that resulted in dramatic change rather than stable equilibrium, such as the conversion of the Earth's atmosphere from a [[reducing environment]] to an [[oxygen]]-rich one at the end of the [[Archean|Archaean]] and the beginning of the [[Proterozoic]] periods.<br />
生物学家和地球科学家通常将平衡一个时期的特征的因素视为系统的无方向[[涌现属性]]或[[有目的行为]];例如,由于每个物种都追求自身利益,它们的联合行动可能对环境变化产生抵消作用。反对这一观点的人有时会举出一些导致了巨大变化而非平衡的事件作为反例,例如在[[太古宙|太古代]]末期和[[元古代]]时期开始时,地球大气从[[还原环境]]转变为富含[[氧气]]。 <br />
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Gaia evolves through a cybernetic feedback system operated unconsciously by the biota, leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially microorganisms, with inorganic elements. These processes establish a global control system that regulates Earth's surface temperature, atmosphere composition and ocean salinity, powered by the global thermodynamic disequilibrium state of the Earth system.<!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
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盖亚通过一个由生物群无意识操作的控制论反馈系统实现进化,在完全的内稳态中广泛获得稳定的可居住条件。地球表面的许多过程对生命的保障条件至关重要,这些过程依赖于生命形式,特别是微生物与无机元素的相互作用。这些过程建立了一个全球控制系统,由地球系统的全球热力学不平衡状态提供动力,调节地球表面温度、大气成分和海洋盐度。<br />
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Less accepted versions of the hypothesis claim that changes in the biosphere are brought about through the [[Superorganism|coordination of living organisms]] and maintain those conditions through [[homeostasis]]. In some versions of [[Gaia philosophy]], all lifeforms are considered part of one single living planetary being called ''Gaia''. In this view, the atmosphere, the seas and the terrestrial crust would be results of interventions carried out by Gaia through the [[Coevolution|coevolving]] diversity of living organisms.<br />
一种不太被接受的假说声称生物圈的变化是通过[[超级有机体|生物体的协调]]来实现的,并通过[[内稳态]]来维持这些条件。在一些版本的[[盖亚哲学]]中,所有的生命形式都是一个被称为“盖亚”的生命行星的一部分。在这种观点下,大气、海洋和地壳将是盖亚通过生物多样性进行干预的结果。 <br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of biogeochemistry, and it is being investigated also in other fields like Earth system science. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<br />
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以前在生物地球化学领域已经观察到受生命形式影响的行星内稳态的存在,而且地球系统科学等其他领域也在研究这一现象。盖亚假说的原创性依赖于这样一种观点: 即使地球或外部事件威胁到内稳态平衡,盖亚也会为了保持生命的最佳状态而积极追求这种平衡。<br />
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The Gaia hypothesis was an influence on the [[deep ecology]] movement.<ref>David Landis Barnhill, Roger S. Gottlieb (eds.), ''Deep Ecology and World Religions: New Essays on Sacred Ground'', SUNY Press, 2010, p. 32.</ref><br />
盖亚假说对[[深层生态学]]运动产生了影响 <br />
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==Details细节==<br />
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Rob Rohde's palaeotemperature graphs<br />
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罗布·罗德的古温度图<br />
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The Gaia hypothesis posits that the Earth is a self-regulating [[complex system]] involving the [[biosphere]], the [[Earth's atmosphere|atmosphere]], the [[hydrosphere]]s and the [[pedosphere]], tightly coupled as an evolving system. The hypothesis contends that this system as a whole, called Gaia, seeks a physical and chemical environment optimal for contemporary life.<ref name="vanishing255">Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 255. {{ISBN|978-0-465-01549-8}}</ref><br />
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盖亚假说假设地球是一个自我调节的[[复杂系统]],包括[[生物圈]]、[[地球大气|大气]]、[[水圈]]和[[土壤圈]],作为一个进化系统紧密耦合。该假说认为,这个系统作为一个整体,称为盖亚,寻求一个最适合当代生活的物理和化学环境 <br />
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Since life started on Earth, the energy provided by the Sun has increased by 25% to 30%; however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on Titan. research has suggested that "oxygen shocks" and reduced methane levels led, during the Huronian, Sturtian and Marinoan/Varanger Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre Phanerozoic biosphere to fully self-regulate.<br />
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自从地球上有生命以来,太阳提供的能量增加了25%到30%;然而,地球表面温度一直保持在适宜居住的水平上,不曾突破上限或是下限。洛夫洛克还假设,产甲烷菌在早期大气中产生了较高水平的甲烷,这与在石化烟雾中发现的成分相似,在某些方面与土卫六上的大气相似。研究表明,在休伦期、斯图尔特期和马里诺/瓦朗格冰期,“氧冲击”和甲烷含量降低导致世界几乎变成了一个坚实的“雪球”。这些时代是前显生宙生物圈完全拥有自我调节能力的证据。<br />
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Gaia evolves through a [[Cybernetic#In biology|cybernetic]] [[feedback]] system operated unconsciously by the [[biota (ecology)|biota]], leading to broad stabilization of the conditions of habitability in a full homeostasis. Many processes in the Earth's surface essential for the conditions of life depend on the interaction of living forms, especially [[microorganisms]], with inorganic elements. These processes establish a global control system that regulates Earth's [[Sea surface temperature|surface temperature]], [[atmosphere composition]] and [[ocean]] [[salinity]], powered by the global thermodynamic disequilibrium state of the Earth system.<ref>Kleidon, Axel. ''How does the earth system generate and maintain thermodynamic disequilibrium and what does it imply for the future of the planet?''. Article submitted to the ''Philosophical Transactions of the Royal Society'' on Thu, 10 Mar 2011</ref><!-- Article submitted to Royal Society is not a valid reference. This must be replaced by actual article citation if accepted, or an alternative reference --><br />
盖亚通过一个[[控制论|生物学|控制论]][[反馈]]系统在[[生物群(生态学)|生物群]]的无意识运作中实现进化,导致在完全的内稳态中广泛存在稳定的可居住条件。地球表面对生命条件至关重要的许多过程都依赖于生物,特别是[微生物]与无机元素的相互作用。这些过程建立了一个全球控制系统,调节地球的[[海表温度|表面温度]]、[[大气组成]]和[[海洋]][[盐度]],其动力来自地球系统的全球热力学不平衡状态。<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
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说明了处理温室气体CO2在维持地球温度在可居住范围内起着关键作用。<br />
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The existence of a planetary homeostasis influenced by living forms had been observed previously in the field of [[biogeochemistry]], and it is being investigated also in other fields like [[Earth system science]]. The originality of the Gaia hypothesis relies on the assessment that such homeostatic balance is actively pursued with the goal of keeping the optimal conditions for life, even when terrestrial or external events menace them.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 179. {{ISBN|978-0-465-01549-8}}</ref><br />
受生命形式影响的行星内稳态的存在,以前在[[生物地球化学]]领域就已被观察到,而且其他领域,如[[地球系统科学]]也在研究这种稳态。盖亚假说的独创性依赖于这样一种观点,即盖亚积极追求这种内平衡,以保持维护生命的最佳状态,即使是在地球或外部事件威胁它们的时候。<br />
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The CLAW hypothesis, inspired by the Gaia hypothesis, proposes a feedback loop that operates between ocean ecosystems and the Earth's climate. The hypothesis specifically proposes that particular phytoplankton that produce dimethyl sulfide are responsive to variations in climate forcing, and that these responses lead to a negative feedback loop that acts to stabilise the temperature of the Earth's atmosphere.<br />
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受盖亚假说的启发,CLAW 假说提出了一个在海洋生态系统和地球气候之间运行的反馈回路。该假说特别提出,产生二甲硫醚的浮游植物对气候变化有反应,这些反应导致了一个负反馈循环,稳定了地球大气的温度。<br />
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===Regulation of global surface temperature地球表面温度的调控===<br />
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[[File:All palaeotemps.png|thumb|480px|Rob Rohde's palaeotemperature graphs]]<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of greenhouse gases may cause negative feedbacks in the environment to become positive feedback. Lovelock has stated that this could bring an extremely accelerated global warming, but he has since stated the effects will likely occur more slowly.<br />
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目前,人口的增加及其活动对环境的影响,例如温室气体的增加,可能导致环境中的负反馈成为正反馈。洛夫洛克表示,这可能会极大地加速全球变暖,但他后来又表示,这种影响也可能发生得更慢。<br />
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{{See also|Paleoclimatology}}<br />
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Since life started on Earth, the energy provided by the [[Sun]] has increased by 25% to 30%;<ref name="Owen1979">{{cite journal | author = Owen, T. | author2 = Cess, R.D. | author3 = Ramanathan, V. | date = 1979 | title = Earth: An enhanced carbon dioxide greenhouse to compensate for reduced solar luminosity | journal = [[Nature (journal)|Nature]] | volume = 277 | pages = 640–2 | doi = 10.1038/277640a0 | issue=5698 | bibcode = 1979Natur.277..640O | ref = harv }}</ref> however, the surface temperature of the planet has remained within the levels of habitability, reaching quite regular low and high margins. Lovelock has also hypothesised that methanogens produced elevated levels of methane in the early atmosphere, giving a view similar to that found in petrochemical smog, similar in some respects to the atmosphere on [[Titan (moon)|Titan]].<ref name="agesofgaia"/> This, he suggests tended to screen out ultraviolet until the formation of the ozone screen, maintaining a degree of homeostasis. However, the [[Snowball Earth]]<ref>Hoffman, P.F. 2001. [http://www.snowballearth.org ''Snowball Earth theory'']</ref> research has suggested that "oxygen shocks" and reduced methane levels led, during the [[Huronian]], [[Sturtian]] and [[Marinoan]]/[[Cryogenian|Varanger]] Ice Ages, to a world that very nearly became a solid "snowball". These epochs are evidence against the ability of the pre [[Phanerozoic]] biosphere to fully self-regulate.<br />
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Plots from a standard black and white [[Daisyworld simulation]]<br />
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从一个标准的黑白图[[雏菊世界模拟]]<br />
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Processing of the greenhouse gas CO<sub>2</sub>, explained below, plays a critical role in the maintenance of the Earth temperature within the limits of habitability.<br />
说明了在温室气体维持低于临界温度的过程中,CO2起着至关重要的作用。 <br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic group selection and cooperation between organisms, James Lovelock and Andrew Watson developed a mathematical model, Daisyworld, in which ecological competition underpinned planetary temperature regulation.<br />
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有人批评盖亚假说似乎需要有机体之间不切实际的群体选择与合作,为了回应这种批评,James Lovelock 和 Andrew Watson建立了一个数学模型---- 雏菊世界,其中生态竞争支撑着地。<br />
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The [[CLAW hypothesis]], inspired by the Gaia hypothesis, proposes a [[feedback|feedback loop]] that operates between [[ocean]] [[ecosystem]]s and the [[Earth]]'s [[climate]].<ref name="CLAW87">{{cite journal |doi=10.1038/326655a0 |author=[[Robert Jay Charlson|Charlson, R. J.]], [[James Lovelock|Lovelock, J. E]], Andreae, M. O. and Warren, S. G. |title=Oceanic phytoplankton, atmospheric sulphur, cloud albedo and climate |journal=Nature |volume=326 |issue=6114 |pages=655–661 |date=1987 |bibcode=1987Natur.326..655C |ref=harv }}</ref> The [[hypothesis]] specifically proposes that particular [[phytoplankton]] that produce [[dimethyl sulfide]] are responsive to variations in [[climate forcing]], and that these responses lead to a [[negative feedback|negative feedback loop]] that acts to stabilise the [[temperature]] of the [[Earth's atmosphere]].<br />
受到盖亚假说启发的[[爪假说]]提出了一个在[[海洋]][[生态系统]]和[[地球]]的[[气候]]之间运行的[[反馈|反馈回路]]。<br />
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Daisyworld examines the energy budget of a planet populated by two different types of plants, black daisies and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the albedo of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
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《雏菊世界》调查了一个星球的能量预算,这个星球上生长着两种不同的植物,黑色雏菊和白色雏菊,这两种植物占据了星球表面的很大一部分。雏菊的颜色影响了地球的反照率,黑色的雏菊吸收更多的光线,使地球变暖,而白色的雏菊则反射更多的光线,使地球变冷。人们认为黑色雏菊在较低的温度下生长和繁殖最好,而白色雏菊则被认为在较高的温度下生长最好。当温度上升到接近白色雏菊所喜欢的温度时,白色雏菊繁殖率高于黑色雏菊,导致更大比例的白色表面,更多的阳光被反射,减少热量输入,最终使地球降温。相反,随着气温的下降,黑色雏菊繁殖率高于白色雏菊,吸收了更多的阳光,使地球变暖。因此,温度会收敛于两种植物繁殖率相等时对应温度的值。<br />
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Currently the increase in human population and the environmental impact of their activities, such as the multiplication of [[greenhouse gases]] may cause [[negative feedback]]s in the environment to become [[positive feedback]]. Lovelock has stated that this could bring an [[James Lovelock#The revenge of Gaia|extremely accelerated global warming]],<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, {{ISBN|978-0-465-01549-8}}</ref> but he has since stated the effects will likely occur more slowly.<ref>Lovelock J., NBC News. [http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite Link] Published 23 April 2012, accessed 22 August 2012. {{Webarchive|url=https://web.archive.org/web/20120913163635/http://worldnews.nbcnews.com/_news/2012/04/23/11144098-gaia-scientist-james-lovelock-i-was-alarmist-about-climate-change?lite |date=13 September 2012 }}</ref><br />
目前,人口的增加及其活动对环境的影响,如[[温室气体]]的倍增,可能导致环境中的[[负反馈]]变成[[正反馈]]。洛夫洛克曾表示,这可能会带来一场【【James Loveloc【《盖亚的复仇』极度加速的全球变暖】】 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this negative feedback due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
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洛夫洛克和沃森指出,在有限的条件下,如果太阳的能量输出发生变化,由于竞争产生的负反馈可以将地球温度稳定在支持生命存在的范围内,而没有生命的地球则会表现出巨大的温度波动。白色和黑色雏菊的百分比会不断变化,以保持植物繁殖率相等的温度值,使两种生命形式都能茁壮成长。<br />
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====Daisyworld simulations雏菊世界模拟====<br />
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[[File:StandardDaisyWorldRun2color.gif|thumb|280px|Plots from a standard black and white [[Daisyworld]] simulation]]<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<br />
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有人认为,这些结果是可以预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的答案。<br />
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{{Main|Daisyworld}}<br />
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In response to the criticism that the Gaia hypothesis seemingly required unrealistic [[group selection]] and [[Cooperation (evolution)|cooperation]] between organisms, James Lovelock and [[Andrew Watson (scientist)|Andrew Watson]] developed a mathematical model, [[Daisyworld]], in which [[Competition (biology)|ecological competition]] underpinned planetary temperature regulation.<ref name="daisyworld">{{cite journal<br />
有人批评盖亚假说似乎需要有机体之间不切实际的[[群体选择]]和[[合作(进化)|合作]],詹姆斯·洛夫洛克和[[安德鲁·沃森(科学家)|安德鲁·沃森]]开发了一个数学模型,[[雏菊世界]],其中[[竞争(生物学)|生态竞争]]为基础行星温度调节。 <br />
|date = 1983<br />
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Ocean salinity has been constant at about 3.5% for a very long time. Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested that salinity may also be strongly influenced by seawater circulation through hot basaltic rocks, and emerging as hot water vents on mid-ocean ridges. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<br />
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长期以来,海洋盐度一直保持在3.5% 左右。海洋环境中盐度的稳定性很重要,因为大多数细胞需要相当恒定的盐度,一般不能耐受超过5% 的盐度值。海洋盐度为何恒定是一个长期的奥秘,因为没有任何方法可以抵消来自河流的流入盐。最近有人提出,盐分也会洋中脊的热水喷口排出,因此盐度可能受到穿过炽热玄武岩的海水循环的强烈影响。然而,海水的组成离平衡还很远,如果没有有机过程的影响,很难解释这一事实。有一种解释认为,地球历史上盐滩的形成是盐度平衡的原因之一。据推测,这些盐滩是由细菌菌落产生的,它们在生命过程中固定离子和重金属。<br />
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|title = Biological homeostasis of the global environment: the parable of Daisyworld<br />
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|journal = Tellus<br />
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|volume = 35B<br />
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Vostok, Antarctica research station. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
沃斯托克,南极洲研究站。当前期间在左边。<!--基于此图表的GIMP-FX版本的非源材料。现在的版本是正确的,原版的。必须删除这句话:请注意,当前CO2水平超过390ppm,远高于过去40万年来的任何时候-->] <br />
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|pages = 286–9<br />
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|bibcode = 1983TellB..35..284W<br />
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|doi = 10.1111/j.1600-0889.1983.tb00031.x<br />
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The Gaia hypothesis states that the Earth's atmospheric composition is kept at a dynamically steady state by the presence of life. The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than noble gases present in the atmosphere are either made by organisms or processed by them.<br />
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盖亚假说认为,地球的大气组成是由于生命的存在而保持在动态稳定的状态。大气成分提供了支持现代生命的条件。大气中除惰性气体以外的所有大气气体,要么是由生物体产生的,要么是由生物体加工的。<br />
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|last1 = Watson | first1= A.J. | last2= Lovelock | first2= J.E<br />
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|issue = 4<br />
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The stability of the atmosphere in Earth is not a consequence of chemical equilibrium. Oxygen is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the Great Oxygenation Event. Since the start of the Cambrian period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume. Traces of methane (at an amount of 100,000 tonnes produced per year) should not exist, as methane is combustible in an oxygen atmosphere.<br />
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地球大气层的稳定性不是化学平衡的结果。氧是一种活性化合物,最终会与地球大气层和地壳中的气体和矿物质结合。在大氧化事件开始之前,大约5000万年前,氧气才开始在大气中持续少量存在。自寒武纪以来,大气中氧浓度一直在大气体积的15% 至35% 之间波动。微量的甲烷(每年产生100,000吨)不适合存在,因为甲烷在氧气氛中是可燃的。<br />
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|ref = harv<br />
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}}</ref><br />
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Dry air in the atmosphere of Earth contains roughly (by volume) 78.09% nitrogen, 20.95% oxygen, 0.93% argon, 0.039% carbon dioxide, and small amounts of other gases including methane. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. <br />
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地球大气层中的干燥空气大致(按体积计算)含有78.09% 的氮气、20.95% 的氧气、0.93% 的氩气、0.039% 的二氧化碳以及少量的其他气体,包括甲烷。洛夫洛克最初推测,高于25% 的氧气浓度会增加森林大火和森林大火的发生频率。石炭纪和白垩纪煤系地质时期O2浓度确实超过了25%时,正是这一时期形成了火成木炭。这一结果支持了 Lovelock 的论点。<br />
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Daisyworld examines the [[Earth's energy budget|energy budget]] of a [[planet]] populated by two different types of plants, black [[Asteraceae|daisies]] and white daisies, which are assumed to occupy a significant portion of the surface. The colour of the daisies influences the [[albedo]] of the planet such that black daisies absorb more light and warm the planet, while white daisies reflect more light and cool the planet. The black daisies are assumed to grow and reproduce best at a lower temperature, while the white daisies are assumed to thrive best at a higher temperature. As the temperature rises closer to the value the white daisies like, the white daisies outreproduce the black daisies, leading to a larger percentage of white surface, and more sunlight is reflected, reducing the heat input and eventually cooling the planet. Conversely, as the temperature falls, the black daisies outreproduce the white daisies, absorbing more sunlight and warming the planet. The temperature will thus converge to the value at which the reproductive rates of the plants are equal.<br />
Daisyworld研究了居住着两种不同类型的植物的[[地球的能源预算|能源预算]],这两种植物是黑色的[[菊科的雏菊]]和白色的雏菊,这两种植物被认为占据了地表的很大一部分。雏菊的颜色影响着这个星球的[反照率],因此黑色雏菊吸收更多的光并温暖地球,而白色雏菊则反射更多的光并使地球降温。黑雏菊在较低温度下生长繁殖最好,而白雏菊在较高温度下生长繁殖最好。当温度上升到接近白色雏菊的最适生长温度时,白色雏菊的繁殖能力超过了黑色雏菊,导致白色表面的比例增大,更多的阳光被反射,减少了热量输入,最终使地球变冷。相反,随着温度的下降,黑雏菊的繁殖能力超过了白雏菊,吸收了更多的阳光,使地球变暖。因此,温度将收敛到两种植物繁殖率相等对应的温度值。 <br />
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Lovelock and Watson showed that, over a limited range of conditions, this [[negative feedback]] due to competition can stabilize the planet's temperature at a value which supports life, if the energy output of the Sun changes, while a planet without life would show wide temperature swings. The percentage of white and black daisies will continually change to keep the temperature at the value at which the plants' reproductive rates are equal, allowing both life forms to thrive.<br />
Lovelock和Watson表明,在有限的条件范围内,如果太阳的能量输出发生变化,由于竞争而产生的[[负反馈]]可以将地球的温度稳定在支持生命的值上,而没有生命的行星则会出现大范围的温度波动。白雏菊和黑雏菊的比例会不断变化,以使温度保持在植物繁殖率相等的值,从而使两种生命形式都能茁壮成长。 <br />
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Gaia scientists see the participation of living organisms in the carbon cycle as one of the complex processes that maintain conditions suitable for life. The only significant natural source of atmospheric carbon dioxide (CO<sub>2</sub>) is volcanic activity, while the only significant removal is through the precipitation of carbonate rocks. Carbon precipitation, solution and fixation are influenced by the bacteria and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
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盖亚假说的科学家们把生物体参与碳循环看作是维持适合生命条件的复杂过程之一。火山活动是大气中二氧化碳的最重要的自然来源,而碳酸盐岩的沉淀是大气中二氧化碳最重要的去除途径。碳沉淀、溶解和固定受到土壤中细菌和植物根系的影响,这些细菌和植物根系可以改善气体循环,或者在珊瑚礁中,碳酸钙以固体的形式沉积在海底。碳酸钙被活的有机体用来制造含碳的结构和外壳。一旦死亡,生物体的外壳就会沉到海底,在那里它们产生白垩和石灰石的沉淀物。<br />
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It has been suggested that the results were predictable because Lovelock and Watson selected examples that produced the responses they desired.<ref>{{cite journal | doi = 10.1023/A:1023494111532 | date = 2003 | last1 = Kirchner | first1 = James W. | journal = Climatic Change | volume = 58 |issue=1–2| pages = 21–45 |title=The Gaia Hypothesis: Conjectures and Refutations | ref = harv}}</ref><br />
有人认为,结果是可预测的,因为洛夫洛克和沃森选择的例子产生了他们想要的反应。 <br />
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One of these organisms is Emiliania huxleyi, an abundant coccolithophore algae which also has a role in the formation of clouds. CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants. Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean algal blooms are also increasing.<br />
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其中一种是赫氏圆石藻,这是一种数量丰富的颗石藻类,也参与了云的形成。通过增加球石氟化物的寿命来补偿过量的CO < sub > 2 </sub > ,增加了锁定在海底的 CO < sub > 2 </sub > 的数量。球石粉会增加云量,从而控制地表温度,有助于降低整个地球的温度,有利于地球上植物所必需的降水。近年来,大气中 CO < < sub > 2 </sub > 浓度有所增加,有证据表明,海洋藻华的浓度也在增加。<br />
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===Regulation of oceanic salinity海洋盐度调节 ===<br />
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Lichen and other organisms accelerate the weathering of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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地衣和其他生物加速了岩石表面的风化,而岩石在土壤中的分解也加快了,这要归功于根、真菌、细菌和地下动物的活动。因此,二氧化碳从大气层流向土壤的过程是在生物的帮助下调节的。当大气中 CO2水平升高时,温度升高,植物生长。这种生长会增加植物对二氧化碳的消耗,植物会将二氧化碳处理到土壤中,从大气中排出。<br />
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Ocean [[salinity]] has been constant at about 3.5% for a very long time.<ref name=":0">{{Cite book|title=The Introduction to Ocean Sciences|last=Segar|first=Douglas|publisher=Library of Congress|year=2012|isbn=978-0-9857859-0-1|location=http://www.reefimages.com/oceans/SegarOcean3Chap05.pdf|pages=Chapter 5 3rd Edition|quote=|via=}}</ref> Salinity stability in oceanic environments is important as most cells require a rather constant salinity and do not generally tolerate values above 5%. The constant ocean salinity was a long-standing mystery, because no process counterbalancing the salt influx from rivers was known. Recently it was suggested<ref name="Gorham19912">{{cite journal|last=Gorham|first=Eville|date=1 January 1991|title=Biogeochemistry: its origins and development|journal=Biogeochemistry|publisher=Kluwer Academic|volume=13|issue=3|pages=199–239|doi=10.1007/BF00002942|issn=1573-515X|ref=harv}}</ref> that salinity may also be strongly influenced by [[seawater]] circulation through hot [[basalt]]ic rocks, and emerging as hot water vents on [[mid-ocean ridge]]s. However, the composition of seawater is far from equilibrium, and it is difficult to explain this fact without the influence of organic processes. One suggested explanation lies in the formation of salt plains throughout Earth's history. It is hypothesized that these are created by bacterial colonies that fix ions and heavy metals during their life processes.<ref name=":0" /><br />
在很长一段时间内,海洋盐度一直保持在3.5%左右。[23]海洋环境中的盐度稳定性非常重要,因为大多数细胞需要相当恒定的盐度,并且通常不能耐受超过5%的盐度值。恒定的海洋盐度是一个长期存在的谜团,因为没有任何过程可以抵消河流中的盐流入。大洋中脊上的热水喷口会排出盐分,有人认为[24]这说明盐分也会受到海水循环的强烈影响。然而,海水的组成远未达到平衡,如果没有有机过程的影响,很难解释这一事实。地球历史中盐滩的形成是一个常用的证据。据推测,这些盐滩是由在生命过程中固定离子和重金属的菌落产生的<br />
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In the biogeochemical processes of Earth, sources and sinks are the movement of elements. The composition of salt ions within our oceans and seas is: sodium (Na<sup>+</sup>), chlorine (Cl<sup>−</sup>), sulfate (SO<sub>4</sub><sup>2−</sup>), magnesium (Mg<sup>2+</sup>), calcium (Ca<sup>2+</sup>) and potassium (K<sup>+</sup>). The elements that comprise salinity do not readily change and are a conservative property of seawater.<ref name=":0" /> There are many mechanisms that change salinity from a particulate form to a dissolved form and back. The known sources of sodium i.e. salts are when weathering, erosion, and dissolution of rocks are transported into rivers and deposited into the oceans.<br />
在地球的生物地球化学过程中,源和汇是元素的运动。我们海洋中盐离子的组成是:钠(Na+)、氯(Cl-)、硫酸盐(SO42-)、镁(Mg2+)、钙(Ca2+)和钾(K+)。构成盐度的元素不易变化,是海水的一种保守属性。[23]有许多机制可以将盐度从颗粒形态改变为溶解形态,然后再返回。已知的钠(即盐)因为岩石的风化、侵蚀和溶解作用被输送到河流中并沉积到海洋中。 <br />
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The [[Mediterranean Sea]] as being Gaia's kidney is found ([http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/ here]) by Kenneth J. Hsue, a correspondence author in 2001. The "[[desiccation]]" of the Mediterranean is the evidence of a functioning kidney. Earlier "kidney functions" were performed during the "[[Deposition (geology)|deposition]] of the [[Cretaceous]] ([[Atlantic Ocean|South Atlantic]]), [[Jurassic]] ([[Gulf of Mexico]]), [[Permian–Triassic extinction event|Permo-Triassic]] ([[Europe]]), [[Devonian]] ([[Canada]]), [[Cambrian]]/[[Precambrian]] ([[Gondwana]]) saline giants."<ref>{{Cite web|url=http://scimar.icm.csic.es/scimar/index.php/secId/6/IdArt/209/|title=Scientia Marina: List of Issues|last=http://www.webviva.com|first=Justino Martinez. Web Viva 2007|website=scimar.icm.csic.es|language=English|access-date=2017-02-04}}</ref><br />
地中海是盖亚的肾脏,由肯尼斯·J·休伊(KennethJ.Hsue)在2001年发现的。地中海的“干涸”是肾功能正常的证据。早期的“肾功能”是在“白垩纪(南大西洋)、侏罗纪(墨西哥湾)、二叠纪-三叠纪(欧洲)、泥盆纪(加拿大)、寒武纪/前寒武纪(冈瓦纳)盐沼沉积时期进行的。” <br />
[[Earthrise taken from Apollo 8 on December 24, 1968]]<br />
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[1968年12月24日阿波罗8号拍摄的地出]<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The mythical Gaia was the primal Greek goddess personifying the Earth, the Greek version of "Mother Nature" (from Ge = Earth, and Aia = <br />
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地球是一个完整的整体,一个有生命的存在,这个观念有着悠久的传统。神话中的盖亚是拟人化地球的原始希腊女神,是希腊版本的“自然母亲”(来自 Ge = 地球,和 Aia = <br />
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===Regulation of oxygen in the atmosphere大气层的氧气调节===<br />
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PIE grandmother), or the Earth Mother. James Lovelock gave this name to his hypothesis after a suggestion from the novelist William Golding, who was living in the same village as Lovelock at the time (Bowerchalke, Wiltshire, UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry. Later, the naturalist and explorer Alexander von Humboldt recognized the coevolution of living organisms, climate, and Earth's crust. His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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派祖母,或地球母亲。詹姆斯·洛夫洛克根据小说家威廉·戈尔丁的建议给他的假设起了这个名字,他当时和洛夫洛克住在同一个村子里(英国威尔特郡鲍尔查尔克)。戈尔丁的建议是以Gea为基础的,Gea是希腊女神名字的另一种拼写,在地质学、地球物理和地球化学中,Gea是前缀。后来,博物学家和探险家亚历山大·冯·洪堡认识到生物、气候和地壳的共同进化。他的远见卓识的声明在西方没有被广泛接受,几十年后,盖亚假说刚提出时同样受到了科学界的抵制。<br />
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[[File:Vostok 420ky 4curves insolation.jpg|thumb|280px|Levels of gases in the atmosphere in 420,000 years of ice core data from [[Vostok Station|Vostok, Antarctica research station]]. Current period is at the left. <!-- Unsourced material based on GIMP FX version of this chart. The current version here is correct, original. This verbiage must be removed: Note that current CO<sub>2</sub> levels are more than 390 ppm, far higher than at any time in the last 400,000 years -->]]<br />
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{{See also|Geological history of oxygen}}<br />
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Also in the turn to the 20th century Aldo Leopold, pioneer in the development of modern environmental ethics and in the movement for wilderness conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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同样在20世纪之交,现代环境伦理学发展的先驱、荒野保护运动的先驱奥尔多 · 利奥波德在他的生物中心或整体的土地伦理学中提出了一个有生命的地球。<br />
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The Gaia hypothesis states that the Earth's [[Atmospheric chemistry#Atmospheric composition|atmospheric composition]] is kept at a dynamically steady state by the presence of life.<ref>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, p. 163. {{ISBN|978-0-465-01549-8}}</ref> The atmospheric composition provides the conditions that contemporary life has adapted to. All the atmospheric gases other than [[noble gas]]es present in the atmosphere are either made by organisms or processed by them.<br />
盖亚假说指出,地球的大气成分由于生命的存在而保持在动态稳定的状态。大气中除惰性气体以外的所有大气气体都是由生物体制造或加工而成。<br />
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The stability of the atmosphere in Earth is not a consequence of [[chemical equilibrium]]. [[Oxygen]] is a reactive compound, and should eventually combine with gases and minerals of the Earth's atmosphere and crust. Oxygen only began to persist in the atmosphere in small quantities about 50 million years before the start of the [[Great Oxygenation Event]].<ref name=Anabar2007>{{Cite journal| last4 = Arnold| last6 = Creaser| last3 = Lyons| first1 = A. | first2 = Y.| last9 = Scott| last2 = Duan | first3 = T. | first4 = G.| last8 = Gordon | first5 = B. | first10 = J. | first6 = R.| last10 = Garvin | first7 = A.| last11 = Buick | first8 = G. | first11 = R. | first9 = C.| title = A whiff of oxygen before the great oxidation event?| journal = Science| volume = 317| issue = 5846| year = 2007| last7 = Kaufman| pages = 1903–1906| last5 = Kendall| pmid = 17901330| last1 = Anbar | doi = 10.1126/science.1140325|bibcode = 2007Sci...317.1903A }}</ref> Since the start of the [[Cambrian]] period, atmospheric oxygen concentrations have fluctuated between 15% and 35% of atmospheric volume.<ref name=Berner1999>{{Cite journal<br />
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Another influence for the Gaia hypothesis and the environmental movement in general came as a side effect of the Space Race between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph Earthrise taken by astronaut William Anders in 1968 during the Apollo 8 mission became, through the Overview Effect an early symbol for the global ecology movement.<br />
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盖亚假说和环境运动的另一个影响来自于苏联和美利坚合众国之间太空竞赛。在20世纪60年代,第一批进入太空的人类可以看到地球作为一个整体的样子。1968年,宇航员威廉 · 安德斯在阿波罗8号任务期间拍摄的地出照片,通过总体效应成为全球生态运动的早期象征。<br />
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| pmid = 10500106<br />
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| date=Sep 1999 | last1 = Berner | first1 = R. A.<br />
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| title = Atmospheric oxygen over Phanerozoic time<br />
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[[James Lovelock, 2005]]<br />
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[ James Lovelock,2005]<br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the Jet Propulsion Laboratory in California on methods of detecting life on Mars. The first paper to mention it was Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life, co-authored with C.E. Giffin. A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the Pic du Midi observatory, planets like Mars or Venus had atmospheres in chemical equilibrium. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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65年9月,洛夫洛克在加利福尼亚喷气推进实验室研究探测火星生命的方法时,开始定义由生物群落控制的自我调节地球的概念。第一篇提到它的论文是行星大气:与C.E.Giffin合著的与生命存在有关的成分和其他变化。一个主要的概念是,通过大气的化学成分可以在行星尺度上探测到生命。根据picdumidi天文台收集的数据,像火星或金星这样的行星,其大气层处于化学平衡状态。这种与地球大气的差异被认为是这些行星上没有生命的证据。 <br />
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Lovelock formulated the Gaia Hypothesis in journal articles in 1972 and 1974, and a popular book length version of the hypothesis, published in 1979 as The Quest for Gaia, began to attract scientific and critical attention.<br />
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洛夫洛克在1972年和1974年的期刊文章中提出了盖亚假说,并在1979年出版了一本畅销书,名为《寻找盖亚》 ,开始引起科学界和批判界的关注。<br />
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Lovelock called it first the Earth feedback hypothesis, and it was a way to explain the fact that combinations of chemicals including oxygen and methane persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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洛夫洛克首先将其称为地球反馈假说,解释氧气和甲烷等化学物质在地球大气中如何保持稳定浓度。洛夫洛克认为,在其他行星的大气层中探测这种组合,是一种相对便宜可靠的探测生命的方法。<br />
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| doi = 10.1073/pnas.96.20.10955<br />
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[[Lynn Margulis]]<br />
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[琳 · 玛格丽丝]<br />
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|bibcode = 1999PNAS...9610955B }}</ref> Traces of [[Atmospheric methane|methane]] (at an amount of 100,000 tonnes produced per year)<ref name="Cicerone1988">{{cite journal |last1=Cicerone |first1=R.J. |last2=Oremland |first2=R.S. |date=1988 |title=Biogeochemical aspects of atmospheric methane |journal=Global Biogeochemical Cycles |volume=2 |issue=4 |pages=299–327 |url=//webfiles.uci.edu/setrumbo/public/Methane_papers/Cicerone_Global%20Biogeochem%20Cy_1988.pdf |doi=10.1029/GB002i004p00299 |bibcode=1988GBioC...2..299C}}</ref> should not exist, as methane is combustible in an oxygen atmosphere.<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<br />
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后来出现了其他关系,例如海洋生物产生的硫和碘的数量与陆地生物所需的数量大致相同,这些都支持了这一假说。<br />
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Dry air in the [[atmosphere of Earth]] contains roughly (by volume) 78.09% [[nitrogen]], 20.95% oxygen, 0.93% [[argon]], 0.039% [[Carbon dioxide in the Earth's atmosphere|carbon dioxide]], and small amounts of other gases including [[methane]]. Lovelock originally speculated that concentrations of oxygen above about 25% would increase the frequency of wildfires and conflagration of forests. Recent work on the findings of fire-caused charcoal in Carboniferous and Cretaceous coal measures, in geologic periods when O<sub>2</sub> did exceed 25%, has supported Lovelock's contention. {{citation needed|date=June 2012}}<br />
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[[地球大气]]中的干空气大约(按体积)包含78.09%[[氮]],20.95%的氧,0.93%[[氩]],0.039%[地球大气中的二氧化碳|二氧化碳]],以及少量其他气体,包括[[甲烷]]。洛夫洛克最初推测,氧气浓度超过25%会增加森林火灾和火灾的发生率。最近在石炭纪和白垩纪煤系中火成木炭的研究(这两个地质时期O<sub>2</sub>浓度超过25%)支持了Lovelock的观点 <br />
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In 1971 microbiologist Dr. Lynn Margulis joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet. The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of eukaryotic organelles and her contributions to the endosymbiotic theory, nowadays accepted. Margulis dedicated the last of eight chapters in her book, The Symbiotic Planet, to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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1971年,微生物学家 Lynn Margulis 博士加入了 Lovelock 的行列,努力将最初的假设充实为科学证明的概念。Margulis 贡献了她关于微生物如何影响大气层和地球表面不同层次的知识。这位美国生物学家也唤受到科学界的批评,因为她倡导真核细胞器起源的理论,以及她对美国共生发源学会的贡献——现在被接受了。玛格丽丝在她的书《共生星球》中将最后八章用于描述盖亚。然而,她反对对盖亚的广泛拟人化,并强调盖亚“不是一个有机体” ,而是“有机体之间相互作用的一个新兴属性”。她将盖亚定义为“组成地球表面一个巨大生态系统的一系列相互作用的生态系统”。句号”。这本书最令人难忘的“口号”实际上是由马古利斯的一个学生打趣说的: “从太空看,盖亚只是共生而已。”。<br />
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===Processing of CO<sub>2</sub>二氧化碳处理===<br />
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{{See also|Carbon cycle}}<br />
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James Lovelock called his first proposal the Gaia hypothesis but has also used the term Gaia theory. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments and provided a number of useful predictions. In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating. The principal sponsor was the National Audubon Society. Speakers included James Lovelock, George Wald, Mary Catherine Bateson, Lewis Thomas, John Todd, Donald Michael, Christopher Bird, Thomas Berry, David Abram, Michael Cohen, and William Fields. Some 500 people attended.<br />
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詹姆斯 · 洛夫洛克称他的第一个提议为盖亚假说,但也使用了盖亚理论这个术语。洛夫洛克说,最初的提法是基于观察,但仍然缺乏科学的解释。盖亚假说从那以后得到了一些科学实验的支持,并提供了一些有用的预测。事实上,更广泛的研究证明了最初的假设是错误的,在这个意义上,不是生命本身,而是整个地球系统在调节。主要赞助者是奥杜邦学会。讲者包括 James Lovelock、 George Wald、 Mary Catherine Bateson、 Lewis Thomas、 John Todd、 Donald Michael、 Christopher Bird、 Thomas Berry、 David Abram、 Michael Cohen 和 William Fields。大约有500人参加。<br />
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Gaia scientists see the participation of living organisms in the [[carbon cycle]] as one of the complex processes that maintain conditions suitable for life. The only significant natural source of [[Carbon dioxide in Earth's atmosphere|atmospheric carbon dioxide]] ([[Carbon dioxide|CO<sub>2</sub>]]) is [[volcanic activity]], while the only significant removal is through the precipitation of [[carbonate rocks]].<ref name="Karhu1996">{{cite journal | author = Karhu, J.A. | author2 = Holland, H.D. | date = 1 October 1996 | title = Carbon isotopes and the rise of atmospheric oxygen | journal = [[Geology (journal)|Geology]] | volume = 24 | issue = 10 | pages = 867–870 | doi = 10.1130/0091-7613(1996)024<0867:CIATRO>2.3.CO;2|bibcode = 1996Geo....24..867K | ref = harv}}</ref> Carbon precipitation, solution and [[Carbon fixation|fixation]] are influenced by the [[bacteria]] and plant roots in soils, where they improve gaseous circulation, or in coral reefs, where calcium carbonate is deposited as a solid on the sea floor. Calcium carbonate is used by living organisms to manufacture carbonaceous tests and shells. Once dead, the living organisms' shells fall to the bottom of the oceans where they generate deposits of chalk and limestone.<br />
盖亚的科学家认为,生物参与[[碳循环]是维持适宜生命条件的复杂过程之一。[[地球大气中的二氧化碳|大气二氧化碳]]([[二氧化碳| CO2]])最重要的自然来源是[[火山活动]],而最重要的去除过程是[[碳酸盐岩]]的沉淀,溶液和[[固碳|固碳]]受土壤中的[[细菌]]和植物根系的影响,它们改善了气体循环,珊瑚礁中碳酸钙以固体形式沉积在海底。碳酸钙被生物用来制造含碳结构和贝壳。一旦死亡,这些生物的壳就会落到海底,在那里它们会产生白垩和石灰岩的沉积物。 <br />
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One of these organisms is ''[[Emiliania huxleyi]]'', an abundant [[coccolithophore]] [[algae]] which also has a role in the formation of [[cloud]]s.<ref name="Harding2006">{{cite book |author=Harding, Stephan |title=Animate Earth |publisher=Chelsea Green Publishing |date=2006 |pages=65 |isbn=978-1-933392-29-5 }}</ref> CO<sub>2</sub> excess is compensated by an increase of coccolithophoride life, increasing the amount of CO<sub>2</sub> locked in the ocean floor. Coccolithophorides increase the cloud cover, hence control the surface temperature, help cool the whole planet and favor precipitations necessary for terrestrial plants.{{citation needed|date=July 2015}} Lately the atmospheric CO<sub>2</sub> concentration has increased and there is some evidence that concentrations of ocean [[algal bloom]]s are also increasing.<ref>{{Cite web | date = 12 September 2007 | title = Interagency Report Says Harmful Algal Blooms Increasing | url = http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | url-status = dead | archiveurl = https://web.archive.org/web/20080209234239/http://www.publicaffairs.noaa.gov/releases2007/sep07/noaa07-r435.html | archivedate = 9 February 2008 }}</ref><br />
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In 1988, climatologist Stephen Schneider organised a conference of the American Geophysical Union. The first Chapman Conference on Gaia,<br />
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在1988年,气候学家史蒂芬·史奈德组织了一次美国美国地球物理联盟协会的会议。关于盖亚假说的第一次查普曼会议,<br />
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[[Lichen]] and other organisms accelerate the [[weathering]] of rocks in the surface, while the decomposition of rocks also happens faster in the soil, thanks to the activity of roots, fungi, bacteria and subterranean animals. The flow of carbon dioxide from the atmosphere to the soil is therefore regulated with the help of living beings. When CO<sub>2</sub> levels rise in the atmosphere the temperature increases and plants grow. This growth brings higher consumption of CO<sub>2</sub> by the plants, who process it into the soil, removing it from the atmosphere.<br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the Daisyworld Model (and its modifications, above) as evidence against most of these criticisms.<br />
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然而,洛夫洛克和其他支持盖亚理论的科学家确实试图反驳这样一种说法,即这种假设不科学,因为不可能通过控制实验来检验它。例如,针对盖亚假说是目的论的指责,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修正,上文)反驳这些批评。<br />
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==History历史==<br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of teleologism ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,这一版本中盖亚并不是有意地在她的环境中维持生命赖以生存的复杂平衡。看起来,盖亚假说“故意”行为的说法只是他那本广受欢迎的书中的一个比喻性陈述,并不是字面意义上的理解。这种对盖亚假说的新陈述更能为科学界所接受。在这次会议之后,大多数关于目的论的指责都停止了。<br />
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===Precedents先例===<br />
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[[File:NASA-Apollo8-Dec24-Earthrise.jpg|thumb|''[[Earthrise]]'' taken from [[Apollo 8]] on December 24, 1968]]<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000, the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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到2000年6月23日在西班牙巴伦西亚举行关于盖亚假说的第二次查普曼会议时,情况发生了重大变化。与其讨论盖亚假说的目的论观点,或盖亚假说的“类型” ,不如将重点放在具体的机制上,通过这些机制,短期内基本稳态在重要的进化长期结构变化的框架内得以维持。<br />
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The idea of the Earth as an integrated whole, a living being, has a long tradition. The [[Gaia (mythology)|mythical Gaia]] was the primal Greek goddess personifying the [[Earth]], the Greek version of "[[Mother Nature]]" (from Ge = Earth, and Aia = <br />
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[[PIE]] grandmother), or the [[Earth Mother]]. James Lovelock gave this name to his hypothesis after a suggestion from the novelist [[William Golding]], who was living in the same village as Lovelock at the time ([[Bowerchalke]], [[Wiltshire]], UK). Golding's advice was based on Gea, an alternative spelling for the name of the Greek goddess, which is used as prefix in geology, geophysics and geochemistry.<ref name=vanish09 /> Golding later made reference to Gaia in his [[Nobel prize]] acceptance speech.<br />
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The major questions were:<br />
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主要的问题是:<br />
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In the eighteenth century, as [[geology]] consolidated as a modern science, [[James Hutton]] maintained that geological and biological processes are interlinked.<ref name=CapraWeb>{{cite book |author=Capra, Fritjof |title=The web of life: a new scientific understanding of living systems |publisher=Anchor Books |location=Garden City, N.Y |date=1996 |page=[https://archive.org/details/weboflifenewscie00capr/page/23 23] |isbn=978-0-385-47675-1 |url=https://archive.org/details/weboflifenewscie00capr/page/23 }}</ref> Later, the [[naturalist]] and explorer [[Alexander von Humboldt]] recognized the coevolution of living organisms, climate, and Earth's crust.<ref name=CapraWeb /> In the twentieth century, [[Vladimir Vernadsky]] formulated a theory of Earth's development that is now one of the foundations of ecology. Vernadsky was a Ukrainian [[geochemist]] and was one of the first scientists to recognize that the oxygen, nitrogen, and carbon dioxide in the Earth's atmosphere result from biological processes. During the 1920s he published works arguing that living organisms could reshape the planet as surely as any physical force. Vernadsky was a pioneer of the scientific bases for the environmental sciences.<ref>S.R. Weart, 2003, ''The Discovery of Global Warming'', Cambridge, Harvard Press</ref> His visionary pronouncements were not widely accepted in the West, and some decades later the Gaia hypothesis received the same type of initial resistance from the scientific community.<br />
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"How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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“被称为盖亚的全球生物地球化学/气候系统是如何及时发生变化的?它的历史是什么?盖亚假说能够在一个时间尺度上保持系统的稳定性,但是在更长的时间尺度上仍然经历矢量变化吗?如何利用地质记录来检验这些问题? ”<br />
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"What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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“盖亚假说的结构是什么?这些反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由在任何特定时间进行的学科研究务实地决定的,还是有一些部分应该被认为是最真实的,以了解盖亚假说随着时间的推移包含进化中的生物体?盖亚系统这些不同部分之间的反馈是什么? 对盖亚假说作为全球生态系统的结构和生命的生产力来说,物质的近乎封闭意味着什么? ”<br />
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Also in the turn to the 20th century [[Aldo Leopold]], pioneer in the development of modern [[environmental ethics]] and in the movement for [[wilderness]] conservation, suggested a living Earth in his biocentric or holistic ethics regarding land.<br />
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"How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
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“盖亚假说过程和现象的模型如何与现实相关,它们如何帮助解决和理解盖亚?雏菊世界的成果如何转移到现实世界?什么是“雏菊”的主要候选人?我们发现雏菊与否对盖亚理论重要吗?我们应该怎样寻找雏菊,我们应该加紧寻找吗?如何利用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制? ”<br />
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{{quotation|It is at least not impossible to regard the earth's parts—soil, mountains, rivers, atmosphere etc,—as organs or parts of organs of a coordinated whole, each part with its definite function. And if we could see this whole, as a whole, through a great period of time, we might perceive not only organs with coordinated functions, but possibly also that process of consumption as replacement which in biology we call metabolism, or growth. In such case we would have all the visible attributes of a living thing, which we do not realize to be such because it is too big, and its life processes too slow.| Stephan Harding | ''Animate Earth''.<ref>Harding, Stephan. ''Animate Earth Science, Intuition and Gaia''. Chelsea Green Publishing, 2006, p. 44. {{ISBN|1-933392-29-0}}</ref>}}<br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise entropy production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
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1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是一种向远离平衡的稳态演化的结果,这种平衡状态使熵产生最大化,克莱顿(2004)同意这样的说法:“自稳态行为可以从与行星反照率相关的MEP状态中产生”;“……一个如盖亚假说所述,处于MEP状态的生物地球很可能导致地球系统在长时间尺度上的近稳态行为。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。<br />
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Another influence for the Gaia hypothesis and the [[environmental movement]] in general came as a side effect of the [[Space Race]] between the Soviet Union and the United States of America. During the 1960s, the first humans in space could see how the Earth looked as a whole. The photograph ''[[Earthrise]]'' taken by astronaut [[William Anders]] in 1968 during the [[Apollo 8]] mission became, through the [[Overview Effect]] an early symbol for the global ecology movement.<ref>[http://digitaljournalist.org/issue0309/lm11.html 100 Photographs that Changed the World by Life - The Digital Journalist]</ref><br />
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盖亚假说和[[环境运动]]的另一个总体影响来自苏联和美利坚合众国之间[[太空竞赛]]的副作用。在20世纪60年代,第一批进入太空的人类可以看到地球的整体面貌。1968年宇航员[[William Anders]]在[[Apollo 8]]任务期间拍摄的照片“[[地球升起]”,通过[[概述效果]]成为全球生态运动的早期标志<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<br />
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第四次关于盖亚假说的国际会议,由北弗吉尼亚地区公园管理局和其他机构主办,于2006年10月在弗吉尼亚州乔治梅森大学的阿灵顿校区举行。<br />
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===Formulation of the hypothesis假说形成===<br />
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[[File:James Lovelock in 2005.jpg|thumb|[[James Lovelock]], 2005]]<br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
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马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。Lynn Margulis是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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Lovelock started defining the idea of a self-regulating Earth controlled by the community of living organisms in September 1965, while working at the [[Jet Propulsion Laboratory]] in California on methods of detecting [[life on Mars (planet)|life on Mars]].<ref name="Lovelock1965">{{cite journal | author = Lovelock, J.E. | date = 1965 | title = A physical basis for life detection experiments | journal = [[Nature (journal)|Nature]] | volume = 207 | issue = 7 | pages = 568–570 | doi = 10.1038/207568a0 | pmid=5883628|bibcode = 1965Natur.207..568L | ref = harv}}</ref><ref>{{Cite web |url=http://www.jameslovelock.org/page4.html |title=Geophysiology |access-date=2007-05-05 |archive-url=https://web.archive.org/web/20070506073502/http://www.jameslovelock.org/page4.html |archive-date=2007-05-06 |url-status=dead }}</ref> The first paper to mention it was ''Planetary Atmospheres: Compositional and other Changes Associated with the Presence of Life'', co-authored with C.E. Giffin.<ref>{{cite journal | author1 = Lovelock, J.E. | author2 = Giffin, C.E. | date = 1969 | title = Planetary Atmospheres: Compositional and other changes associated with the presence of Life | journal = Advances in the Astronautical Sciences | volume = 25 | pages = 179–193 | isbn = 978-0-87703-028-7 | ref = harv}}</ref> A main concept was that life could be detected in a planetary scale by the chemical composition of the atmosphere. According to the data gathered by the [[Pic du Midi de Bigorre|Pic du Midi observatory]], planets like Mars or Venus had atmospheres in [[chemical equilibrium]]. This difference with the Earth atmosphere was considered to be a proof that there was no life in these planets.<br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
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这次会议将盖亚假说作为一种科学和隐喻的手段,来理解我们如何开始解决21世纪的问题,如气候变化和持续的环境破坏。<br />
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Lovelock formulated the ''Gaia Hypothesis'' in journal articles in 1972<ref name="J1972">{{cite journal | author = J. E. Lovelock | title = Gaia as seen through the atmosphere | date = 1972 | journal = [[Atmospheric Environment]] | volume = 6 | issue = 8 | pages = 579–580 | doi = 10.1016/0004-6981(72)90076-5 | ref = harv|bibcode = 1972AtmEn...6..579L }}</ref> and 1974,<ref name="lovelock1974" /> followed by a popularizing 1979 book ''Gaia: A new look at life on Earth''. An article in the ''[[New Scientist]]'' of February 6, 1975,<ref>Lovelock, John and Sidney Epton, (February 8, 1975). "The quest for Gaia". [https://books.google.com/books?id=pnV6UYEkU4YC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false New Scientist], p. 304.</ref> and a popular book length version of the hypothesis, published in 1979 as ''The Quest for Gaia'', began to attract scientific and critical attention.<br />
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Lovelock called it first the Earth feedback hypothesis,<ref name="Lovelock01">{{harvnb|Lovelock, James|2001}}</ref> and it was a way to explain the fact that combinations of chemicals including [[oxygen]] and [[methane]] persist in stable concentrations in the atmosphere of the Earth. Lovelock suggested detecting such combinations in other planets' atmospheres as a relatively reliable and cheap way to detect life.<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as Ford Doolittle, Richard Dawkins and Stephen Jay Gould. Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists, He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as autopoietic or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole. With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<br />
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在最初几乎没有引起科学家的注意之后(从1969年到1977年) ,有一段时间,最初的盖亚假说受到了一些科学家的批评,如福特杜利特,理查德道金斯和史蒂芬·古尔德。洛夫洛克说,因为他的假说是以一位希腊女神的名字命名的,并得到许多非科学家的拥护,他想知道实现自我调节体内平衡的实际机制。在为盖亚辩护时,戴维•阿布拉姆认为,古尔德忽视了一个事实,即“机制”本身就是一个隐喻——尽管这个隐喻极其常见,而且往往不为人所知——这个隐喻让我们把自然和生命系统看作是由外部组织和建造的机器(而不是自动生成或自组织现象)。根据阿布拉姆的说法,机械隐喻使我们忽略了生命实体的活跃性或代表性,而盖亚假说的有机隐喻强调了生物群和整个生物圈的活跃性。关于盖亚的因果关系,洛夫洛克认为没有单一的机制是负责任的,各种已知机制之间的联系可能永远不会被人知道,这在生物学和生态学的其他领域是理所当然地被接受的,并且由于其他原因,特定的敌意是保留给他自己的假设的。<br />
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[[File:Lynn Margulis.jpg|thumb|left|[[Lynn Margulis]]]]<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of greedy reductionism in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<br />
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除了澄清他的语言和理解什么是生命形式,洛夫洛克自己把大部分的批评归因于他的批评者缺乏对非线性数学的理解,以及贪婪还原主义的线性化形式,在这种形式中,所有事件都必须立即归因于事件发生之前的特定原因。他还表示,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,以及一些自我调节现象可能无法在数学上解释。<br />
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Later, other relationships such as sea creatures producing sulfur and iodine in approximately the same quantities as required by land creatures emerged and helped bolster the hypothesis.<ref>{{cite journal | first1=W.D. | last1=Hamilton | first2=T.M. | last2=Lenton | title=Spora and Gaia: how microbes fly with their clouds | journal=Ethology Ecology & Evolution | volume=10 | pages=1–16 | date=1998 | issue=1 | url=http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | format=PDF | doi=10.1080/08927014.1998.9522867 | ref=harv | url-status=dead | archiveurl=https://web.archive.org/web/20110723055017/http://ejour-fup.unifi.it/index.php/eee/article/viewFile/787/733 | archivedate=2011-07-23 }}</ref><br />
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Evolutionary biologist W. D. Hamilton called the concept of Gaia Copernican, adding that it would take another Newton to explain how Gaian self-regulation takes place through Darwinian natural selection. More recently Ford Doolittle building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis. <br />
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进化生物学家W.D.Hamilton称盖亚假说为哥白尼式的概念,并补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。最近,Ford Doolittle在他和Inkpen的ITSNTS(这是歌手而不是歌曲)的建议中提出,差异持续性可以在自然选择进化中起到与差异生殖相似的作用,从而为自然选择理论和盖亚假说之间提供了一种可能的调和。 <br />
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In 1971 [[microbiologist]] Dr. [[Lynn Margulis]] joined Lovelock in the effort of fleshing out the initial hypothesis into scientifically proven concepts, contributing her knowledge about how microbes affect the atmosphere and the different layers in the surface of the planet.<ref name="Turney, Jon 2003">{{cite book |author=Turney, Jon |title=Lovelock and Gaia: Signs of Life |publisher=Icon Books |location=UK |date=2003 |isbn=978-1-84046-458-0 |url-access=registration |url=https://archive.org/details/lovelockgaiasign0000turn }}</ref> The American biologist had also awakened criticism from the scientific community with her advocacy of the theory on the origin of [[eukaryote|eukaryotic]] [[organelle]]s and her contributions to the [[endosymbiotic theory]], nowadays accepted. Margulis dedicated the last of eight chapters in her book, ''The Symbiotic Planet'', to Gaia. However, she objected to the widespread personification of Gaia and stressed that Gaia is "not an organism", but "an emergent property of interaction among organisms". She defined Gaia as "the series of interacting ecosystems that compose a single huge ecosystem at the Earth's surface. Period". The book's most memorable "slogan" was actually quipped by a student of Margulis': "Gaia is just symbiosis as seen from space".<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal Climatic Change in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it. to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background" The CLAW hypothesis, In 2009 the Medea hypothesis was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<br />
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盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论据是,生命对环境产生了有害或不稳定的影响,而不是采取行动加以调节。为了“令人不安地徘徊在污点隐喻、事实和虚假科学之间,我宁愿把盖亚假说牢牢地放在背景下。”爪假说,2009年提出的美狄亚假说:生命对行星条件有高度有害的(生物杀灭)影响,与盖亚假说直接相反。 <br />
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James Lovelock called his first proposal the ''Gaia hypothesis'' but has also used the term ''Gaia theory''. Lovelock states that the initial formulation was based on observation, but still lacked a scientific explanation. The Gaia hypothesis has since been supported by a number of scientific experiments<ref name="J1990">{{cite journal | author = J. E. Lovelock | title = Hands up for the Gaia hypothesis | date = 1990 | journal = [[Nature (journal)|Nature]] | volume = 344 | issue = 6262 | pages = 100–2 | doi = 10.1038/344100a0|bibcode = 1990Natur.344..100L | ref = harv}}</ref> and provided a number of useful predictions.<ref name="Volk2003">{{cite book |author=Volk, Tyler |title=Gaia's Body: Toward a Physiology of Earth |publisher=[[MIT Press]] |location=Cambridge, Massachusetts |date=2003 |isbn=978-0-262-72042-7 }}</ref> In fact, wider research proved the original hypothesis wrong, in the sense that it is not life alone but the whole Earth system that does the regulating.<ref name="vanishing255"/><br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it". Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works". This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<br />
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2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新想法,并倡导一种整体的方法来研究地球”。在其他地方,他提出了自己的结论:“盖亚假说并不是我们这个世界如何运转的精确图像”。这种说法需要被理解为是指盖亚假说的“强”和“中”形式,生物群遵循的原则是使地球成为最佳(强度5)或有利于生命(强度4),或是作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化的盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释。<br />
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===First Gaia conference第一次盖亚会议===<br />
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In 1985, the first public symposium on the Gaia hypothesis, ''Is The Earth A Living Organism?'' was held at [[University of Massachusetts Amherst]], August 1–6.<ref>{{cite news |last=Joseph |first=Lawrence E. |title=Britain's Whole Earth Guru |work=The New York Times Magazine |date=November 23, 1986 |url=https://www.nytimes.com/1986/11/23/magazine/britain-s-whole-earth-guru.html |accessdate=1 December 2013}}</ref> The principal sponsor was the [[National Audubon Society]]. Speakers included James Lovelock, [[George Wald]], [[Mary Catherine Bateson]], [[Lewis Thomas]], [[John Todd (Canadian biologist)|John Todd]], Donald Michael, [[Christopher Bird]], [[Thomas Berry]], [[David Abram]], [[Michael A. Cohen|Michael Cohen]], and William Fields. Some 500 people attended.<ref>Bunyard, Peter (1996), "Gaia in Action: Science of the Living Earth" (Floris Books)</ref><br />
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1985年,关于盖亚假说的第一次公开研讨会,“地球是一个活的有机体吗?”在马萨诸塞大学阿默斯特举行 <br />
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===Second Gaia conference第二次盖亚会议===<br />
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In 1988, [[climatology|climatologist]] [[Stephen Schneider]] organised a conference of the [[American Geophysical Union]]. The first Chapman Conference on Gaia,<ref name="ReferenceB"/> was held in San Diego, California on March 7, 1988.<br />
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1988年,climatology和Stephen Schneider组织了一次美国地球物理联合会会议。关于盖亚假说的第一次查普曼会议 <br />
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During the "philosophical foundations" session of the conference, [[David Abram]] spoke on the influence of metaphor in science, and of the Gaia hypothesis as offering a new and potentially game-changing metaphorics, while [[James Kirchner]] criticised the Gaia hypothesis for its imprecision. Kirchner claimed that Lovelock and Margulis had not presented one Gaia hypothesis, but four -<br />
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在会议的“哲学基础”会议上,David Abram谈到了隐喻在科学中的影响,盖亚假说提供了一种新的、可能改变游戏规则的隐喻,而James Kirchner则批评盖亚假说的不精确性。基什纳声称,洛夫洛克和马古利斯提出的盖亚假说不是一个,而是四个- <br />
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* [[Coevolution|CoEvolutionary]] Gaia: that life and the environment had evolved in a coupled way. Kirchner claimed that this was already accepted scientifically and was not new.<br />
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* [[Homeostatic]] Gaia: that life maintained the stability of the natural environment, and that this stability enabled life to continue to exist.<br />
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* [[Geophysics|Geophysical]] Gaia: that the Gaia hypothesis generated interest in geophysical cycles and therefore led to interesting new research in terrestrial geophysical dynamics.<br />
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* Optimising Gaia: that Gaia shaped the planet in a way that made it an optimal environment for life as a whole. Kirchner claimed that this was not testable and therefore was not scientific.<br />
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盖亚:生命和环境是以耦合的方式进化的。基什内尔声称,这已经被科学界接受,并不是什么新鲜事。 <br />
盖亚:生命维持着自然环境的稳定,这种稳定性使生命得以继续存在。 <br />
盖亚:盖亚假说引起了人们对地球物理周期的兴趣,因此导致了地球物理动力学中有趣的新研究。 <br />
优化盖亚:盖亚塑造了地球,使之成为整个生命的最佳环境。基什内尔声称,这是不可测试的,因此是不科学的。 <br />
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Of Homeostatic Gaia, Kirchner recognised two alternatives. "Weak Gaia" asserted that life tends to make the environment stable for the flourishing of all life. "Strong Gaia" according to Kirchner, asserted that life tends to make the environment stable, ''to enable'' the flourishing of all life. Strong Gaia, Kirchner claimed, was untestable and therefore not scientific.<ref>{{cite journal | bibcode=1989RvGeo..27..223K | doi = 10.1029/RG027i002p00223 | title=The Gaia hypothesis: Can it be tested? | date=1989 | last1=Kirchner | first1=James W. | journal=Reviews of Geophysics | volume=27 | issue=2 | pages=223 | ref=harv}}</ref><br />
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基什内尔发现了两种选择“软弱的盖亚”断言,为了所有生命的繁衍,生命往往会使环境变得稳定根据基什内尔的说法,“强大的盖亚”断言,生命趋向于使环境稳定,“使”所有生命繁荣昌盛。基什内尔声称,强大的盖亚是不稳定的,因此不科学。 <br />
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Lovelock and other Gaia-supporting scientists, however, did attempt to disprove the claim that the hypothesis is not scientific because it is impossible to test it by controlled experiment. For example, against the charge that Gaia was teleological, Lovelock and Andrew Watson offered the [[Daisyworld]] Model (and its modifications, above) as evidence against most of these criticisms.<ref name="daisyworld"/> Lovelock said that the Daisyworld model "demonstrates that self-regulation of the global environment can emerge from competition amongst types of life altering their local environment in different ways".<ref>{{cite journal | pmid=10968941 | date=2000 | last1=Lenton | first1=TM | last2=Lovelock | first2=JE | s2cid=5486128 | title=Daisyworld is Darwinian: Constraints on adaptation are important for planetary self-regulation | volume=206 | issue=1 | pages=109–14 | doi=10.1006/jtbi.2000.2105 | journal=Journal of Theoretical Biology | ref=harv}}</ref><br />
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然而,洛夫洛克和其他支持盖亚假说的科学家,确实试图反驳这种说法,即这个假设是不科学的,因为不可能通过受控实验来检验它。例如,针对盖亚假说是目的论的指控,洛夫洛克和安德鲁·沃森提出了雏菊世界模型(及其修改,洛夫洛克说,雏菊世界模型“证明了全球环境的自我调节可以通过不同方式改变当地环境的生活类型之间的竞争产生”。 <br />
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Lovelock was careful to present a version of the Gaia hypothesis that had no claim that Gaia intentionally or consciously maintained the complex balance in her environment that life needed to survive. It would appear that the claim that Gaia acts "intentionally" was a metaphoric statement in his popular initial book and was not meant to be taken literally. This new statement of the Gaia hypothesis was more acceptable to the scientific community. Most accusations of [[teleology|teleologism]] ceased, following this conference.<br />
洛夫洛克谨慎地提出了盖亚假说的一个版本,没有声称盖亚有意或有意识地维持着生命生存所需的复杂平衡。看来盖亚假说“故意”的行为是他最受欢迎的第一本书中的隐喻性陈述,并不是字面意思。盖亚假说的这一新说法更为科学界所接受。在这次会议之后,[[目的论|目的论]]的大多数指控都停止了。<br />
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===Third Gaia conference第三次盖亚会议===<br />
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By the time of the 2nd Chapman Conference on the Gaia Hypothesis, held at Valencia, Spain, on 23 June 2000,<ref>{{cite news|last=Simón|first=Federico|title=GEOLOGÍA Enfoque multidisciplinar La hipótesis Gaia madura en Valencia con los últimos avances científicos|journal=El País|date=21 June 2000|url=http://elpais.com/diario/2000/06/21/futuro/961538404_850215.html|accessdate=1 December 2013|language=spanish}}</ref> the situation had changed significantly. Rather than a discussion of the Gaian teleological views, or "types" of Gaia hypotheses, the focus was upon the specific mechanisms by which basic short term homeostasis was maintained within a framework of significant evolutionary long term structural change.<br />
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The major questions were:<ref>{{cite web|title=General Information Chapman Conference on the Gaia Hypothesis University of Valencia Valencia, Spain June 19-23, 2000 (Monday through Friday) |url=http://www.agu.org/meetings/chapman/chapman_archive/cc00bcall.html |work=AGU Meetings |accessdate=7 January 2017 |author=American Geophysical Union }}</ref><br />
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# "How has the global biogeochemical/climate system called Gaia changed in time? What is its history? Can Gaia maintain stability of the system at one time scale but still undergo vectorial change at longer time scales? How can the geologic record be used to examine these questions?"<br />
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# "What is the structure of Gaia? Are the feedbacks sufficiently strong to influence the evolution of climate? Are there parts of the system determined pragmatically by whatever disciplinary study is being undertaken at any given time or are there a set of parts that should be taken as most true for understanding Gaia as containing evolving organisms over time? What are the feedbacks among these different parts of the Gaian system, and what does the near closure of matter mean for the structure of Gaia as a global ecosystem and for the productivity of life?"<br />
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# "How do models of Gaian processes and phenomena relate to reality and how do they help address and understand Gaia? How do results from Daisyworld transfer to the real world? What are the main candidates for "daisies"? Does it matter for Gaia theory whether we find daisies or not? How should we be searching for daisies, and should we intensify the search? How can Gaian mechanisms be investigated using process models or global models of the climate system that include the biota and allow for chemical cycling?"<br />
“被称为盖亚的全球生物地球化学/气候系统是如何随时间变化的?它的历史是什么?盖亚能在一个时间尺度上保持系统的稳定性,但在较长的时间尺度上仍能经历向量变化吗?如何利用地质记录来检验这些问题?” <br />
“盖亚假说的结构是什么?反馈是否足够强烈,足以影响气候的演变?系统的某些部分是由任何给定时间正在进行的任何学科研究实际确定的,还是有一组应该被视为最真实的部分来理解盖亚假说,即随着时间的推移包含进化中的有机体?盖亚系统的这些不同部分之间的反馈是什么?物质的接近封闭对盖亚作为全球生态系统的结构和生命的生产力意味着什么?” <br />
“盖亚假说过程和现象的模型如何与现实联系起来,它们如何帮助解决和理解盖亚假说?雏菊世界的结果如何传递到真实世界?“雏菊”的主要候选对象是什么?我们是否找到雏菊对盖亚理论有意义吗?我们应该如何寻找雏菊,我们应该加强搜索?如何使用气候系统的过程模型或全球模型(包括生物群并允许化学循环)来研究盖亚机制?” <br />
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In 1997, Tyler Volk argued that a Gaian system is almost inevitably produced as a result of an evolution towards far-from-equilibrium homeostatic states that maximise [[entropy]] production, and Kleidon (2004) agreed stating: "...homeostatic behavior can emerge from a state of MEP associated with the planetary albedo"; "...the resulting behavior of a biotic Earth at a state of MEP may well lead to near-homeostatic behavior of the Earth system on long time scales, as stated by the Gaia hypothesis". Staley (2002) has similarly proposed "...an alternative form of Gaia theory based on more traditional Darwinian principles... In [this] new approach, environmental regulation is a consequence of population dynamics, not Darwinian selection. The role of selection is to favor organisms that are best adapted to prevailing environmental conditions. However, the environment is not a static backdrop for evolution, but is heavily influenced by the presence of living organisms. The resulting co-evolving dynamical process eventually leads to the convergence of equilibrium and optimal conditions".<br />
1997年,泰勒·沃尔克认为,盖亚系统几乎不可避免地会产生,这是朝着使熵产量最大化的远非平衡的状态演化的结果,克莱顿(2004)同意这样的说法:“自稳行为可以从与行星反照率相关的MEP状态中产生”;“……生物地球在MEP状态下的行为很可能导致地球系统在长时间尺度上的近稳态行为,正如盖亚假说所述”。Staley(2002)同样提出了“……一种基于更传统的达尔文原理的盖亚理论的替代形式。在这种新方法中,环境调控是人口动态的结果,而不是达尔文的选择。选择的作用是偏爱最能适应当前环境条件的有机体。然而,环境并不是进化的静态背景,而是受到生物存在的严重影响。由此产生的共同进化动态过程最终导致平衡和最优条件的收敛。 <br />
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===Fourth Gaia conference第四次盖亚会议===<br />
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A fourth international conference on the Gaia hypothesis, sponsored by the Northern Virginia Regional Park Authority and others, was held in October 2006 at the Arlington, VA campus of George Mason University.<ref>{{cite web|title=Gaia Theory Conference at George Mason University Law School|url=http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|accessdate=1 December 2013|author=Official Site of Arlington County Virginia|archive-url=https://web.archive.org/web/20131203043657/http://www.arlingtonva.us/departments/Communications/PressReleases/page7530.aspx|archive-date=2013-12-03|url-status=dead}}</ref><br />
第四届盖亚假说国际会议于2006年10月在乔治梅森大学阿灵顿分校举行,会议由北弗吉尼亚州公园管理局和其他机构赞助。 <br />
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Martin Ogle, Chief Naturalist, for NVRPA, and long-time Gaia hypothesis proponent, organized the event. Lynn Margulis, Distinguished University Professor in the Department of Geosciences, University of Massachusetts-Amherst, and long-time advocate of the Gaia hypothesis, was a keynote speaker. Among many other speakers: Tyler Volk, Co-director of the Program in Earth and Environmental Science at New York University; Dr. Donald Aitken, Principal of Donald Aitken Associates; Dr. Thomas Lovejoy, President of the Heinz Center for Science, Economics and the Environment; Robert Correll, Senior Fellow, Atmospheric Policy Program, American Meteorological Society and noted environmental ethicist, J. Baird Callicott.<br />
马丁奥格尔,NVRPA的首席博物学家,也是盖亚假说的长期支持者,组织了这次活动。林恩 马古拉斯是马萨诸塞州阿默斯特大学地球科学系的杰出大学教授,也是盖亚假说的长期倡导者。其他许多发言者包括:纽约大学地球与环境科学项目联合主任泰勒·沃尔克、唐纳德·艾特肯博士、唐纳德·艾特肯博士、海因茨科学、经济与环境中心主席托马斯·洛夫乔伊博士、大气政策计划高级研究员罗伯特·科雷尔,美国气象学会和著名环境伦理学家J。贝尔德。卡利科特。 <br />
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This conference approached the Gaia hypothesis as both science and metaphor as a means of understanding how we might begin addressing 21st century issues such as climate change and ongoing environmental destruction.<br />
这次会议将盖亚假说作为一种科学和隐喻来探讨,以此来理解我们如何着手解决21世纪的问题,如气候变化和持续的环境破坏<br />
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==Criticism批评==<br />
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After initially receiving little attention from scientists (from 1969 until 1977), thereafter for a period the initial Gaia hypothesis was criticized by a number of scientists, such as [[Ford Doolittle]],<ref name=":1">{{Cite journal|last=Doolittle|first=W. F.|year=1981|title=Is Nature Really Motherly|url=|journal=The Coevolution Quarterly|volume=Spring|pages=58–63|via=}}</ref> [[Richard Dawkins]]<ref name=":2">{{Cite book|title=The Extended Phenotype: the Long Reach of the Gene|last=Dawkins|first=Richard|publisher=Oxford University Press|year=1982|isbn=978-0-19-286088-0|location=|pages=}}</ref> and [[Stephen Jay Gould]].<ref name="ReferenceB">Turney, Jon. "Lovelock and Gaia: Signs of Life" (Revolutions in Science)</ref> Lovelock has said that because his hypothesis is named after a Greek goddess, and championed by many non-scientists,<ref name="Lovelock01"/> the Gaia hypothesis was interpreted as a [[neo-Pagan]] [[religion]]. Many scientists in particular also criticised the approach taken in his popular book ''Gaia, a New Look at Life on Earth'' for being [[teleology|teleological]]—a belief that things are purposeful and aimed towards a goal. Responding to this critique in 1990, Lovelock stated, "Nowhere in our writings do we express the idea that planetary self-regulation is purposeful, or involves foresight or planning by the [[biota (ecology)|biota]]".<br />
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最初很少受到科学家的关注(从1969年到1977年),此后的一段时间里,最初的盖亚假说受到了许多科学家的批评,比如福特·杜利特,理查德·道金斯和斯蒂芬·杰伊·古尔德洛夫洛克曾说过,因为他的假设是以希腊女神的名字命名的,新盖亚假说被许多非教派的科学家解释为。特别是许多科学家还批评了他的畅销书《盖亚》中采用的方法,认为地球上的生命是目的论的,认为事物是有目的的,是有目的的。洛夫洛克在1990年回应这一批评时说:“在我们的著作中我们没有任何地方表达行星自我调节是有目的的,或涉及生物群的远见或计划。”<br />
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[[Stephen Jay Gould]] criticised Gaia as being "a metaphor, not a mechanism."<ref name="Gould 1997">{{cite journal |author=Gould S.J. |title=Kropotkin was no crackpot |journal=Natural History |volume=106 |pages=12–21 |date=June 1997 |url=http://libcom.org/library/kropotkin-was-no-crackpot |ref=harv}}</ref> He wanted to know the actual mechanisms by which self-regulating homeostasis was achieved. In his defense of Gaia, David Abram argues that Gould overlooked the fact that "mechanism", itself, is a metaphor — albeit an exceedingly common and often unrecognized metaphor — one which leads us to consider natural and living systems as though they were machines organized and built from outside (rather than as [[autopoiesis|autopoietic]] or self-organizing phenomena). Mechanical metaphors, according to Abram, lead us to overlook the active or agential quality of living entities, while the organismic metaphorics of the Gaia hypothesis accentuate the active agency of both the biota and the biosphere as a whole.<ref>Abram, D. (1988) "The Mechanical and the Organic: On the Impact of Metaphor in Science" in Scientists on Gaia, edited by Stephen Schneider and Penelope Boston, Cambridge, Massachusetts: MIT Press, 1991</ref><ref>{{cite web|url=http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |title=The Mechanical and the Organic |accessdate=August 27, 2012 |url-status=dead |archiveurl=https://web.archive.org/web/20120223165936/http://www.wildethics.org/essays/the_mechanical_and_the_organic.html |archivedate=February 23, 2012 }}</ref> With regard to causality in Gaia, Lovelock argues that no single mechanism is responsible, that the connections between the various known mechanisms may never be known, that this is accepted in other fields of biology and ecology as a matter of course, and that specific hostility is reserved for his own hypothesis for other reasons.<ref name="Lovelock, James 2001">Lovelock, James (2001), ''Homage to Gaia: The Life of an Independent Scientist'' (Oxford University Press)</ref><br />
史蒂芬·杰伊·古尔德批评盖亚假说是“一种隐喻,而不是一种机制。”他想知道实现自我调节内稳态的实际机制。在为盖亚假说辩护时,大卫·艾布拉姆认为古尔德忽略了一个事实,即“机制”本身就是一个隐喻——尽管这是一个非常常见且常常未被人认识的隐喻——它使我们把自然和生命系统看作是从外部组织和建造的机器(而不是自动或自组织的)现象)。艾布拉姆认为,机械隐喻使我们忽视了生命实体的活动性或能动性,而盖亚假说的有机体隐喻强调了生物群和生物圈作为一个整体的能动性。关于盖亚假说的因果关系,洛夫洛克认为没有单一的机制负责各种已知机制之间的联系可能永远不为人所知,这一点在其他生物学和生态学领域都是理所当然的,而具体的敌意是出于其他原因留给他自己的假设的<br />
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Aside from clarifying his language and understanding of what is meant by a life form, Lovelock himself ascribes most of the criticism to a lack of understanding of non-linear mathematics by his critics, and a linearizing form of [[greedy reductionism]] in which all events have to be immediately ascribed to specific causes before the fact. He also states that most of his critics are biologists but that his hypothesis includes experiments in fields outside biology, and that some self-regulating phenomena may not be mathematically explainable.<ref name="Lovelock, James 2001"/><br />
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除了澄清自己的语言和对生命形式的理解之外,洛夫洛克自己将大部分批评归咎于批评家对非线性数学缺乏理解,以及贪婪还原论的线性化形式,在这种形式中,所有事件都必须在事实发生之前立即归因于特定的原因。他还指出,批评他的人大多是生物学家,但他的假设包括生物学以外领域的实验,有些自我调节的现象可能无法用数学解释 <br />
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===Natural selection and evolution自然选择和进化===<br />
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Lovelock has suggested that global biological feedback mechanisms could evolve by [[natural selection]], stating that organisms that improve their environment for their survival do better than those that damage their environment. However, in the early 1980s, [[Ford Doolittle|W. Ford Doolittle]] and [[Richard Dawkins]] separately argued against this aspect of Gaia. Doolittle argued that nothing in the [[genome]] of individual organisms could provide the feedback mechanisms proposed by Lovelock, and therefore the Gaia hypothesis proposed no plausible mechanism and was unscientific.<ref name=":1" /> Dawkins meanwhile stated that for organisms to act in concert would require foresight and planning, which is contrary to the current scientific understanding of evolution.<ref name=":2" /> Like Doolittle, he also rejected the possibility that feedback loops could stabilize the system.<br />
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洛夫洛克提出,全球生物反馈机制可以通过自然选择而进化,他指出,为生存而改善环境的生物比那些破坏环境的生物做得更好。然而,在20世纪80年代早期,W·福特·杜立德和理查德·道金斯分别反对盖亚假说的这一方面。杜立德认为,单个生物体的基因组中没有任何东西能够提供洛夫洛克提出的反馈机制,因此盖亚假说没有提出任何合理的机制,是不科学的。道金斯同时指出,要使有机体协同行动,就需要有远见和计划,这与当前科学界对进化论的理解相悖和杜立德一样,他也拒绝了反馈回路可以稳定系统的可能性。<br />
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[[Lynn Margulis]], a microbiologist who collaborated with Lovelock in supporting the Gaia hypothesis, argued in 1999, that "[[Charles Darwin|Darwin]]'s grand vision was not wrong, only incomplete. In accentuating the direct competition between individuals for resources as the primary selection mechanism, Darwin (and especially his followers) created the impression that the environment was simply a static arena". She wrote that the composition of the Earth's atmosphere, hydrosphere, and lithosphere are regulated around "set points" as in [[homeostasis]], but those set points change with time.<ref name="ReferenceA">Margulis, Lynn. Symbiotic Planet: A New Look At Evolution. Houston: Basic Book 1999</ref><br />
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Lynn Margulis,一位与Lovelock合作支持盖亚假说的微生物学家,在1999年指出,“达尔文的宏伟愿景没有错,只是不完整。达尔文(特别是他的追随者)强调个人之间对资源的直接竞争是主要的选择机制,他给人的印象是环境只是一个静态的竞技场”。她写道,地球大气、水圈和岩石圈的组成都是围绕着“设定点”来调节的,就像在体内平衡中一样,但是这些设定点会随着时间的推移而变化 <br />
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Evolutionary biologist [[W. D. Hamilton]] called the concept of Gaia [[Nicolaus Copernicus|Copernican]], adding that it would take another [[Isaac Newton|Newton]] to explain how Gaian self-regulation takes place through Darwinian [[natural selection]].<ref name=vanish09>Lovelock, James. ''The Vanishing Face of Gaia''. Basic Books, 2009, pp. 195-197. {{ISBN|978-0-465-01549-8}}</ref>{{better source|date=September 2012|reason=it should be possible to find the original place where Hamilton said this}} More recently [[Ford Doolittle]] building on his and Inkpen's ITSNTS (It's The Singer Not The Song) proposal<ref name="ITSNTS">Doolittle WF, Inkpen SA. Processes and patterns of interaction as units of selection: An introduction to ITSNTS thinking. [https://www.pnas.org/content/115/16/4006 PNAS April 17, 2018 115 (16)] 4006-4014 </ref> proposed that differential persistence can play a similar role to differential reproduction in evolution by natural selections, thereby providing a possible reconciliation between the theory of natural selection and the Gaia hypothesis<ref name="Darwinizing Gaia">Doolittle WF. Darwinizing Gaia. [https://doi.org/10.1016/j.jtbi.2017.02.015 Journal of Theoretical BiologyVolume 434], 7 December 2017, Pages 11-19 </ref>. <br />
进化生物学家汉密尔顿称盖亚哥白尼为盖亚的概念,他补充说,需要另一个牛顿来解释盖亚的自我调节是如何通过达尔文的自然选择发生的。通过自然选择在进化过程中的繁殖,从而为自然选择理论和盖亚假说提供了可能的调和。 <br />
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===Criticism in the 21st century21世纪的批评===<br />
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The Gaia hypothesis continues to be broadly skeptically received by the scientific community. For instance, arguments both for and against it were laid out in the journal ''Climatic Change'' in 2002 and 2003. A significant argument raised against it are the many examples where life has had a detrimental or destabilising effect on the environment rather than acting to regulate it.<ref name="kirchner2002"/><ref name="volk2002"/> Several recent books have criticised the Gaia hypothesis, expressing views ranging from "... the Gaia hypothesis lacks unambiguous observational support and has significant theoretical difficulties"<ref>{{cite book |last=Waltham |first=David |authorlink=David Waltham |date=2014 |title=Lucky Planet: Why Earth is Exceptional – and What that Means for Life in the Universe |url=https://archive.org/details/luckyplanetwhyea0000walt |location= |publisher=Icon Books |page= |isbn=9781848316560 |accessdate= |url-access=registration }}</ref> to "Suspended uncomfortably between tainted metaphor, fact, and false science, I prefer to leave Gaia firmly in the background"<ref name="beerling2007"/> to "The Gaia hypothesis is supported neither by evolutionary theory nor by the empirical evidence of the geological record".<ref>{{cite book |last1=Cockell |first1=Charles |authorlink1=Charles Cockell |last2=Corfield |first2=Richard |last3=Dise |first3= Nancy |last4=Edwards |first4=Neil |last5=Harris |first5=Nigel |date=2008 |title= An Introduction to the Earth-Life System |url= http://www.cambridge.org/us/academic/subjects/earth-and-environmental-science/palaeontology-and-life-history/introduction-earth-life-system |location=Cambridge (UK) |publisher= Cambridge University Press |page= |isbn= 9780521729536 |accessdate= }}</ref> The [[CLAW hypothesis]],<ref name="CLAW87" /> initially suggested as a potential example of direct Gaian feedback, has subsequently been found to be less credible as understanding of [[cloud condensation nuclei]] has improved.<ref>{{Citation |last1= Quinn |first1=P.K. |last2= Bates |first2=T.S. |title =The case against climate regulation via oceanic phytoplankton sulphur emissions |journal =Nature |volume=480 |issue=7375 |pages =51–56 |date = 2011 |doi=10.1038/nature10580|bibcode = 2011Natur.480...51Q |pmid=22129724|url=https://zenodo.org/record/1233319 }}</ref> In 2009 the [[Medea hypothesis]] was proposed: that life has highly detrimental (biocidal) impacts on planetary conditions, in direct opposition to the Gaia hypothesis.<ref>Peter Ward (2009), ''The Medea Hypothesis: Is Life on Earth Ultimately Self-Destructive?'', {{ISBN|0-691-13075-2}}</ref><br />
盖亚假说仍然受到科学界的广泛怀疑。例如,在2003年和2002年的《气候变化》杂志上都提出了反对意见。反对它的一个重要论点是在许多例子中,生命对环境产生了有害或不稳定的影响,而不是采取行动来调节它。最近几本书批评了盖亚假说,譬如“盖亚假说缺乏明确的观察支持,并且有重大的理论困难”“(盖亚假说)令人不安地徘徊在污点、隐喻、事实和虚假科学之间,我宁愿把盖亚牢牢地放在原有的背景中”“盖亚假说既没有进化论的支持,也没有地质记录的经验证据的支持。爪假说最初被认为是盖亚直接反馈的一个潜在例子,后来被发现对云的理解不那么可信凝聚核已经得到了改善。2009年,美狄亚假说提出:生命对行星的状况非常有害,这与盖亚假说直接相反。 <br />
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In a 2013 book-length evaluation of the Gaia hypothesis considering modern evidence from across the various relevant disciplines, Toby Tyrrell concluded that: "I believe Gaia is a dead end. Its study has, however, generated many new and thought provoking questions. While rejecting Gaia, we can at the same time appreciate Lovelock's originality and breadth of vision, and recognise that his audacious concept has helped to stimulate many new ideas about the Earth, and to champion a holistic approach to studying it".<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=209 |isbn=9780691121581 |accessdate= }}</ref> Elsewhere he presents his conclusion "The Gaia hypothesis is not an accurate picture of how our world works".<ref>{{Citation |last= Tyrrell |first = Toby |title =Gaia: the verdict is… |journal = New Scientist |volume = 220 |issue = 2940 |pages = 30–31 |date= 26 October 2013 |doi=10.1016/s0262-4079(13)62532-4}}</ref> This statement needs to be understood as referring to the "strong" and "moderate" forms of Gaia—that the biota obeys a principle that works to make Earth optimal (strength 5) or favourable for life (strength 4) or that it works as a homeostatic mechanism (strength 3). The latter is the "weakest" form of Gaia that Lovelock has advocated. Tyrrell rejects it. However, he finds that the two weaker forms of Gaia—Coeveolutionary Gaia and Influential Gaia, which assert that there are close links between the evolution of life and the environment and that biology affects the physical and chemical environment—are both credible, but that it is not useful to use the term "Gaia" in this sense and that those two forms were already accepted and explained by the processes of natural selection and adaptation.<ref>{{citation |last=Tyrrell |first=Toby |authorlink= |date= 2013|title= On Gaia: A Critical Investigation of the Relationship between Life and Earth |url=http://press.princeton.edu/titles/9959.html |location=Princeton |publisher=Princeton University Press |page=208 |isbn=9780691121581 |accessdate= }}</ref><br />
2013年,托比·泰瑞尔在对盖亚假说的一本书长度评估中总结道:“我认为盖亚假说是一条死胡同。然而,它的研究产生了许多新的和发人深省的问题。在拒绝盖亚假说的同时,我们也能欣赏到洛夫洛克的独创性和广博的视野,并认识到他大胆的概念有助于激发许多关于地球的新思想,并倡导一种研究地球的整体方法。”在其他地方,他提出了自己的结论:“盖亚假说并不是一个关于如何进行的精确描述我们的世界在运转。”这种说法需要被理解为是指盖亚假说的“强大”和“温和”形式,生物群遵循的原则是使地球处于最佳状态(强度5)或有利于生命(强度4),或者它作为一种内稳态机制(强度3)。后者是洛夫洛克所提倡的盖亚假说的“最弱”形式。泰瑞尔拒绝了。然而,他发现盖亚假说的两种较弱的形式:共同进化德盖亚假说和有影响力的盖亚假说,它们断言生命的进化和环境之间有密切的联系,生物学影响物理和化学环境,这两种说法都是可信的,但在这个意义上使用“盖亚假说”一词是没有用的,两种形式已经被自然选择和适应过程所接受和解释 <br />
Category:Cybernetics<br />
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类别: 控制论<br />
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Category:Ecological theories<br />
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范畴: 生态学理论<br />
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==See also==<br />
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Category:Superorganisms<br />
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类别: 超级有机体<br />
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{{Portal|Environment|Earth sciences|Geography}}<br />
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Category:Climate change feedbacks<br />
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类别: 气候变化反馈<br />
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Category:1965 introductions<br />
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类别: 1965年引言<br />
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* {{annotated link|Biocoenosis}}<br />
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Category:Biogeochemistry<br />
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类别: 生物地球化学<br />
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* {{annotated link|Earth science}}<br />
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Category:Earth<br />
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类别: 地球<br />
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* {{annotated link|Environmentalism}}<br />
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Category:Biological hypotheses<br />
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类别: 生物学假说<br />
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* {{annotated link|Gaianism}}<br />
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Category:Astronomical hypotheses<br />
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类别: 天文学假设<br />
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* {{annotated link|Holism}}<br />
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Category:Meteorological hypotheses<br />
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类别: 气象假说<br />
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<small>This page was moved from [[wikipedia:en:Gaia hypothesis]]. Its edit history can be viewed at [[盖亚假说/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%B7%A5%E4%BD%9C%E8%AE%B0%E5%BF%86&diff=21546工作记忆2021-02-04T02:34:59Z<p>Vicky:/* 资源理论 Resource theories */</p>
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<div>已由[[Xebec]]进行初步翻译。由和光同尘审校。<br />
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{{short description|Cognitive system for temporarily holding information}}<br />
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{{Use dmy dates|date=June 2020}}<br />
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'''Working memory''' is a cognitive system with a limited capacity that can [[Memory|hold information]] temporarily.<ref>{{Cite book|title=Models of working memory. Mechanisms of active maintenance and executive control|editor1=Miyake, A.|editor2=Shah, P.|publisher=Cambridge University Press|year=1999 |isbn=0-521-58325-X}}</ref> Working memory is important for reasoning and the guidance of decision-making and behavior.<ref name="Executive functions">{{cite journal | author = Diamond A | title = Executive functions | journal = Annu Rev Psychol | volume = 64 | pages = 135–168 | year = 2013 | pmid = 23020641 | pmc = 4084861 | doi = 10.1146/annurev-psych-113011-143750 | quote = WM (holding information in mind and manipulating it) is distinct from short-term memory (just holding information in mind). They cluster onto separate factors in factor analyses of children, adolescents, and adults (Alloway et al. 2004, Gathercole et al. 2004). They are linked to different neural subsystems. WM relies more on dorsolateral prefrontal cortex, whereas maintaining information in mind but not manipulating it [as long as the number of items is not huge (suprathreshold)] does not need involvement of dorsolateral prefrontal cortex (D’Esposito et al. 1999, Eldreth et al. 2006, Smith & Jonides 1999). Imaging studies show frontal activation only in ventrolateral prefrontal cortex for memory maintenance that is not suprathreshold.<br /><br />WM and short-term memory also show different developmental progressions; the latter develops earlier and faster.}}</ref><ref name="NHM-Cognitive Control">{{cite book|title=Molecular Neuropharmacology: A Foundation for Clinical Neuroscience|vauthors=Malenka RC, Nestler EJ, Hyman SE|publisher=McGraw-Hill Medical|year=2009|isbn=978-0-07-148127-4|veditors=Sydor A, Brown RY|edition=2nd|location=New York|pages=313–321|chapter=Chapter 13: Higher Cognitive Function and Behavioral Control|quote={{bull}} Executive function, the cognitive control of behavior, depends on the prefrontal cortex, which is highly developed in higher primates and especially humans.<br />{{bull}} Working memory is a short-term, capacity-limited cognitive buffer that stores information and permits its manipulation to guide decision-making and behavior.&nbsp;...<br /> working memory may be impaired in ADHD, the most common childhood psychiatric disorder seen in clinical settings&nbsp;... ADHD can be conceptualized as a disorder of executive function; specifically, ADHD is characterized by reduced ability to exert and maintain cognitive control of behavior. Compared with healthy individuals, those with ADHD have diminished ability to suppress inappropriate prepotent responses to stimuli (impaired response inhibition) and diminished ability to inhibit responses to irrelevant stimuli (impaired interference suppression).&nbsp;... Early results with structural MRI show thinning of the cerebral cortex in ADHD subjects compared with age-matched controls in prefrontal cortex and posterior parietal cortex, areas involved in working memory and attention.}}</ref> Working memory is often used synonymously with [[short-term memory]], but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information.<ref name="Executive functions" /><ref name="Cowan">{{Cite book | title = What are the differences between long-term, short-term, and working memory? | author=Cowan, Nelson | journal=Prog. Brain Res. | year=2008 | issue=169 | pages=323–338 |pmid=18394484 | doi=10.1016/S0079-6123(07)00020-9 | pmc=2657600 | volume=169| series=Progress in Brain Research | isbn=978-0-444-53164-3 }}</ref> Working memory is a theoretical concept central to [[cognitive psychology]], neuropsychology, and [[neuroscience]].<br />
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Working memory is a cognitive system with a limited capacity that can hold information temporarily. Working memory is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information. Working memory is a theoretical concept central to cognitive psychology, neuropsychology, and neuroscience.<br />
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'''<font color="#ff8000">工作记忆 Working Memory</font>'''是一种能临时容纳有限信息的认知系统<ref>{{Cite book|title=Models of working memory. Mechanisms of active maintenance and executive control|editor1=Miyake, A.|editor2=Shah, P.|publisher=Cambridge University Press|year=1999 |isbn=0-521-58325-X}}</ref>,对推理、决策倾向和行为倾向有着重要影响<ref name="Executive functions">{{cite journal | author = Diamond A | title = Executive functions | journal = Annu Rev Psychol | volume = 64 | pages = 135–168 | year = 2013 | pmid = 23020641 | pmc = 4084861 | doi = 10.1146/annurev-psych-113011-143750 | quote = WM (holding information in mind and manipulating it) is distinct from short-term memory (just holding information in mind). They cluster onto separate factors in factor analyses of children, adolescents, and adults (Alloway et al. 2004, Gathercole et al. 2004). They are linked to different neural subsystems. WM relies more on dorsolateral prefrontal cortex, whereas maintaining information in mind but not manipulating it [as long as the number of items is not huge (suprathreshold)] does not need involvement of dorsolateral prefrontal cortex (D’Esposito et al. 1999, Eldreth et al. 2006, Smith & Jonides 1999). Imaging studies show frontal activation only in ventrolateral prefrontal cortex for memory maintenance that is not suprathreshold.<br /><br />WM and short-term memory also show different developmental progressions; the latter develops earlier and faster.}}</ref><ref name="NHM-Cognitive Control">{{cite book|title=Molecular Neuropharmacology: A Foundation for Clinical Neuroscience|vauthors=Malenka RC, Nestler EJ, Hyman SE|publisher=McGraw-Hill Medical|year=2009|isbn=978-0-07-148127-4|veditors=Sydor A, Brown RY|edition=2nd|location=New York|pages=313–321|chapter=Chapter 13: Higher Cognitive Function and Behavioral Control|quote={{bull}} Executive function, the cognitive control of behavior, depends on the prefrontal cortex, which is highly developed in higher primates and especially humans.<br />{{bull}} Working memory is a short-term, capacity-limited cognitive buffer that stores information and permits its manipulation to guide decision-making and behavior.&nbsp;...<br /> working memory may be impaired in ADHD, the most common childhood psychiatric disorder seen in clinical settings&nbsp;... ADHD can be conceptualized as a disorder of executive function; specifically, ADHD is characterized by reduced ability to exert and maintain cognitive control of behavior. Compared with healthy individuals, those with ADHD have diminished ability to suppress inappropriate prepotent responses to stimuli (impaired response inhibition) and diminished ability to inhibit responses to irrelevant stimuli (impaired interference suppression).&nbsp;... Early results with structural MRI show thinning of the cerebral cortex in ADHD subjects compared with age-matched controls in prefrontal cortex and posterior parietal cortex, areas involved in working memory and attention.}}</ref>。工作记忆常作为'''<font color="#ff8000">短期记忆 short-term Memory</font>'''的同义词,但一些理论学者认为,工作记忆能够调用存储的信息,而短期记忆仅指短期存储的信息,故二者不同<ref name="Executive functions" /><ref name="Cowan">{{Cite book | title = What are the differences between long-term, short-term, and working memory? | author=Cowan, Nelson | journal=Prog. Brain Res. | year=2008 | issue=169 | pages=323–338 |pmid=18394484 | doi=10.1016/S0079-6123(07)00020-9 | pmc=2657600 | volume=169| series=Progress in Brain Research | isbn=978-0-444-53164-3 }}</ref>。工作记忆是'''<font color="#ff8000">认知心理学 cognitive psychology </font>'''、'''<font color="#ff8000">神经心理学 neuropsychology </font>'''和'''<font color="#ff8000">神经科学 neuroscience </font>'''的核心概念之一。<br />
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== 历史 History ==<br />
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The term "working memory" was coined by [[George Armitage Miller|Miller]], [[Eugene Galanter|Galanter]], and [[Karl H. Pribram|Pribram]],<ref name="isbn0-03-010075-5">{{cite book |author1=Pribram, Karl H. |author2=Miller, George A. |author3=Galanter, Eugene |title=Plans and the structure of behavior |publisher=Holt, Rinehart and Winston |location=New York |year=1960 |pages=[https://archive.org/details/plansstructureo00mill/page/65 65] |isbn=978-0-03-010075-8 |oclc=190675 |url-access=registration |url=https://archive.org/details/plansstructureo00mill/page/65 }}</ref><ref>{{Cite journal|author=Baddeley A |title=Working memory: looking back and looking forward |journal=Nature Reviews Neuroscience |volume=4 |issue=10 |pages=829–39 |date=October 2003 |pmid=14523382 |doi=10.1038/nrn1201}}</ref> and was used in the 1960s in the context of theories that likened the mind to a computer. In 1968, [[Atkinson–Shiffrin memory model|Atkinson and Shiffrin]]<ref name="Atkinson Shiffrin 1968">{{cite book | last1 = Atkinson | first1 = R.C. | last2 = Shiffrin | first2 = R.M. | title = Human Memory: A Proposed System and its Control Processes | volume = 2 |pages = 89–195| editor1 = Kenneth W Spence |editor2= Janet T Spence | work = The psychology of learning and motivation | publisher = Academic Press | year = 1968 | isbn = 978-0-12-543302-0 |oclc = 185468704 |doi = 10.1016/S0079-7421(08)60422-3}}</ref> used the term to describe their "short-term store". What we now call working memory was formerly referred to variously as a "short-term store" or [[short-term memory]], primary memory, immediate memory, operant memory, and provisional memory.<ref name="Fuster 1997">{{cite book |author=Fuster, Joaquin M. |title=The prefrontal cortex: anatomy, physiology, and neuropsychology of the frontal lobe |publisher=Lippincott-Raven |location=Philadelphia |year=1997 |isbn=978-0-397-51849-4 |oclc=807338522 }}{{Page needed|date=September 2010}}</ref> Short-term memory is the ability to remember information over a brief period (in the order of seconds). Most theorists today use the concept of working memory to replace or include the older concept of short-term memory, marking a stronger emphasis on the notion of manipulating information rather than mere maintenance.<br />
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The term "working memory" was coined by Miller, Galanter, and Pribram, and was used in the 1960s in the context of theories that likened the mind to a computer. In 1968, Atkinson and Shiffrin used the term to describe their "short-term store". What we now call working memory was formerly referred to variously as a "short-term store" or short-term memory, primary memory, immediate memory, operant memory, and provisional memory. Short-term memory is the ability to remember information over a brief period (in the order of seconds). Most theorists today use the concept of working memory to replace or include the older concept of short-term memory, marking a stronger emphasis on the notion of manipulating information rather than mere maintenance.<br />
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“'''<font color="#ff800">工作记忆 Working Memory</font>'''”这个术语由米勒 Miller、加兰特 Galanter和普里布拉姆 Pribram 提出<ref name="isbn0-03-010075-5">{{cite book |author1=Pribram, Karl H. |author2=Miller, George A. |author3=Galanter, Eugene |title=Plans and the structure of behavior |publisher=Holt, Rinehart and Winston |location=New York |year=1960 |pages=[https://archive.org/details/plansstructureo00mill/page/65 65] |isbn=978-0-03-010075-8 |oclc=190675 |url-access=registration |url=https://archive.org/details/plansstructureo00mill/page/65 }}</ref><ref>{{Cite journal|author=Baddeley A |title=Working memory: looking back and looking forward |journal=Nature Reviews Neuroscience |volume=4 |issue=10 |pages=829–39 |date=October 2003 |pmid=14523382 |doi=10.1038/nrn1201}}</ref>,在20世纪60年代被应用于把大脑比作计算机的理论研究之中。1968年,阿特金森 Atkinson和谢福林 Shiffrin <ref name="Atkinson Shiffrin 1968">{{cite book | last1 = Atkinson | first1 = R.C. | last2 = Shiffrin | first2 = R.M. | title = Human Memory: A Proposed System and its Control Processes | volume = 2 |pages = 89–195| editor1 = Kenneth W Spence |editor2= Janet T Spence | work = The psychology of learning and motivation | publisher = Academic Press | year = 1968 | isbn = 978-0-12-543302-0 |oclc = 185468704 |doi = 10.1016/S0079-7421(08)60422-3}}</ref>用该术语来表述“短期存储”。我们现在所说的工作记忆就是之前所谓的“短期存储”、“短期记忆”、“初级记忆”、“即时记忆”、“操作记忆”或“临时记忆”<ref name="Fuster 1997">{{cite book |author=Fuster, Joaquin M. |title=The prefrontal cortex: anatomy, physiology, and neuropsychology of the frontal lobe |publisher=Lippincott-Raven |location=Philadelphia |year=1997 |isbn=978-0-397-51849-4 |oclc=807338522 }}{{Page needed|date=September 2010}}</ref>。短期记忆是在短时间内(以秒为单位)记住信息的能力。如今,大多数理论学者会使用“工作记忆”这一概念取代或包含早期“短期记忆”的概念,这体现出对信息操纵观念的重视。<br />
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The earliest mention of experiments on the neural basis of working memory can be traced back to more than 100 years ago, when [[Eduard Hitzig|Hitzig]] and [[David Ferrier|Ferrier]] described [[ablation]] experiments of the [[prefrontal cortex]] (PFC); they concluded that the frontal cortex was important for cognitive rather than sensory processes.<ref name=Fuster1>{{Cite book|last1= Fuster|first1= Joaquin |title= The prefrontal cortex |page= 126 |url= https://books.google.com/books?id=zuZlvNICdhUC&pg=PT140 |edition= 4 |year= 2008 |publisher= Elsevier |location= Oxford, UK |isbn= 978-0-12-373644-4}}</ref> In 1935 and 1936, Carlyle Jacobsen and colleagues were the first to show the deleterious effect of prefrontal ablation on delayed response.<ref name=Fuster1 /><ref name=Benton>{{Cite book|last1= Benton|first1= A.&nbsp;L.|editor1-first= Harvey,&nbsp;S.|editor1-last= Levin|editor2-first= Howard,&nbsp;M.|editor2-last= Eisenberg|editor3-first= Arthur,&nbsp;L.|editor3-last= Benton|title= Frontal lobe function and dysfunction|chapter-url= https://books.google.com/books?id=9b1htO0V0rwC&pg=PA19&lpg=PA19&dq=Jacobsen++prefrontal+ablation&q=Jacobsen%20%20prefrontal%20ablation|year= 1991|publisher= Oxford University Press|location= New York|isbn= 978-0-19-506284-7|page= 19|chapter= The prefrontal region:Its early history}}</ref><br />
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The earliest mention of experiments on the neural basis of working memory can be traced back to more than 100 years ago, when Hitzig and Ferrier described ablation experiments of the prefrontal cortex (PFC); they concluded that the frontal cortex was important for cognitive rather than sensory processes. In 1935 and 1936, Carlyle Jacobsen and colleagues were the first to show the deleterious effect of prefrontal ablation on delayed response.<br />
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关于工作记忆神经学基础的实验最早可追溯到100多年前希齐格 Hitzig 和费里尔 Ferrier 对前额叶皮质消融实验的研究(PFC)。'''<font color="#ff8000">额叶皮层 frontal cortex</font>'''对认知程序比对感官程序更重要是当时研究得出的一大结论<ref name=Fuster1>{{Cite book|last1= Fuster|first1= Joaquin |title= The prefrontal cortex |page= 126 |url= https://books.google.com/books?id=zuZlvNICdhUC&pg=PT140 |edition= 4 |year= 2008 |publisher= Elsevier |location= Oxford, UK |isbn= 978-0-12-373644-4}}</ref>。在1935年和1936年, 卡莱尔 · 雅各布森 Carlyle Jacobsen及其同事们首次披露了前额叶切除对延时反映的不良影响<ref name=Fuster1 /><ref name=Benton>{{Cite book|last1= Benton|first1= A.&nbsp;L.|editor1-first= Harvey,&nbsp;S.|editor1-last= Levin|editor2-first= Howard,&nbsp;M.|editor2-last= Eisenberg|editor3-first= Arthur,&nbsp;L.|editor3-last= Benton|title= Frontal lobe function and dysfunction|chapter-url= https://books.google.com/books?id=9b1htO0V0rwC&pg=PA19&lpg=PA19&dq=Jacobsen++prefrontal+ablation&q=Jacobsen%20%20prefrontal%20ablation|year= 1991|publisher= Oxford University Press|location= New York|isbn= 978-0-19-506284-7|page= 19|chapter= The prefrontal region:Its early history}}</ref><br />
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== 理论 Theories ==<br />
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Numerous models have been proposed for how working memory functions, both anatomically and cognitively. Of those, the two that have been most influential are summarized below.<br />
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Numerous models have been proposed for how working memory functions, both anatomically and cognitively. Of those, the two that have been most influential are summarized below.<br />
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基于解剖学和认识学,人们设计出工作记忆运行的神经模型,其中最有影响力的两个模型概括如下:<br />
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=== 多组件模型 The multicomponent model ===<br />
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{{Main|Baddeley's model of working memory}}<br />
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[[File:Baddeley and Hitch's Working Memory Model.png|thumb|300px|巴德利 Baddeley和希池 Hitch 的工作记忆模型]]<br />
[图1:巴德利 Baddeley和希池 Hitch 的工作记忆模型]<br />
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In 1974, [[Alan Baddeley|Baddeley]] and [[Graham Hitch|Hitch]]<ref name="Baddeley Hitch 1974">{{cite book | last1 = Baddeley | first1 = Alan D. | last2 = Hitch | first2 = Graham | title = Working Memory | volume = 2 | editor = Gordon H. Bower | work = The psychology of learning and motivation | publisher = Academic Press | year = 1974 | pages = 47–89 | isbn = 978-0-12-543308-2 |oclc = 777285348 |doi= 10.1016/S0079-7421(08)60452-1}}</ref> introduced the [[Baddeley's model of working memory|multicomponent model of working memory]]. The theory proposed a model containing three components: the central executive, the phonological loop, and the visuospatial sketchpad with the central executive functioning as a control center of sorts, directing info between the phonological and visuospatial components.<ref name="Levin 2011">{{Cite book|title = Working Memory : Capacity, Developments and Improvement Techniques|last = Levin|first = E.S.|publisher = [[Nova Science Publishers, Inc.]]|year = 2011|location = New York}}</ref> The [[Baddeley's model of working memory#Central executive|central executive]] is responsible for, among other things, directing [[attention]] to relevant information, suppressing irrelevant information and inappropriate actions, and coordinating cognitive processes when more than one task is simultaneously performed. A "central executive" is responsible for supervising the integration of information and for coordinating subordinate systems responsible for the short-term maintenance of information. One subordinate system, the [[phonological loop]] (PL), stores phonological information (that is, the sound of language) and prevents its decay by continuously refreshing it in a [[memory rehearsal|rehearsal]] loop. It can, for example, maintain a seven-digit telephone number for as long as one repeats the number to oneself again and again.<ref>{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = New York|pages = 281–282|edition = 9}}</ref> The other subordinate system, the [[Baddeley's model of working memory#Visuospatial sketchpad|visuospatial sketchpad]], stores visual and spatial information. It can be used, for example, for constructing and manipulating visual images and for representing mental maps. The sketchpad can be further broken down into a visual subsystem (dealing with such phenomena as shape, colour, and texture), and a spatial subsystem (dealing with location).<br />
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In 1974, Baddeley and Hitch introduced the multicomponent model of working memory. The theory proposed a model containing three components: the central executive, the phonological loop, and the visuospatial sketchpad with the central executive functioning as a control center of sorts, directing info between the phonological and visuospatial components. The central executive is responsible for, among other things, directing attention to relevant information, suppressing irrelevant information and inappropriate actions, and coordinating cognitive processes when more than one task is simultaneously performed. A "central executive" is responsible for supervising the integration of information and for coordinating subordinate systems responsible for the short-term maintenance of information. One subordinate system, the phonological loop (PL), stores phonological information (that is, the sound of language) and prevents its decay by continuously refreshing it in a rehearsal loop. It can, for example, maintain a seven-digit telephone number for as long as one repeats the number to oneself again and again. The other subordinate system, the visuospatial sketchpad, stores visual and spatial information. It can be used, for example, for constructing and manipulating visual images and for representing mental maps. The sketchpad can be further broken down into a visual subsystem (dealing with such phenomena as shape, colour, and texture), and a spatial subsystem (dealing with location).<br />
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1974年,Baddeley和Hitch<ref name="Baddeley Hitch 1974">{{cite book | last1 = Baddeley | first1 = Alan D. | last2 = Hitch | first2 = Graham | title = Working Memory | volume = 2 | editor = Gordon H. Bower | work = The psychology of learning and motivation | publisher = Academic Press | year = 1974 | pages = 47–89 | isbn = 978-0-12-543308-2 |oclc = 777285348 |doi= 10.1016/S0079-7421(08)60452-1}}</ref>提出了'''<font color="#ff8000">工作记忆多组件模型 Multicomponent Model of Working Memory</font>'''——该模型由三个组件构成:'''<font color="#ff8000">中央执行器 Central Executive</font>'''、'''<font color="#ff8000">语音回路(PL) Phonological Loop (PL)</font>'''、'''<font color="#ff8000">视觉绘板 Visuospatial Sketchpad</font>'''<ref name="Levin 2011">{{Cite book|title = Working Memory : Capacity, Developments and Improvement Techniques|last = Levin|first = E.S.|publisher = [[Nova Science Publishers, Inc.]]|year = 2011|location = New York}}</ref>。其中,中央执行器作为某种控制中心,负责疏通语音回路和视觉绘板之间的信息传递通道,引导相关信息,抑制无关信息及不当行为,保持认知程序在执行多任务时的协调。中央执行器还会监督信息的整合以及协调各个负责短期信息维护的子系统。语音回路(PL)组件用于存储语音信息并通过不断刷新防止其受损,例如,只要不断重复一个7位数的电话号码它就可以被很好地储存<ref>{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = New York|pages = 281–282|edition = 9}}</ref>。而视觉绘板组件则负责存储视觉和空间信息,例如构建、操控视觉图像及展现精神世界。视觉绘板还可进一步分为'''<font color="#ff8000">视觉子系统visual subsystem</font>'''(处理形状、颜色和纹理等)和'''<font color="#ff8000">空间子系统spatial subsystem</font>'''(处理位置)。<br />
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In 2000, Baddeley extended the model by adding a fourth component, the [[Baddeley's model of working memory#Episodic buffer|episodic buffer]], which holds representations that integrate phonological, visual, and spatial information, and possibly information not covered by the subordinate systems (e.g.,&nbsp;semantic information, musical information). The episodic buffer is also the link between working memory and long-term memory.<ref name="Weiten 2013 281–282">{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = Belmont, CA|pages = 281–282|edition = 9}}</ref> The component is episodic because it is assumed to bind information into a unitary episodic representation. The episodic buffer resembles Tulving's concept of [[episodic memory]], but it differs in that the episodic buffer is a temporary store.<ref>{{cite journal | url=http://nbu.bg/cogs/events/2002/materials/Markus/ep_bufer.pdf | title=The episodic buffer: a new component of working memory? | author=Baddeley, A. D. | journal=Trends Cogn. Sci. | year=2000 | volume=4 | issue=11 | pages=417–423 | doi=10.1016/S1364-6613(00)01538-2 | pmid=11058819}}</ref><br />
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In 2000, Baddeley extended the model by adding a fourth component, the episodic buffer, which holds representations that integrate phonological, visual, and spatial information, and possibly information not covered by the subordinate systems (e.g.,&nbsp;semantic information, musical information). The episodic buffer is also the link between working memory and long-term memory. The component is episodic because it is assumed to bind information into a unitary episodic representation. The episodic buffer resembles Tulving's concept of episodic memory, but it differs in that the episodic buffer is a temporary store.<br />
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2000年,Baddeley 增加了第四个组件'''<font color="#ff8000">情景缓冲区 Episodic Buffer</font>''',这进一步扩展了该模型。情景缓冲区可以整合语音、视觉、空间信息,及可能未被子系统涵盖的信息(例如语义、音乐)。它同时是工作记忆和长期记忆之间的枢纽<ref name="Weiten 2013 281–282">{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = Belmont, CA|pages = 281–282|edition = 9}}</ref>。该组件的基本原理是把信息绑定到单一情节,因此它的运行是情节性的。情景缓冲区与图尔文 Tulving'''<font color="#ff8000">情景记忆 Episodic Memory</font>'''的概念类似,不同之处在于情景缓冲区是临时存储<ref>{{cite journal | url=http://nbu.bg/cogs/events/2002/materials/Markus/ep_bufer.pdf | title=The episodic buffer: a new component of working memory? | author=Baddeley, A. D. | journal=Trends Cogn. Sci. | year=2000 | volume=4 | issue=11 | pages=417–423 | doi=10.1016/S1364-6613(00)01538-2 | pmid=11058819}}</ref><br />
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=== 作为长期记忆一部分的工作记忆 Working memory as part of long-term memory ===<br />
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{{Annotated image|caption=The central executive of working memory is retrieving memory from long-term memory.|image=WorkingMemory Label Free.jpg|width=320|height=179|image-width=320|image-left=0|image-top=0|annotations={{Annotation|130|15|Central Executive|font-weight=bold|font-size=10}}<br />
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{{Annotation|10|160|Long-term Memory|font-weight=bold|font-size=10}}}}[[Anders Ericsson]] and [[Walter Kintsch]]<ref>{{cite journal|year=1995|title=Long-term working memory.|journal=Psychological Review|volume=102|issue=2|pages=211–245|doi=10.1037/0033-295X.102.2.211|pmid=7740089|author=Ericsson, K. A.|author2=Kintsch, W.|lastauthoramp=y}}</ref> have introduced the notion of "long-term working memory", which they define as a set of "retrieval structures" in long-term memory that enable seamless access to the information relevant for everyday tasks. In this way, parts of long-term memory effectively function as working memory. In a similar vein, [[Nelson Cowan|Cowan]] does not regard working memory as a separate system from [[long-term memory]]. Representations in working memory are a subset of representations in long-term memory. Working memory is organized into two embedded levels. The first consists of long-term memory representations that are activated. There can be many of these—there is theoretically no limit to the activation of representations in long-term memory. The second level is called the focus of attention. The focus is regarded as having a limited capacity and holds up to four of the activated representations.<ref name="Cowan 1995">{{cite book |author=Cowan, Nelson |title=Attention and memory: an integrated framework |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=1995 |isbn=978-0-19-506760-6 |oclc=30475237 }}{{Page needed|date=September 2010}}</ref><br />
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Anders Ericsson and Walter Kintsch have introduced the notion of "long-term working memory", which they define as a set of "retrieval structures" in long-term memory that enable seamless access to the information relevant for everyday tasks. In this way, parts of long-term memory effectively function as working memory. In a similar vein, Cowan does not regard working memory as a separate system from long-term memory. Representations in working memory are a subset of representations in long-term memory. Working memory is organized into two embedded levels. The first consists of long-term memory representations that are activated. There can be many of these—there is theoretically no limit to the activation of representations in long-term memory. The second level is called the focus of attention. The focus is regarded as having a limited capacity and holds up to four of the activated representations.<br />
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{{Annotated image|caption=The central executive of working memory is retrieving memory from long-term memory.|image=WorkingMemory Label Free.jpg|width=320|height=179|image-width=320|image-left=0|image-top=0|annotations={{Annotation|130|15|Central Executive|font-weight=bold|font-size=10}}<br />
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{{Annotation|10|160|Long-term Memory|font-weight=bold|font-size=10}}}}安德斯 · 埃里克森 Anders Ericsson 和沃尔特 · 金奇 Walter Kintsch <ref>{{cite journal|year=1995|title=Long-term working memory.|journal=Psychological Review|volume=102|issue=2|pages=211–245|doi=10.1037/0033-295X.102.2.211|pmid=7740089|author=Ericsson, K. A.|author2=Kintsch, W.|lastauthoramp=y}}</ref>引入了“'''<font color="#ff8000">长期工作记忆 Long-term Working Memory</font>'''”这一概念,即一组能让人从'''<font color="#ff8000">长期记忆 Long-term Memory</font>'''中无缝获取日常所需信息的“检索结构” 。也就是说,一部分长期记忆有效地发挥了工作记忆的作用。同样,考恩 Cowan 并不认为工作记忆完全独立于长期记忆的。工作记忆的表征是长期记忆表征的一个子集。工作记忆被处理成两个嵌入层次。第一层为被激活的长期记忆表征(可能会很多,毕竟理论上长期记忆表征的激活是没有上限的)。第二层叫做注意力'''<font color="#ff8000">焦点focus</font>''',焦点被认为是一种有限能力,可容纳四个激活的表征<ref name="Cowan 1995">{{cite book |author=Cowan, Nelson |title=Attention and memory: an integrated framework |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=1995 |isbn=978-0-19-506760-6 |oclc=30475237 }}{{Page needed|date=September 2010}}</ref>。<br />
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Oberauer has extended Cowan's model by adding a third component, a more narrow focus of attention that holds only one chunk at a time. The one-element focus is embedded in the four-element focus and serves to select a single chunk for processing. For example, four digits can be held in mind at the same time in Cowan's "focus of attention". When the individual wishes to perform a process on each of these digits—for example, adding the number two to each digit—separate processing is required for each digit since most individuals cannot perform several mathematical processes in parallel.<ref>{{Cite journal|title = Attention, working memory, and long-term memory in multimedia learning: A integrated perspective based on process models of working memory|last = Schweppe|first = J.|date = 2014|journal = Educational Psychology Review|doi = 10.1007/s10648-013-9242-2|issue = 2|volume = 26|page = 289}}</ref> Oberauer's attentional component selects one of the digits for processing and then shifts the attentional focus to the next digit, continuing until all digits have been processed.<ref>{{Cite journal|author=Oberauer K |title=Access to information in working memory: exploring the focus of attention |journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |volume=28 |issue=3 |pages=411–21 |date=May 2002 |pmid=12018494 |doi=10.1037/0278-7393.28.3.411|citeseerx=10.1.1.163.4979 }}</ref><br />
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Oberauer has extended Cowan's model by adding a third component, a more narrow focus of attention that holds only one chunk at a time. The one-element focus is embedded in the four-element focus and serves to select a single chunk for processing. For example, four digits can be held in mind at the same time in Cowan's "focus of attention". When the individual wishes to perform a process on each of these digits—for example, adding the number two to each digit—separate processing is required for each digit since most individuals cannot perform several mathematical processes in parallel. Oberauer's attentional component selects one of the digits for processing and then shifts the attentional focus to the next digit, continuing until all digits have been processed.<br />
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奥伯奥尔 Oberauer 在Cowan模型的基础上又添加了一个组件——一个更窄的注意力焦点,一次只能容纳一个'''<font color="#ff8000">组块chunk</font>'''。单元素焦点系统嵌在四元素焦点系统之中,用于挑选要处理的单个块。例如,根据Cowan 的“注意力焦点”理论,四个数字可以同时出现在脑海中。当个体要加工所有数字时(例如,将数字2加到每个数字)必须要先对每个数字进行独立加工(因为大多数人不能同时处理多个数学问题)<ref>{{Cite journal|title = Attention, working memory, and long-term memory in multimedia learning: A integrated perspective based on process models of working memory|last = Schweppe|first = J.|date = 2014|journal = Educational Psychology Review|doi = 10.1007/s10648-013-9242-2|issue = 2|volume = 26|page = 289}}</ref>。此时Oberauer 的注意力组件将选择其中一个数字进行处理,结束后就把焦点转到下一个数字,直到处理完毕<ref>{{Cite journal|author=Oberauer K |title=Access to information in working memory: exploring the focus of attention |journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |volume=28 |issue=3 |pages=411–21 |date=May 2002 |pmid=12018494 |doi=10.1037/0278-7393.28.3.411|citeseerx=10.1.1.163.4979 }}</ref>。<br />
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== 容量 Capacity ==<br />
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Working memory is widely acknowledged as having limited capacity. An early quantification of the capacity limit associated with short-term memory was the "[[The Magical Number Seven, Plus or Minus Two|magical number seven]]" suggested by Miller in 1956.<ref name="miller">{{Cite journal|author=Miller GA |title=The magical number seven plus or minus two: some limits on our capacity for processing information |journal=Psychological Review |volume=63 |issue=2 |pages=81–97 |date=March 1956 |pmid=13310704 |doi=10.1037/h0043158|citeseerx=10.1.1.308.8071 }} Republished: {{Cite journal|author=Miller GA |title=The magical number seven, plus or minus two: some limits on our capacity for processing information. 1956 |journal=Psychological Review |volume=101 |issue=2 |pages=343–52 |date=April 1994 |pmid=8022966 |doi=10.1037/0033-295X.101.2.343}}</ref> He claimed that the information-processing capacity of young adults is around seven elements, which he called "chunks", regardless of whether the elements are digits, letters, words, or other units. Later research revealed this number depends on the category of chunks used (e.g., span may be around seven for digits, six for letters, and five for words), and even on features of the [[chunking (psychology)|chunks]] within a category. For instance, span is lower for long than short words. In general, memory span for verbal contents (digits, letters, words, etc.) depends on the phonological complexity of the content (i.e., the number of phonemes, the number of syllables),<ref>{{Cite journal|last=Service|first=Elisabet|date=1998-05-01|title=The Effect of Word Length on Immediate Serial Recall Depends on Phonological Complexity, Not Articulatory Duration|journal=The Quarterly Journal of Experimental Psychology Section A|volume=51|issue=2|pages=283–304|doi=10.1080/713755759|issn=0272-4987}}</ref> and on the lexical status of the contents (whether the contents are words known to the person or not).<ref>{{Cite journal|first1=Charles |last1=Hulme |first2=Steven |last2=Roodenrys |first3=Gordon |last3=Brown |first4=Robin |last4=Mercer |date=November 1995 |title=The role of long-term memory mechanisms in memory span |journal=British Journal of Psychology |volume=86 |issue=4 |pages=527–36 |doi=10.1111/j.2044-8295.1995.tb02570.x}}</ref> Several other factors affect a person's measured span, and therefore it is difficult to pin down the capacity of short-term or working memory to a number of chunks. Nonetheless, Cowan proposed that working memory has a capacity of about four chunks in young adults (and fewer in children and old adults).<ref>{{Cite journal|first1=Nelson |last1=Cowan |year=2001 |title=The magical number 4 in short-term memory: A reconsideration of mental storage capacity |journal=Behavioral and Brain Sciences |volume=24 |issue=1 |pages=87–185 |doi=10.1017/S0140525X01003922 |pmid=11515286|doi-access=free }}</ref><br />
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Working memory is widely acknowledged as having limited capacity. An early quantification of the capacity limit associated with short-term memory was the "magical number seven" suggested by Miller in 1956. He claimed that the information-processing capacity of young adults is around seven elements, which he called "chunks", regardless of whether the elements are digits, letters, words, or other units. Later research revealed this number depends on the category of chunks used (e.g., span may be around seven for digits, six for letters, and five for words), and even on features of the chunks within a category. For instance, span is lower for long than short words. In general, memory span for verbal contents (digits, letters, words, etc.) depends on the phonological complexity of the content (i.e., the number of phonemes, the number of syllables), and on the lexical status of the contents (whether the contents are words known to the person or not). Several other factors affect a person's measured span, and therefore it is difficult to pin down the capacity of short-term or working memory to a number of chunks. Nonetheless, Cowan proposed that working memory has a capacity of about four chunks in young adults (and fewer in children and old adults).<br />
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工作记忆通常被认为容量有限。1956年,米勒 Miller提出了“'''<font color="#ff8000">神奇数字7 The Magical Number Seven</font>'''”来量化短期记忆<ref name="miller">{{Cite journal|author=Miller GA |title=The magical number seven plus or minus two: some limits on our capacity for processing information |journal=Psychological Review |volume=63 |issue=2 |pages=81–97 |date=March 1956 |pmid=13310704 |doi=10.1037/h0043158|citeseerx=10.1.1.308.8071 }} Republished: {{Cite journal|author=Miller GA |title=The magical number seven, plus or minus two: some limits on our capacity for processing information. 1956 |journal=Psychological Review |volume=101 |issue=2 |pages=343–52 |date=April 1994 |pmid=8022966 |doi=10.1037/0033-295X.101.2.343}}</ref>。他认为年轻人的信息处理能力容量大约是7个元素,称之为组块。组块内容可以是数字、字母、单词等。后续的研究发现,这个数字的大小取决于所用组块的类别(例如,数字对应7个,字母对应6个,单词对应5个)甚至取决于该类别中组块的特征。例如,长词的组块数会低于短词的组块数。一般而言,口头内容(数字、字母、单词)的记忆规模取决于内容的音系复杂度(即音素、音节的量)<ref>{{Cite journal|last=Service|first=Elisabet|date=1998-05-01|title=The Effect of Word Length on Immediate Serial Recall Depends on Phonological Complexity, Not Articulatory Duration|journal=The Quarterly Journal of Experimental Psychology Section A|volume=51|issue=2|pages=283–304|doi=10.1080/713755759|issn=0272-4987}}</ref>以及所用词汇状态(内容所用单词是否为主体所知)<ref>{{Cite journal|first1=Charles |last1=Hulme |first2=Steven |last2=Roodenrys |first3=Gordon |last3=Brown |first4=Robin |last4=Mercer |date=November 1995 |title=The role of long-term memory mechanisms in memory span |journal=British Journal of Psychology |volume=86 |issue=4 |pages=527–36 |doi=10.1111/j.2044-8295.1995.tb02570.x}}</ref>。除此之外,还有其他若干因素也会影响人的记忆规模,因此难以确定短期记忆或工作记忆的组块数。尽管如此,Cowan还是认为年轻人的工作记忆容量大约是4个组块(儿童和老年人则更少)<ref>{{Cite journal|first1=Nelson |last1=Cowan |year=2001 |title=The magical number 4 in short-term memory: A reconsideration of mental storage capacity |journal=Behavioral and Brain Sciences |volume=24 |issue=1 |pages=87–185 |doi=10.1017/S0140525X01003922 |pmid=11515286|doi-access=free }}</ref><br />
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Whereas most adults can repeat about seven digits in correct order, some individuals have shown impressive enlargements of their digit span—up to 80 digits. This feat is possible by extensive training on an encoding strategy by which the digits in a list are grouped (usually in groups of three to five) and these groups are encoded as a single unit (a chunk). For this to succeed, participants must be able to recognize the groups as some known string of digits. One person studied by Ericsson and his colleagues, for example, used an extensive knowledge of racing times from the history of sports in the process of coding chunks: several such chunks could then be combined into a higher-order chunk, forming a hierarchy of chunks. In this way, only some chunks at the highest level of the hierarchy must be retained in working memory, and for retrieval the chunks are unpacked. That is, the chunks in working memory act as retrieval cues that point to the digits they contain. Practicing memory skills such as these does not expand working memory capacity proper: it is the capacity to transfer (and retrieve) information from long-term memory that is improved, according to Ericsson and Kintsch (1995; see also Gobet & Simon, 2000<ref name="Gobet F 2000 551–70">{{Cite journal|date=November 2000|title=Some shortcomings of long-term working memory|journal=British Journal of Psychology|volume=91|issue=Pt 4|pages=551–70|doi=10.1348/000712600161989|pmid=11104178|author=Gobet F|url=http://bura.brunel.ac.uk/handle/2438/807|type=Submitted manuscript}}</ref>).<br />
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Whereas most adults can repeat about seven digits in correct order, some individuals have shown impressive enlargements of their digit span—up to 80 digits. This feat is possible by extensive training on an encoding strategy by which the digits in a list are grouped (usually in groups of three to five) and these groups are encoded as a single unit (a chunk). For this to succeed, participants must be able to recognize the groups as some known string of digits. One person studied by Ericsson and his colleagues, for example, used an extensive knowledge of racing times from the history of sports in the process of coding chunks: several such chunks could then be combined into a higher-order chunk, forming a hierarchy of chunks. In this way, only some chunks at the highest level of the hierarchy must be retained in working memory, and for retrieval the chunks are unpacked. That is, the chunks in working memory act as retrieval cues that point to the digits they contain. Practicing memory skills such as these does not expand working memory capacity proper: it is the capacity to transfer (and retrieve) information from long-term memory that is improved, according to Ericsson and Kintsch (1995; see also Gobet & Simon, 2000).<br />
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大多数成年人能够正确地重复7个数字,但有些个体的记忆规模则得到了显著扩充——高达80个数字。这可以通过编码策略培训来实现。按编码策略将列表中的数字分组(通常分3到5组)并将这些组编码为一个独立单元(一个组块)。要实现这一点,参与者必须要将组识别为某些已知的数字字符串。例如,埃里克森 Ericsson 和他同事的一位研究对象利用了体育史中各大比赛的时间来编写代码组块: 几个这样的组块可组合成一个更高级的组块,形成组块层次结构。如此,只要层次结构最高级别的组块保持在工作记忆中即可——当然这些组块是可检索的。也就是说,工作记忆中的组块是提取数字内容的指向性线索。埃里克森 Ericsson 和 金茨 Kintsch (1995; 参见 Gobet & Simon,2000<ref name="Gobet F 2000 551–70">{{Cite journal|date=November 2000|title=Some shortcomings of long-term working memory|journal=British Journal of Psychology|volume=91|issue=Pt 4|pages=551–70|doi=10.1348/000712600161989|pmid=11104178|author=Gobet F|url=http://bura.brunel.ac.uk/handle/2438/807|type=Submitted manuscript}}</ref>)认为,练习这种记忆技巧并不能真正提高工作记忆容量,所提高的是从长期记忆中传递(和检索)信息的能力。<br />
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=== 测量和关联 Measures and correlates ===<br />
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Working memory capacity can be tested by a variety of tasks. A commonly used measure is a dual-task paradigm, combining a [[memory span]] measure with a concurrent processing task, sometimes referred to as "complex span". Daneman and Carpenter invented the first version of this kind of task, the "[[reading span]]", in 1980.<ref>{{Cite journal|first1=Meredyth |last1=Daneman |first2=Patricia A. |last2=Carpenter |date=August 1980 |title=Individual differences in working memory and reading |journal=Journal of Verbal Learning & Verbal Behavior |volume=19 |issue=4 |pages=450–66 |doi=10.1016/S0022-5371(80)90312-6}}</ref> Subjects read a number of sentences (usually between two and six) and tried to remember the last word of each sentence. At the end of the list of sentences, they repeated back the words in their correct order. Other tasks that do not have this dual-task nature have also been shown to be good measures of working memory capacity.<ref>{{Cite journal|last2=Süss|first2=H.-M.|last3=Schulze|first3=R.|last4=Wilhelm|first4=O.|last5=Wittmann|first5=W.&nbsp;W.|date=December 2000|title=Working memory capacity—facets of a cognitive ability construct|journal=Personality and Individual Differences|volume=29|issue=6|pages=1017–45|doi=10.1016/S0191-8869(99)00251-2|first1=K.|last1=Oberauer}}</ref> Whereas Daneman and Carpenter believed that the combination of "storage" (maintenance) and processing is needed to measure working memory capacity, we know now that the capacity of working memory can be measured with short-term memory tasks that have no additional processing component.<ref>{{Cite journal|last1=Unsworth|first1=Nash|last2=Engle|first2=Randall W.|title=On the division of short-term and working memory: An examination of simple and complex span and their relation to higher order abilities.|journal=Psychological Bulletin|volume=133|issue=6|pages=1038–1066|doi=10.1037/0033-2909.133.6.1038|pmid=17967093|year=2007}}</ref><ref>{{Cite journal|last=Colom, R. Abad, F. J. Quiroga, M. A. Shih, P. C. Flores-Mendoza, C.|year=2008|title=Working memory and intelligence are highly related constructs, but why?|journal=Intelligence|volume=36|issue=6|pages=584–606|doi=10.1016/j.intell.2008.01.002}}</ref> Conversely, working memory capacity can also be measured with certain processing tasks that don't involve maintenance of information.<ref>{{Cite journal|last=Oberauer, K. Süß, H.-M. Wilhelm, O. Wittmann, W. W.|year=2003|title=The multiple faces of working memory - storage, processing, supervision, and coordination|doi=10.1016/s0160-2896(02)00115-0|journal=Intelligence|volume=31|issue=2|pages=167–193|url=https://www.zora.uzh.ch/id/eprint/97155/1/intelligence.pdf}}</ref><ref>{{Cite journal|last=Chuderski|first=Adam|date=2013-09-25|title=The relational integration task explains fluid reasoning above and beyond other working memory tasks|journal=Memory & Cognition|language=en|volume=42|issue=3|pages=448–463|doi=10.3758/s13421-013-0366-x|issn=0090-502X|pmc=3969517|pmid=24222318}}</ref> The question of what features a task must have to qualify as a good measure of working memory capacity is a topic of ongoing research.<br />
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Working memory capacity can be tested by a variety of tasks. A commonly used measure is a dual-task paradigm, combining a memory span measure with a concurrent processing task, sometimes referred to as "complex span". Daneman and Carpenter invented the first version of this kind of task, the "reading span", in 1980. Subjects read a number of sentences (usually between two and six) and tried to remember the last word of each sentence. At the end of the list of sentences, they repeated back the words in their correct order. Other tasks that do not have this dual-task nature have also been shown to be good measures of working memory capacity. Whereas Daneman and Carpenter believed that the combination of "storage" (maintenance) and processing is needed to measure working memory capacity, we know now that the capacity of working memory can be measured with short-term memory tasks that have no additional processing component. Conversely, working memory capacity can also be measured with certain processing tasks that don't involve maintenance of information. The question of what features a task must have to qualify as a good measure of working memory capacity is a topic of ongoing research.<br />
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我们可以通过一系列任务来测量工作记忆的容量。其中一个方法是双任务范例,它将'''<font color="#ff8000">记忆广度测度 memory span measure</font>'''与'''<font color="#ff8000">并发处理任务concurrent processing task</font>'''(有时称为“复杂规模”)结合起来。1980年,丹曼 Daneman 和 卡朋特 Carpenter 发明了该方法的第一个版本——“阅读广度”<ref>{{Cite journal|first1=Meredyth |last1=Daneman |first2=Patricia A. |last2=Carpenter |date=August 1980 |title=Individual differences in working memory and reading |journal=Journal of Verbal Learning & Verbal Behavior |volume=19 |issue=4 |pages=450–66 |doi=10.1016/S0022-5371(80)90312-6}}</ref>。受试者阅读大量的句子(通常2至6个),并努力记住每个句子的最后一个单词。阅读完后他们按照自己认为正确的顺序复述单词<ref>{{Cite journal|last1=Unsworth|first1=Nash|last2=Engle|first2=Randall W.|title=On the division of short-term and working memory: An examination of simple and complex span and their relation to higher order abilities.|journal=Psychological Bulletin|volume=133|issue=6|pages=1038–1066|doi=10.1037/0033-2909.133.6.1038|pmid=17967093|year=2007}}</ref><ref>{{Cite journal|last=Colom, R. Abad, F. J. Quiroga, M. A. Shih, P. C. Flores-Mendoza, C.|year=2008|title=Working memory and intelligence are highly related constructs, but why?|journal=Intelligence|volume=36|issue=6|pages=584–606|doi=10.1016/j.intell.2008.01.002}}</ref>。其他一些不具备双任务性质的任务同样也是测量工作记忆容量的好办法<ref>{{Cite journal|last2=Süss|first2=H.-M.|last3=Schulze|first3=R.|last4=Wilhelm|first4=O.|last5=Wittmann|first5=W.&nbsp;W.|date=December 2000|title=Working memory capacity—facets of a cognitive ability construct|journal=Personality and Individual Differences|volume=29|issue=6|pages=1017–45|doi=10.1016/S0191-8869(99)00251-2|first1=K.|last1=Oberauer}}</ref>。Daneman 和Carpenter 相信“存储”(维护)和加工的结合是测量工作记忆容量所必须的,现在我们知道工作记忆的容量既可以用没有额外处理组件的短时记忆任务来测量,也可以用不涉及信息维护的某些处理任务来衡量<ref>{{Cite journal|last=Oberauer, K. Süß, H.-M. Wilhelm, O. Wittmann, W. W.|year=2003|title=The multiple faces of working memory - storage, processing, supervision, and coordination|doi=10.1016/s0160-2896(02)00115-0|journal=Intelligence|volume=31|issue=2|pages=167–193|url=https://www.zora.uzh.ch/id/eprint/97155/1/intelligence.pdf}}</ref><ref>{{Cite journal|last=Chuderski|first=Adam|date=2013-09-25|title=The relational integration task explains fluid reasoning above and beyond other working memory tasks|journal=Memory & Cognition|language=en|volume=42|issue=3|pages=448–463|doi=10.3758/s13421-013-0366-x|issn=0090-502X|pmc=3969517|pmid=24222318}}</ref>。至于用于测量工作记忆容量的好的任务方案应当具备哪些特征,这仍是一个待研究的课题。<br />
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Measures of working-memory capacity are strongly related to performance in other complex cognitive tasks, such as reading comprehension, problem solving, and with measures of [[intelligence quotient]].<ref>{{Cite journal|vauthors=Conway AR, Kane MJ, Engle RW |title=Working memory capacity and its relation to general intelligence |journal=Trends in Cognitive Sciences |volume=7 |issue=12 |pages=547–52 |date=December 2003 |pmid=14643371 |doi=10.1016/j.tics.2003.10.005|citeseerx=10.1.1.538.4967 }}</ref><br />
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Measures of working-memory capacity are strongly related to performance in other complex cognitive tasks, such as reading comprehension, problem solving, and with measures of intelligence quotient.<br />
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工作记忆容量的测量与其他复杂认知任务中的表现有密切联系,例如'''<font color="#ff8000">阅读理解 reading comprehension</font>'''、'''<font color="#ff8000">问题解决 problem solving</font>'''和'''<font color="#ff8000">智商测量intelligence quotient</font>'''。<ref>{{Cite journal|vauthors=Conway AR, Kane MJ, Engle RW |title=Working memory capacity and its relation to general intelligence |journal=Trends in Cognitive Sciences |volume=7 |issue=12 |pages=547–52 |date=December 2003 |pmid=14643371 |doi=10.1016/j.tics.2003.10.005|citeseerx=10.1.1.538.4967 }}</ref>。<br />
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Some researchers have argued<ref>{{Cite journal|author=Engle, R. W.|author2=Tuholski, S. W.|author3=Laughlin, J. E.|author4=Conway, A. R. |title=Working memory, short-term memory, and general fluid intelligence: a latent-variable approach |journal=Journal of Experimental Psychology: General |volume=128 |issue=3 |pages=309–31 |date=September 1999 |pmid=10513398 |doi=10.1037/0096-3445.128.3.309|url=https://semanticscholar.org/paper/cf15817ee5f9c1536ee4da2c4c018555600ca91b}}</ref> that working-memory capacity reflects the efficiency of executive functions, most notably the ability to maintain multiple task-relevant representations in the face of distracting irrelevant information; and that such tasks seem to reflect individual differences in the ability to focus and maintain attention, particularly when other events are serving to capture attention. Both working memory and executive functions rely strongly, though not exclusively, on frontal brain areas.<ref name="Kane MJ, Engle RW 2002 637–71">{{Cite journal|doi=10.3758/BF03196323|author=Kane, M. J.|author2=Engle, R. W.|title=The role of prefrontal cortex in working-memory capacity, executive attention, and general fluid intelligence: an individual-differences perspective |journal=Psychonomic Bulletin & Review |volume=9 |issue=4 |pages=637–71 |date=December 2002 |pmid=12613671 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=12613671|doi-access=free }}</ref><br />
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Some researchers have argued that working-memory capacity reflects the efficiency of executive functions, most notably the ability to maintain multiple task-relevant representations in the face of distracting irrelevant information; and that such tasks seem to reflect individual differences in the ability to focus and maintain attention, particularly when other events are serving to capture attention. Both working memory and executive functions rely strongly, though not exclusively, on frontal brain areas.<br />
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一些研究人员认为<ref>{{Cite journal|author=Engle, R. W.|author2=Tuholski, S. W.|author3=Laughlin, J. E.|author4=Conway, A. R. |title=Working memory, short-term memory, and general fluid intelligence: a latent-variable approach |journal=Journal of Experimental Psychology: General |volume=128 |issue=3 |pages=309–31 |date=September 1999 |pmid=10513398 |doi=10.1037/0096-3445.128.3.309|url=https://semanticscholar.org/paper/cf15817ee5f9c1536ee4da2c4c018555600ca91b}}</ref>,工作记忆容量能够反映执行功能的效率,其中最具代表性的是面对不相关信息时协调多个任务相关表征的能力; 且这样的任务似乎也反映出在集中注意力和保持注意力方面的个体能力差异(特别是当其他事件能吸引注意力时)。工作记忆和执行功能都非常依赖(但不限于)额叶大脑区域<ref name="Kane MJ, Engle RW 2002 637–71">{{Cite journal|doi=10.3758/BF03196323|author=Kane, M. J.|author2=Engle, R. W.|title=The role of prefrontal cortex in working-memory capacity, executive attention, and general fluid intelligence: an individual-differences perspective |journal=Psychonomic Bulletin & Review |volume=9 |issue=4 |pages=637–71 |date=December 2002 |pmid=12613671 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=12613671|doi-access=free }}</ref><br />
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Other researchers have argued that the capacity of working memory is better characterized as the ability to mentally form relations between elements, or to grasp relations in given information. This idea has been advanced, among others, by Graeme Halford, who illustrated it by our limited ability to understand statistical interactions between variables.<ref>{{Cite journal|author=Halford, G. S.|author2=Baker, R.|author3=McCredden, J. E.|author4=Bain, J. D. |title=How many variables can humans process? |journal=Psychological Science |volume=16 |issue=1 |pages=70–76 |date=January 2005 |pmid=15660854 |doi=10.1111/j.0956-7976.2005.00782.x}}</ref> These authors asked people to compare written statements about the relations between several variables to graphs illustrating the same or a different relation, as in the following sentence: "If the cake is from France, then it has more sugar if it is made with chocolate than if it is made with cream, but if the cake is from Italy, then it has more sugar if it is made with cream than if it is made of chocolate". This statement describes a relation between three variables (country, ingredient, and amount of sugar), which is the maximum most individuals can understand. The capacity limit apparent here is obviously not a memory limit (all relevant information can be seen continuously) but a limit to how many relationships are discerned simultaneously.<br />
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Other researchers have argued that the capacity of working memory is better characterized as the ability to mentally form relations between elements, or to grasp relations in given information. This idea has been advanced, among others, by Graeme Halford, who illustrated it by our limited ability to understand statistical interactions between variables. These authors asked people to compare written statements about the relations between several variables to graphs illustrating the same or a different relation, as in the following sentence: "If the cake is from France, then it has more sugar if it is made with chocolate than if it is made with cream, but if the cake is from Italy, then it has more sugar if it is made with cream than if it is made of chocolate". This statement describes a relation between three variables (country, ingredient, and amount of sugar), which is the maximum most individuals can understand. The capacity limit apparent here is obviously not a memory limit (all relevant information can be seen continuously) but a limit to how many relationships are discerned simultaneously.<br />
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另一些研究人员主张,用个体构建元素间关系或获取信息的能力来测量工作记忆容量更佳。格雷姆 · 哈尔福德Graeme Halford用我们理解变量之间统计交互作用的有限能力来解释这个想法<ref>{{Cite journal|author=Halford, G. S.|author2=Baker, R.|author3=McCredden, J. E.|author4=Bain, J. D. |title=How many variables can humans process? |journal=Psychological Science |volume=16 |issue=1 |pages=70–76 |date=January 2005 |pmid=15660854 |doi=10.1111/j.0956-7976.2005.00782.x}}</ref>。这些发起人要求人们把陈述几个变量之间关系的书面表达与相应的图示(说明相同或不同关系)进行比较,例如: ”如果蛋糕来自法国,那么用巧克力做的比用奶油做的含糖量高。但如果蛋糕来自意大利,那么用奶油做的比用巧克力做的含糖量高”。这个陈述描述了三个变量之间的关系(国家、成分和糖量)——这是大多数人理解能力的上限。这里的容量限制显然不是记忆量限制(所有相关信息都可完整看到),而是可同时识别关系量的限制。<br />
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=== 工作记忆容量的试验研究 Experimental studies of working-memory capacity ===<br />
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There are several hypotheses about the nature of the capacity limit. One is that a limited pool of cognitive resources is needed to keep representations active and thereby available for processing, and for carrying out processes.<ref name=":0">{{Cite journal|author=Just, M. A.|author2=Carpenter, P. A. |title=A capacity theory of comprehension: individual differences in working memory |journal=Psychological Review |volume=99 |issue=1 |pages=122–49 |date=January 1992 |pmid=1546114 |doi=10.1037/0033-295X.99.1.122|url=http://repository.cmu.edu/cgi/viewcontent.cgi?article=1730&context=psychology }}</ref> Another hypothesis is that memory traces in working memory decay within a few seconds, unless refreshed through rehearsal, and because the speed of rehearsal is limited, we can maintain only a limited amount of information.<ref>{{Cite journal|doi=10.3758/BF03198549|author=Towse, J. N.|author2=Hitch, G. J.|author3=Hutton, U.|title=On the interpretation of working memory span in adults |journal=Memory & Cognition |volume=28 |issue=3 |pages=341–8 |date=April 2000 |pmid=10881551|doi-access=free }}</ref> Yet another idea is that representations held in working memory interfere with each other.<ref>{{Cite journal|vauthors=Waugh NC, Norman DA |title=Primary Memory |journal=Psychological Review |volume=72 |issue= 2|pages=89–104 |date=March 1965 |pmid=14282677 |doi=10.1037/h0021797}}</ref><br />
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There are several hypotheses about the nature of the capacity limit. One is that a limited pool of cognitive resources is needed to keep representations active and thereby available for processing, and for carrying out processes. Another hypothesis is that memory traces in working memory decay within a few seconds, unless refreshed through rehearsal, and because the speed of rehearsal is limited, we can maintain only a limited amount of information. Yet another idea is that representations held in working memory interfere with each other.<br />
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关于'''<font color="#ff8000">容量极限capacity limit</font>'''的性质有几种假设。一种观点认为其性质是一种有限认知资源池,作为激活记忆表征以及处理记忆表征的前提<ref name=":0">{{Cite journal|author=Just, M. A.|author2=Carpenter, P. A. |title=A capacity theory of comprehension: individual differences in working memory |journal=Psychological Review |volume=99 |issue=1 |pages=122–49 |date=January 1992 |pmid=1546114 |doi=10.1037/0033-295X.99.1.122|url=http://repository.cmu.edu/cgi/viewcontent.cgi?article=1730&context=psychology }}</ref>,另一种观点认为工作记忆若不反复刷新将会在几秒内衰退。又因为刷新速率是有限的,所以我们只能维持一定的信息量<ref>{{Cite journal|doi=10.3758/BF03198549|author=Towse, J. N.|author2=Hitch, G. J.|author3=Hutton, U.|title=On the interpretation of working memory span in adults |journal=Memory & Cognition |volume=28 |issue=3 |pages=341–8 |date=April 2000 |pmid=10881551|doi-access=free }}</ref>。还有观点认为容量极限是工作记忆中的表征互相干涉的结果<ref>{{Cite journal|vauthors=Waugh NC, Norman DA |title=Primary Memory |journal=Psychological Review |volume=72 |issue= 2|pages=89–104 |date=March 1965 |pmid=14282677 |doi=10.1037/h0021797}}</ref>。<br />
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====衰变理论 Decay theories====<br />
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The assumption that the contents of short-term or working memory [[decay theory|decay]] over time, unless decay is prevented by rehearsal, goes back to the early days of experimental research on short-term memory.<ref>{{Cite journal|last=Brown, J.|year=1958|title=Some tests of the decay theory of immediate memory|journal=Quarterly Journal of Experimental Psychology|volume=10|pages=12–21|doi=10.1080/17470215808416249}}</ref><ref>{{Cite journal|author1=Peterson, L. R. |author2=Peterson, M. J.|year=1959|title=Short-term retention of individual verbal items|journal=Journal of Experimental Psychology|volume=58|issue=3|pages=193–198|doi=10.1037/h0049234|pmid=14432252|citeseerx=10.1.1.227.1807}}</ref> It is also an important assumption in the multi-component theory of working memory.<ref>{{Cite book|title=Working memory|author1=Baddeley, A. D.|publisher=Clarendon|year=1986|location=Oxford}}</ref> The most elaborate decay-based theory of working memory to date is the "time-based resource sharing model".<ref>{{Cite journal|date=March 2004|title=Time constraints and resource sharing in adults' working memory spans|journal=Journal of Experimental Psychology: General|volume=133|issue=1|pages=83–100|doi=10.1037/0096-3445.133.1.83|pmid=14979753|vauthors=Barrouillet P, Bernardin S, Camos V|citeseerx=10.1.1.379.9208}}</ref> This theory assumes that representations in working memory decay unless they are refreshed. Refreshing them requires an attentional mechanism that is also needed for any concurrent processing task. When there are small time intervals in which the processing task does not require attention, this time can be used to refresh memory traces. The theory therefore predicts that the amount of forgetting depends on the temporal density of attentional demands of the processing task—this density is called "cognitive load". The cognitive load depends on two variables, the rate at which the processing task requires individual steps to be carried out, and the duration of each step. For example, if the processing task consists of adding digits, then having to add another digit every half second places a higher cognitive load on the system than having to add another digit every two seconds. In a series of experiments, Barrouillet and colleagues have shown that memory for lists of letters depends neither on the number of processing steps nor the total time of processing but on cognitive load.<ref>{{citation|title=Time and cognitive load in working memory|date=May 2007|journal=J Exp Psychol Learn Mem Cogn|vauthors=Barrouillet P, Bernardin S, Portrat S, Vergauwe E, Camos V|volume=33|issue=3|pages=570–585|doi=10.1037/0278-7393.33.3.570|pmid=17470006|url=https://archive-ouverte.unige.ch/unige:88299}}</ref><br />
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The assumption that the contents of short-term or working memory decay over time, unless decay is prevented by rehearsal, goes back to the early days of experimental research on short-term memory. It is also an important assumption in the multi-component theory of working memory. The most elaborate decay-based theory of working memory to date is the "time-based resource sharing model". This theory assumes that representations in working memory decay unless they are refreshed. Refreshing them requires an attentional mechanism that is also needed for any concurrent processing task. When there are small time intervals in which the processing task does not require attention, this time can be used to refresh memory traces. The theory therefore predicts that the amount of forgetting depends on the temporal density of attentional demands of the processing task—this density is called "cognitive load". The cognitive load depends on two variables, the rate at which the processing task requires individual steps to be carried out, and the duration of each step. For example, if the processing task consists of adding digits, then having to add another digit every half second places a higher cognitive load on the system than having to add another digit every two seconds. In a series of experiments, Barrouillet and colleagues have shown that memory for lists of letters depends neither on the number of processing steps nor the total time of processing but on cognitive load.<br />
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该理论假设短期记忆或工作记忆的内容会随着时间的推移而'''<font color="#ff8000">衰退 decay</font>''',这种衰退只能通过不断刷新来遏制。这种理论来自短期记忆的早期研究<ref>{{Cite journal|last=Brown, J.|year=1958|title=Some tests of the decay theory of immediate memory|journal=Quarterly Journal of Experimental Psychology|volume=10|pages=12–21|doi=10.1080/17470215808416249}}</ref><ref>{{Cite journal|author1=Peterson, L. R. |author2=Peterson, M. J.|year=1959|title=Short-term retention of individual verbal items|journal=Journal of Experimental Psychology|volume=58|issue=3|pages=193–198|doi=10.1037/h0049234|pmid=14432252|citeseerx=10.1.1.227.1807}}</ref>。它同样是工作记忆多元理论中的一个重要假设<ref>{{Cite book|title=Working memory|author1=Baddeley, A. D.|publisher=Clarendon|year=1986|location=Oxford}}</ref>。迄今为止,基于衰减假设的最详尽的工作记忆理论是“'''<font color="#ff8000">基于时间的资源共享模型 time-based resource sharing model” </font>'''<ref>{{Cite journal|date=March 2004|title=Time constraints and resource sharing in adults' working memory spans|journal=Journal of Experimental Psychology: General|volume=133|issue=1|pages=83–100|doi=10.1037/0096-3445.133.1.83|pmid=14979753|vauthors=Barrouillet P, Bernardin S, Camos V|citeseerx=10.1.1.379.9208}}</ref>。该理论假设工作记忆中的表征不断衰退,需要持续刷新来维持。而刷新需要注意力机制——对于任何平行任务都是必需的——的保障。当任务进程中存在不需要注意力的微小时间间隔时,刷新记忆路径的任务可以在此时完成。因此,该理论推测遗忘量取决于任务进程所需即时注意力的密度,这种密度叫做“认知负荷”。认知负荷取决于两个变量,一是任务进程中各个步骤执行的速率,二是每个步骤的持续时间。例如,如果处理的任务内容是数字添加,那么每半秒添加一个数字会比每两秒添加一个数字给系统带来的认知负荷更大。在一系列的实验中,巴鲁耶 Barrouillet 及其同事证明字母列表的记忆并不取决于处理步骤的数量或者处理的总时间,而是取决于认知负荷<ref>{{citation|title=Time and cognitive load in working memory|date=May 2007|journal=J Exp Psychol Learn Mem Cogn|vauthors=Barrouillet P, Bernardin S, Portrat S, Vergauwe E, Camos V|volume=33|issue=3|pages=570–585|doi=10.1037/0278-7393.33.3.570|pmid=17470006|url=https://archive-ouverte.unige.ch/unige:88299}}</ref>。<br />
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==== 资源理论 Resource theories====<br />
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Resource theories assume that the capacity of working memory is a limited resource that must be shared between all representations that need to be maintained in working memory simultaneously.<ref>{{Cite journal|last1=Ma|first1=W. J.|author2=Husain, M.|author3=Bays, P. M.|year=2014|title=Changing concepts of working memory|journal=Nature Reviews Neuroscience|volume=17|issue=3|pages=347–356|doi=10.1038/nn.3655|pmid=24569831|pmc=4159388}}</ref> Some resource theorists also assume that maintenance and concurrent processing share the same resource;<ref name=":0" /> this can explain why maintenance is typically impaired by a concurrent processing demand. Resource theories have been very successful in explaining data from tests of working memory for simple visual features, such as colors or orientations of bars. An ongoing debate is whether the resource is a continuous quantity that can be subdivided among any number of items in working memory, or whether it consists of a small number of discrete "slots", each of which can be assigned to one memory item, so that only a limited number of about 3 items can be maintained in working memory at all.<ref>{{Cite journal|last1=van den Berg|first1=Ronald|last2=Awh|first2=Edward|last3=Ma|first3=Wei Ji|title=Factorial comparison of working memory models.|journal=Psychological Review|volume=121|issue=1|pages=124–149|doi=10.1037/a0035234|pmc=4159389|pmid=24490791|year=2014}}</ref><br />
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Resource theories assume that the capacity of working memory is a limited resource that must be shared between all representations that need to be maintained in working memory simultaneously. Some resource theorists also assume that maintenance and concurrent processing share the same resource;<br />
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'''<font color="#ff8000">资源理论 resource theories</font>'''认为工作记忆容量是一种由储存于工作记忆中的全部表征所共享的有限资源<ref>{{Cite journal|last1=Ma|first1=W. J.|author2=Husain, M.|author3=Bays, P. M.|year=2014|title=Changing concepts of working memory|journal=Nature Reviews Neuroscience|volume=17|issue=3|pages=347–356|doi=10.1038/nn.3655|pmid=24569831|pmc=4159388}}</ref>。一些资源理论学者同时还假设存储和并行处理会占用同样的资源;这可以解释为什么存储能力通常会被并发处理的需求减弱。资源理论已经非常成功地解释了简单视觉特征,如颜色或条等方面的工作记忆测试结果。一个持续的争议是资源是一个连续的变量还是离散的变量,是可以再细分为任意数量的工作记忆,还是一个个小数量的离散的“槽”,每个内存可以分配给一个项目,只可以在有限数量(约为3项)中保持工作记忆?<ref>{{Cite journal|last1=van den Berg|first1=Ronald|last2=Awh|first2=Edward|last3=Ma|first3=Wei Ji|title=Factorial comparison of working memory models.|journal=Psychological Review|volume=121|issue=1|pages=124–149|doi=10.1037/a0035234|pmc=4159389|pmid=24490791|year=2014}}</ref><br />
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==== 干涉理论 Interference theories====<br />
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Several forms of [[Interference theory|interference]] have been discussed by theorists. One of the oldest ideas is that new items simply replace older ones in working memory. Another form of interference is retrieval competition. For example, when the task is to remember a list of 7 words in their order, we need to start recall with the first word. While trying to retrieve the first word, the second word, which is represented in proximity, is accidentally retrieved as well, and the two compete for being recalled. Errors in serial recall tasks are often confusions of neighboring items on a memory list (so-called transpositions), showing that retrieval competition plays a role in limiting our ability to recall lists in order, and probably also in other working memory tasks. A third form of interference is the distortion of representations by superposition: When multiple representations are added on top of each other, each of them is blurred by the presence of all the others.<ref>{{Cite journal|last1=Oberauer|first1=Klaus|last2=Lewandowsky|first2=Stephan|last3=Farrell|first3=Simon|last4=Jarrold|first4=Christopher|last5=Greaves|first5=Martin|date=2012-06-20|title=Modeling working memory: An interference model of complex span|journal=Psychonomic Bulletin & Review|language=en|volume=19|issue=5|pages=779–819|doi=10.3758/s13423-012-0272-4|pmid=22715024|issn=1069-9384|url=http://doc.rero.ch/record/320568/files/13423_2012_Article_272.pdf}}</ref> A fourth form of interference assumed by some authors is feature overwriting.<ref>{{Cite journal|doi=10.1016/j.jml.2006.08.009 |title=A formal model of capacity limits in working memory |date=November 2006 |first1=Klaus |last1=Oberauer |first2=Reinhold |last2=Kliegl |journal=Journal of Memory and Language |volume=55 |issue=4 |pages=601–26|doi-access=free }}</ref><ref>{{Cite journal|doi=10.1007/s00221-010-2501-2 |pmid=21132280 |title=Distractor frequency influences performance in vibrotactile working memory |year=2011 |first1=T. |last1=Bancroft |first2=P. |last2=Servos |journal=Experimental Brain Research |volume=208 |issue=4 |pages=529–32}}</ref> The idea is that each word, digit, or other item in working memory is represented as a bundle of features, and when two items share some features, one of them steals the features from the other. The more items are held in working memory, and the more their features overlap, the more each of them will be degraded by the loss of some features.<br />
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Several forms of interference have been discussed by theorists. One of the oldest ideas is that new items simply replace older ones in working memory. Another form of interference is retrieval competition. For example, when the task is to remember a list of 7 words in their order, we need to start recall with the first word. While trying to retrieve the first word, the second word, which is represented in proximity, is accidentally retrieved as well, and the two compete for being recalled. Errors in serial recall tasks are often confusions of neighboring items on a memory list (so-called transpositions), showing that retrieval competition plays a role in limiting our ability to recall lists in order, and probably also in other working memory tasks. A third form of interference is the distortion of representations by superposition: When multiple representations are added on top of each other, each of them is blurred by the presence of all the others. A fourth form of interference assumed by some authors is feature overwriting. The idea is that each word, digit, or other item in working memory is represented as a bundle of features, and when two items share some features, one of them steals the features from the other. The more items are held in working memory, and the more their features overlap, the more each of them will be degraded by the loss of some features.<br />
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理论家们讨论过多种形式的干涉。最初的观点之一是,新事物只是单纯地取代了工作记忆中的旧事物。另一种干涉形式是'''<font color="#ff8000">检索竞争 retrieval competition</font>'''。例如当任务是按照一定顺序记住7个单词时,我们需要从第一个单词开始回忆。而在试图检索第一个单词时,我们往往会意外地检索到第二个单词,至于我们最终会回忆起哪个单词,这就得看它们竞争的结果了。回忆中出现的错误通常表现为记忆列表中相邻项目的混淆(即所谓的换位) ,这表明检索竞争限制了我们按照正确顺序回忆列表的能力,这种限制也可能发生在其他工作记忆任务中。另一种形式的干涉是叠表征的变形: 当多重表征叠加在一起时,每一表征都因其他表征的相互作用而模糊不清<ref>{{Cite journal|last1=Oberauer|first1=Klaus|last2=Lewandowsky|first2=Stephan|last3=Farrell|first3=Simon|last4=Jarrold|first4=Christopher|last5=Greaves|first5=Martin|date=2012-06-20|title=Modeling working memory: An interference model of complex span|journal=Psychonomic Bulletin & Review|language=en|volume=19|issue=5|pages=779–819|doi=10.3758/s13423-012-0272-4|pmid=22715024|issn=1069-9384|url=http://doc.rero.ch/record/320568/files/13423_2012_Article_272.pdf}}</ref>。一些人认为特征覆盖也是一种干涉形式<ref>{{Cite journal|doi=10.1016/j.jml.2006.08.009 |title=A formal model of capacity limits in working memory |date=November 2006 |first1=Klaus |last1=Oberauer |first2=Reinhold |last2=Kliegl |journal=Journal of Memory and Language |volume=55 |issue=4 |pages=601–26|doi-access=free }}</ref><ref>{{Cite journal|doi=10.1007/s00221-010-2501-2 |pmid=21132280 |title=Distractor frequency influences performance in vibrotactile working memory |year=2011 |first1=T. |last1=Bancroft |first2=P. |last2=Servos |journal=Experimental Brain Research |volume=208 |issue=4 |pages=529–32}}</ref>。该观点认为工作记忆中的每个单词、数字或其他项目都被表现为一系列特征,当两个项目共享某些特征时,其中一个就会窃取另一个的特征。工作记忆中保存的条目越多则重叠的特征越多,因此每个条目丢失的特征越多,减损也就越多。<br />
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==== 极限 Limitations ====<br />
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None of these hypotheses can explain the experimental data entirely. The resource hypothesis, for example, was meant to explain the trade-off between maintenance and processing: The more information must be maintained in working memory, the slower and more error prone concurrent processes become, and with a higher demand on concurrent processing memory suffers. This trade-off has been investigated by tasks like the reading-span task described above. It has been found that the amount of trade-off depends on the similarity of the information to be remembered and the information to be processed. For example, remembering numbers while processing spatial information, or remembering spatial information while processing numbers, impair each other much less than when material of the same kind must be remembered and processed.<ref>{{Cite journal|doi=10.1016/j.jml.2006.07.009 |title=The relationship between processing and storage in working memory span: Not two sides of the same coin |date=February 2007 |first1=Yukio |last1=Maehara |first2=Satoru |last2=Saito |journal=Journal of Memory and Language |volume=56 |issue=2 |pages=212–228}}</ref> Also, remembering words and processing digits, or remembering digits and processing words, is easier than remembering and processing materials of the same category.<ref>{{Cite journal|doi=10.1076/anec.6.2.99.784 |title=Selection from Working Memory: on the Relationship between Processing and Storage Components |date=June 1999 |last1=Li |first1=Karen Z.H. |journal=Aging, Neuropsychology, and Cognition |volume=6 |issue=2 |pages=99–116}}</ref> These findings are also difficult to explain for the decay hypothesis, because decay of memory representations should depend only on how long the processing task delays rehearsal or recall, not on the content of the processing task. A further problem for the decay hypothesis comes from experiments in which the recall of a list of letters was delayed, either by instructing participants to recall at a slower pace, or by instructing them to say an irrelevant word once or three times in between recall of each letter. Delaying recall had virtually no effect on recall accuracy.<ref>{{Cite journal|doi=10.3758/BF03196705|vauthors=Lewandowsky S, Duncan M, Brown GD |title=Time does not cause forgetting in short-term serial recall |journal=Psychonomic Bulletin & Review |volume=11 |issue=5 |pages=771–90 |date=October 2004 |pmid=15732687 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=15732687|doi-access=free }}</ref><ref>{{Cite journal|vauthors=Oberauer K, Lewandowsky S |title=Forgetting in immediate serial recall: decay, temporal distinctiveness, or interference? |journal=Psychological Review |volume=115 |issue=3 |pages=544–76 |date=July 2008 |pmid=18729591 |doi=10.1037/0033-295X.115.3.544|url=https://api.research-repository.uwa.edu.au/files/1546099/11204_PID11204.pdf }}</ref> The [[interference theory]] seems to fare best with explaining why the similarity between memory contents and the contents of concurrent processing tasks affects how much they impair each other. More similar materials are more likely to be confused, leading to retrieval competition.<br />
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None of these hypotheses can explain the experimental data entirely. The resource hypothesis, for example, was meant to explain the trade-off between maintenance and processing: The more information must be maintained in working memory, the slower and more error prone concurrent processes become, and with a higher demand on concurrent processing memory suffers. This trade-off has been investigated by tasks like the reading-span task described above. It has been found that the amount of trade-off depends on the similarity of the information to be remembered and the information to be processed. For example, remembering numbers while processing spatial information, or remembering spatial information while processing numbers, impair each other much less than when material of the same kind must be remembered and processed. Also, remembering words and processing digits, or remembering digits and processing words, is easier than remembering and processing materials of the same category. These findings are also difficult to explain for the decay hypothesis, because decay of memory representations should depend only on how long the processing task delays rehearsal or recall, not on the content of the processing task. A further problem for the decay hypothesis comes from experiments in which the recall of a list of letters was delayed, either by instructing participants to recall at a slower pace, or by instructing them to say an irrelevant word once or three times in between recall of each letter. Delaying recall had virtually no effect on recall accuracy. The interference theory seems to fare best with explaining why the similarity between memory contents and the contents of concurrent processing tasks affects how much they impair each other. More similar materials are more likely to be confused, leading to retrieval competition.<br />
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这些假说都不能完全解释实验数据。例如,资源理论旨在解释维护和加工之间的平衡: 工作记忆中需要保存的信息越多,并发进程就变得越慢、越容易出错,且对并发加工记忆的要求也越高。先前叙述的阅读广度任务等被应用于此现象的研究。研究发现,平衡量取决于所要记忆或处理的信息的相似性。例如,在处理空间信息时去记忆数字,或者在处理数字时去记忆空间信息,这些任务的偏差程度要低于记忆并处理同类材料所造成的损失<ref>{{Cite journal|doi=10.1016/j.jml.2006.07.009 |title=The relationship between processing and storage in working memory span: Not two sides of the same coin |date=February 2007 |first1=Yukio |last1=Maehara |first2=Satoru |last2=Saito |journal=Journal of Memory and Language |volume=56 |issue=2 |pages=212–228}}</ref>。此外,记忆单词时处理数字,或记忆数字时处理单词,也要比记忆和处理同一类别材料更容易<ref>{{Cite journal|doi=10.1076/anec.6.2.99.784 |title=Selection from Working Memory: on the Relationship between Processing and Storage Components |date=June 1999 |last1=Li |first1=Karen Z.H. |journal=Aging, Neuropsychology, and Cognition |volume=6 |issue=2 |pages=99–116}}</ref>。这些发现同样也很难解释衰退假说,因为记忆表征的衰退应该只取决任务处理进程中刷新延迟的时间,而不取决于任务处理的内容。'''<font color="#ff8000">衰退假说 decay theories</font>'''的另一个问题来自于延迟回忆字母列表的实验——通过要求参与者以较慢的速度回忆或在回忆每个字母的间隔说一个不相关单词一至三次来实现延迟效果。但延迟回忆对回忆准确率几乎没有影响<ref>{{Cite journal|doi=10.3758/BF03196705|vauthors=Lewandowsky S, Duncan M, Brown GD |title=Time does not cause forgetting in short-term serial recall |journal=Psychonomic Bulletin & Review |volume=11 |issue=5 |pages=771–90 |date=October 2004 |pmid=15732687 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=15732687|doi-access=free }}</ref><ref>{{Cite journal|vauthors=Oberauer K, Lewandowsky S |title=Forgetting in immediate serial recall: decay, temporal distinctiveness, or interference? |journal=Psychological Review |volume=115 |issue=3 |pages=544–76 |date=July 2008 |pmid=18729591 |doi=10.1037/0033-295X.115.3.544|url=https://api.research-repository.uwa.edu.au/files/1546099/11204_PID11204.pdf }}</ref>。'''<font color="#ff8000">干扰理论 interference theories</font>'''似乎最好地解释了为何记忆内容相似或并发进程内容相似就会造成记忆效果减损。材料越相似就越容易混淆,进而引起检索竞争。<br />
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== 发展 Development ==<br />
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The capacity of working memory increases gradually over childhood<ref name="ReferenceA">{{cite journal | doi = 10.1037/0012-1649.40.2.177 | last1 = Gathercole | first1 = S. E. | last2 = Pickering | first2 = S. J. | last3 = Ambridge | first3 = B. | last4 = Wearing | first4 = H. | year = 2004 | title = The structure of working memory from 4 to 15 years of age | journal = Developmental Psychology | volume = 40 | issue = 2| pages = 177–190 | pmid = 14979759 | citeseerx = 10.1.1.529.2727 }}</ref> and declines gradually in old age.<ref>{{cite journal | doi = 10.1037/0894-4105.8.4.535 | last1 = Salthouse | first1 = T. A. | year = 1994 | title = The aging of working memory | journal = Neuropsychology | volume = 8 | issue = 4| pages = 535–543 }}</ref><br />
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The capacity of working memory increases gradually over childhood and declines gradually in old age.<br />
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工作记忆的容量在儿童时期逐渐增加,在老年时期逐渐下降<ref name="ReferenceA">{{cite journal | doi = 10.1037/0012-1649.40.2.177 | last1 = Gathercole | first1 = S. E. | last2 = Pickering | first2 = S. J. | last3 = Ambridge | first3 = B. | last4 = Wearing | first4 = H. | year = 2004 | title = The structure of working memory from 4 to 15 years of age | journal = Developmental Psychology | volume = 40 | issue = 2| pages = 177–190 | pmid = 14979759 | citeseerx = 10.1.1.529.2727 }}</ref> and declines gradually in old age.<ref>{{cite journal | doi = 10.1037/0894-4105.8.4.535 | last1 = Salthouse | first1 = T. A. | year = 1994 | title = The aging of working memory | journal = Neuropsychology | volume = 8 | issue = 4| pages = 535–543 }}</ref>。<br />
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=== 儿童期 Childhood ===<br />
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{{Main|Neo-Piagetian theories of cognitive development}}<br />
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Measures of performance on tests of working memory increase continuously between early childhood and adolescence, while the structure of correlations between different tests remains largely constant. theorists have argued that the growth of working-memory capacity is a major driving force of cognitive development. This hypothesis has received substantial empirical support from studies showing that the capacity of working memory is a strong predictor of cognitive abilities in childhood.<ref>Jarrold, C., & Bayliss, D. M. (2007). Variation in working memory due to typical and atypical development. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake & J. N. Towse (Eds.), Variation in working memory (pp. 137–161). New York: Oxford University Press.</ref> Particularly strong evidence for a role of working memory for development comes from a longitudinal study showing that working-memory capacity at one age predicts reasoning ability at a later age.<ref>{{cite journal | doi = 10.1111/j.1467-9280.2007.01895.x | last1 = Kail | first1 = R. | year = 2007 | title = Longitudinal evidence that increases in processing speed and working memory enhance children's reasoning | journal = Psychological Science | volume = 18 | issue = 4| pages = 312–313 | pmid = 17470254 }}</ref> Studies in the Neo-Piagetian tradition have added to this picture by analyzing the complexity of cognitive tasks in terms of the number of items or relations that have to be considered simultaneously for a solution. Across a broad range of tasks, children manage task versions of the same level of complexity at about the same age, consistent with the view that working memory capacity limits the complexity they can handle at a given age.<ref>{{cite journal | doi = 10.1016/S0010-0285(02)00002-6 | last1 = Andrews | first1 = G. | last2 = Halford | first2 = G. S. | year = 2002 | title = A cognitive complexity metric applied to cognitive development | journal = Cognitive Psychology | volume = 45 | issue = 2| pages = 153–219 | pmid = 12528901 }}</ref> Although neuroscience studies support the notion that children rely on prefrontal cortex for performing various working memory tasks, an [[fMRI]] meta-analysis on children compared to adults performing the n back task revealed lack of consistent prefrontal cortex activation in children, while posterior regions including the [[insular cortex]] and [[cerebellum]] remain intact.<ref name= "cf">Yaple, Z., Arsalidou, M (2018). N-back working memory task: Meta-analysis of normative fMRI studies with children, Child Development, 89(6), 2010-2022.</ref><br />
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Measures of performance on tests of working memory increase continuously between early childhood and adolescence, while the structure of correlations between different tests remains largely constant. theorists have argued that the growth of working-memory capacity is a major driving force of cognitive development. This hypothesis has received substantial empirical support from studies showing that the capacity of working memory is a strong predictor of cognitive abilities in childhood. Particularly strong evidence for a role of working memory for development comes from a longitudinal study showing that working-memory capacity at one age predicts reasoning ability at a later age. Studies in the Neo-Piagetian tradition have added to this picture by analyzing the complexity of cognitive tasks in terms of the number of items or relations that have to be considered simultaneously for a solution. Across a broad range of tasks, children manage task versions of the same level of complexity at about the same age, consistent with the view that working memory capacity limits the complexity they can handle at a given age. Although neuroscience studies support the notion that children rely on prefrontal cortex for performing various working memory tasks, an fMRI meta-analysis on children compared to adults performing the n back task revealed lack of consistent prefrontal cortex activation in children, while posterior regions including the insular cortex and cerebellum remain intact.<br />
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从儿童到青少年这段时间里,人们在针对工作记忆的测试中表现会越来越好,而不同测试之间的相关性结构基本保持不变。理论学者认为工作记忆容量的增长是认知发展的主要驱动力之一。这一假设得到了大量研究的支持,研究表明工作记忆能力是童年认知能力的一个强预测因子<ref>Jarrold, C., & Bayliss, D. M. (2007). Variation in working memory due to typical and atypical development. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake & J. N. Towse (Eds.), Variation in working memory (pp. 137–161). New York: Oxford University Press.</ref>。工作记忆对认知发展起作用的有力证明来自一项追踪研究。该研究表明,根据人在某一年龄上的工作记忆能力可以预测其之后的推理能力<ref>{{cite journal | doi = 10.1111/j.1467-9280.2007.01895.x | last1 = Kail | first1 = R. | year = 2007 | title = Longitudinal evidence that increases in processing speed and working memory enhance children's reasoning | journal = Psychological Science | volume = 18 | issue = 4| pages = 312–313 | pmid = 17470254 }}</ref>。 对新皮亚杰传统的的研究也支持了这一观点。该研究分析了认知任务复杂性(情境下需要同时考虑的项目及关系的数量)的问题。在一系列任务之中,相同年龄段的儿童可处理难度近似的任务,这与特定年龄下的工作记忆容量会限制人能够处理的问题的复杂度的观点一致<ref>{{cite journal | doi = 10.1016/S0010-0285(02)00002-6 | last1 = Andrews | first1 = G. | last2 = Halford | first2 = G. S. | year = 2002 | title = A cognitive complexity metric applied to cognitive development | journal = Cognitive Psychology | volume = 45 | issue = 2| pages = 153–219 | pmid = 12528901 }}</ref>。虽然神经科学研究认为儿童依靠脑前额叶皮层来完成各种工作记忆任务,但一项功能性磁共振成象元在分析对比了儿童和成人在n back任务中的表现之后,发现儿童相对来说较难做到持续激活脑前额叶皮层,反而是后部区域包括到叶皮质和小脑都表现正常<ref name= "cf">Yaple, Z., Arsalidou, M (2018). N-back working memory task: Meta-analysis of normative fMRI studies with children, Child Development, 89(6), 2010-2022.</ref>。<br />
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=== 老化 Aging ===<br />
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Working memory is among the cognitive functions most sensitive to decline in [[old age]].<ref name="Hertzog 2003">{{cite journal |vauthors=Hertzog C, Dixon RA, Hultsch DF, MacDonald SW |title=Latent change models of adult cognition: are changes in processing speed and working memory associated with changes in episodic memory? |journal=Psychol Aging |volume=18 |issue=4 |pages=755–69 |date=December 2003 |pmid=14692862 |doi=10.1037/0882-7974.18.4.755 }}</ref><ref name="Park, D. C. 2002">{{cite journal |vauthors=Park DC, Lautenschlager G, Hedden T, Davidson NS, Smith AD, Smith PK |title=Models of visuospatial and verbal memory across the adult life span |journal=Psychol Aging |volume=17 |issue=2 |pages=299–320 |date=June 2002 |pmid=12061414 |doi= 10.1037/0882-7974.17.2.299 }}</ref> Several explanations have been offered for this decline in psychology. One is the processing speed theory of cognitive aging by Tim Salthouse.<ref>{{cite journal | doi = 10.1037/0033-295X.103.3.403 | last1 = Salthouse | first1 = T. A. | year = 1996 | title = The processing speed theory of adult age differences in cognition | journal = Psychological Review | volume = 103 | issue = 3| pages = 403–428 | pmid = 8759042 | citeseerx = 10.1.1.464.585 }}</ref> Drawing on the finding of general slowing of cognitive processes as people grow older, Salthouse argues that slower processing leaves more time for working-memory contents to decay, thus reducing effective capacity. However, the decline of working-memory capacity cannot be entirely attributed to slowing because capacity declines more in old age than speed.<ref name="Park, D. C. 2002" /><ref>{{cite journal | doi = 10.1016/0010-0277(95)00689-3 | last1 = Mayr | first1 = U. | last2 = Kliegl | first2 = R. | last3 = Krampe | first3 = R. T. | year = 1996 | title = Sequential and coordinative processing dynamics in figural transformation across the life span | journal = Cognition | volume = 59 | issue = 1| pages = 61–90 | pmid = 8857471 }}</ref> Another proposal is the inhibition hypothesis advanced by [[Lynn Hasher]] and Rose Zacks.<ref>Hasher, L., & Zacks, R.&nbsp;T. (1988). Working memory, comprehension, and aging: A review and new view. In G. H. Bower (Ed.), ''The psychology of learning and motivation'', ''Vol. 22'', (pp. 193–225). New York: Academic Press.</ref> This theory assumes a general deficit in old age in the ability to inhibit irrelevant, or no-longer relevant, information. Therefore, working memory tends to be cluttered with irrelevant contents that reduce the effective capacity for relevant content. The assumption of an inhibition deficit in old age has received much empirical support<ref>Hasher, L., Zacks, R.&nbsp;T., & May, C.&nbsp;P. (1999). Inhibitory control, circadian arousal, and age. In D.&nbsp;Gopher & A.&nbsp;Koriat (Eds.), ''Attention and Performance'' (pp. 653–675). Cambridge, MA: MIT Press.</ref> but, so far, it is not clear whether the decline in inhibitory ability fully explains the decline of working-memory capacity. An explanation on the neural level of the decline of working memory and other cognitive functions in old age has been proposed by West.<ref>{{cite journal | doi = 10.1037/0033-2909.120.2.272 | last1 = West | first1 = R.&nbsp;L. | year = 1996 | title = An application of prefrontal cortex function theory to cognitive aging | journal = Psychological Bulletin | volume = 120 | issue = 2| pages = 272–292 | pmid = 8831298 }}</ref> She argued that working memory depends to a large degree on the [[pre-frontal cortex]], which deteriorates more than other brain regions as we grow old. Age related decline in working memory can be briefly reversed using low intensity transcranial stimulation, synchronizing rhythms in bilateral frontal and left temporal lobe areas.<ref>{{Cite news|url=https://www.theguardian.com/science/2019/apr/08/scientists-use-electrical-pulses-reverse-memory-decline-ageing|title=Scientists reverse memory decline using electrical pulses|last=Devlin, H.|date=2019-04-08|work=The Guardian|access-date=2019-04-09|language=en-GB|issn=0261-3077}}</ref><br />
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Working memory is among the cognitive functions most sensitive to decline in old age. Several explanations have been offered for this decline in psychology. One is the processing speed theory of cognitive aging by Tim Salthouse. Drawing on the finding of general slowing of cognitive processes as people grow older, Salthouse argues that slower processing leaves more time for working-memory contents to decay, thus reducing effective capacity. However, the decline of working-memory capacity cannot be entirely attributed to slowing because capacity declines more in old age than speed. Another proposal is the inhibition hypothesis advanced by Lynn Hasher and Rose Zacks. This theory assumes a general deficit in old age in the ability to inhibit irrelevant, or no-longer relevant, information. Therefore, working memory tends to be cluttered with irrelevant contents that reduce the effective capacity for relevant content. The assumption of an inhibition deficit in old age has received much empirical support but, so far, it is not clear whether the decline in inhibitory ability fully explains the decline of working-memory capacity. An explanation on the neural level of the decline of working memory and other cognitive functions in old age has been proposed by West. She argued that working memory depends to a large degree on the pre-frontal cortex, which deteriorates more than other brain regions as we grow old. Age related decline in working memory can be briefly reversed using low intensity transcranial stimulation, synchronizing rhythms in bilateral frontal and left temporal lobe areas.<br />
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人进入老年期后,一系列认知功能都会有所衰退,其中最严重的就是工作记忆<ref name="Hertzog 2003">{{cite journal |vauthors=Hertzog C, Dixon RA, Hultsch DF, MacDonald SW |title=Latent change models of adult cognition: are changes in processing speed and working memory associated with changes in episodic memory? |journal=Psychol Aging |volume=18 |issue=4 |pages=755–69 |date=December 2003 |pmid=14692862 |doi=10.1037/0882-7974.18.4.755 }}</ref><ref name="Park, D. C. 2002">{{cite journal |vauthors=Park DC, Lautenschlager G, Hedden T, Davidson NS, Smith AD, Smith PK |title=Models of visuospatial and verbal memory across the adult life span |journal=Psychol Aging |volume=17 |issue=2 |pages=299–320 |date=June 2002 |pmid=12061414 |doi= 10.1037/0882-7974.17.2.299 }}</ref>。心理学对此有几种解释。一个是提姆 · 萨尔特豪斯 Tim Salthouse 提出的关于认知老化的'''<font color="#ff8000">加工速度理论 processing speed theory</font>'''<ref>{{cite journal | doi = 10.1037/0033-295X.103.3.403 | last1 = Salthouse | first1 = T. A. | year = 1996 | title = The processing speed theory of adult age differences in cognition | journal = Psychological Review | volume = 103 | issue = 3| pages = 403–428 | pmid = 8759042 | citeseerx = 10.1.1.464.585 }}</ref>。普遍而言,人的认知过程随着年龄增长而滞缓。所以Salthouse 认为工作记忆会有更多的衰减机会,从而使其有效容量降低。然而,工作记忆容量的下降不能完全归因于此,因为老年时期记忆容量的下降速度比速度本身下降的更快<ref name="Park, D. C. 2002" /><ref>{{cite journal | doi = 10.1016/0010-0277(95)00689-3 | last1 = Mayr | first1 = U. | last2 = Kliegl | first2 = R. | last3 = Krampe | first3 = R. T. | year = 1996 | title = Sequential and coordinative processing dynamics in figural transformation across the life span | journal = Cognition | volume = 59 | issue = 1| pages = 61–90 | pmid = 8857471 }}</ref>。另一个是琳恩·哈什尔 Lynn Hasher 和 罗丝·扎克 Rose Zacks 提出的'''<font color="#ff8000">抑制假说 inhibition hypothesis</font>'''<ref>Hasher, L., & Zacks, R.&nbsp;T. (1988). Working memory, comprehension, and aging: A review and new view. In G. H. Bower (Ed.), ''The psychology of learning and motivation'', ''Vol. 22'', (pp. 193–225). New York: Academic Press.</ref>。该理论假设老年人排除不相关信息的能力不足。因此,工作记忆往往会被不相关内容所干扰,从而降低记忆内容的有效容量。老年抑制能力缺失的假设得到了大量研究的支持<ref>Hasher, L., Zacks, R.&nbsp;T., & May, C.&nbsp;P. (1999). Inhibitory control, circadian arousal, and age. In D.&nbsp;Gopher & A.&nbsp;Koriat (Eds.), ''Attention and Performance'' (pp. 653–675). Cambridge, MA: MIT Press.</ref>,但抑制能力的下降能否完全解释为何工作记忆能力下降,目前为止还不清楚。韦斯特 West对老年工作记忆及其他认知功能的衰退则提出了一种神经层面的解释<ref>{{cite journal | doi = 10.1037/0033-2909.120.2.272 | last1 = West | first1 = R.&nbsp;L. | year = 1996 | title = An application of prefrontal cortex function theory to cognitive aging | journal = Psychological Bulletin | volume = 120 | issue = 2| pages = 272–292 | pmid = 8831298 }}</ref>。她认为前额叶皮层对工作记忆有着很大的影响,而随着年龄的增长,前额叶皮与其他大脑区域相比更容易衰退。由衰老引发的工作记忆衰退可通过低强度经颅刺激同步化额叶或左侧颞叶节律来短期逆转<ref>{{Cite news|url=https://www.theguardian.com/science/2019/apr/08/scientists-use-electrical-pulses-reverse-memory-decline-ageing|title=Scientists reverse memory decline using electrical pulses|last=Devlin, H.|date=2019-04-08|work=The Guardian|access-date=2019-04-09|language=en-GB|issn=0261-3077}}</ref>。<br />
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== 训练 Training ==<br />
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{{further|Working memory training|Neurobiological effects of physical exercise#Cognitive control and memory}}<br />
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Torkel Klingberg was the first to investigate whether intensive training of working memory has beneficial effects on other cognitive functions. His pioneering study suggested that working memory can be improved by training in ADHD patients through computerized programs.<ref>{{Cite journal|author=Klingberg, T.|author2=Forssberg, H.|author3=Westerberg, H. |title=Training of working memory in children with ADHD |journal=Journal of Clinical and Experimental Neuropsychology |volume=24 |issue=6 |pages=781–91 |date=September 2002 |pmid=12424652 |doi=10.1076/jcen.24.6.781.8395|citeseerx=10.1.1.326.5165}}</ref> This study has found that a period of [[working memory training]] increases a range of cognitive abilities and increases IQ test scores. Another study of the same group<ref>{{Cite journal|date=January 2004|title=Increased prefrontal and parietal activity after training of working memory|journal=Nature Neuroscience|volume=7|issue=1|pages=75–9|doi=10.1038/nn1165|pmid=14699419|vauthors=Olesen PJ, Westerberg H, Klingberg T}}</ref> has shown that, after training, measured brain activity related to working memory increased in the prefrontal cortex, an area that many researchers have associated with working memory functions. It has been shown in one study that working memory training increases the density of [[prefrontal cortex|prefrontal]] and [[parietal cortex|parietal]] [[dopamine receptor]]s (specifically, [[DRD1]]) in test persons.<ref>{{Cite journal|date=February 2009|title=Changes in cortical dopamine D1 receptor binding associated with cognitive training|journal=Science|volume=323|issue=5915|pages=800–2|bibcode=2009Sci...323..800M|doi=10.1126/science.1166102|pmid=19197069|author=McNab, F.|author2=Varrone, A.|author3=Farde, L.|display-authors=etal}}</ref> However, subsequent work with the same training program has failed to replicate the beneficial effects of training on cognitive performance. A meta-analytic summary of research with Klingberg's training program up to 2011 shows that this training has at best a negligible effect on tests of intelligence and of attention<ref>{{Cite journal|last=Hulme, C. & Melby-Lervåg, M.|year=2012|title=Current evidence does not support the claims made for CogMed working memory training|journal=Journal of Applied Research in Memory and Cognition|volume=1|issue=3|pages=197–200|doi=10.1016/j.jarmac.2012.06.006}}</ref>.<br />
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Torkel Klingberg was the first to investigate whether intensive training of working memory has beneficial effects on other cognitive functions. His pioneering study suggested that working memory can be improved by training in ADHD patients through computerized programs. This study has found that a period of working memory training increases a range of cognitive abilities and increases IQ test scores. Another study of the same group has shown that, after training, measured brain activity related to working memory increased in the prefrontal cortex, an area that many researchers have associated with working memory functions. It has been shown in one study that working memory training increases the density of prefrontal and parietal dopamine receptors (specifically, DRD1) in test persons. However, subsequent work with the same training program has failed to replicate the beneficial effects of training on cognitive performance. A meta-analytic summary of research with Klingberg's training program up to 2011 shows that this training has at best a negligible effect on tests of intelligence and of attention.<br />
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托克尔 · 克林伯格 Torkel Klingberg 是第一个研究工作记忆强化训练是否对其他认知功能有益的人。他实施的开创性研究表明ADHD患者在经过电脑程序训练后工作记忆得到改善<ref>{{Cite journal|author=Klingberg, T.|author2=Forssberg, H.|author3=Westerberg, H. |title=Training of working memory in children with ADHD |journal=Journal of Clinical and Experimental Neuropsychology |volume=24 |issue=6 |pages=781–91 |date=September 2002 |pmid=12424652 |doi=10.1076/jcen.24.6.781.8395|citeseerx=10.1.1.326.5165}}</ref>。该研究发现,'''<font color="#ff8000">工作记忆训练 Working Memory Training</font>'''可以提高人的一系列认知能力及 IQ 测试成绩。针对同一群体的另一项研究<ref>{{Cite journal|date=January 2004|title=Increased prefrontal and parietal activity after training of working memory|journal=Nature Neuroscience|volume=7|issue=1|pages=75–9|doi=10.1038/nn1165|pmid=14699419|vauthors=Olesen PJ, Westerberg H, Klingberg T}}</ref>表明,训练之后脑前额叶外皮层——被许多研究人员认为与工作记忆功能相关——的大脑活动测度有所增加。还有一项研究表明,工作记忆训练能增加受试者前额叶和顶叶多巴胺受体(特别是 DRD1)的密度<ref>{{Cite journal|date=February 2009|title=Changes in cortical dopamine D1 receptor binding associated with cognitive training|journal=Science|volume=323|issue=5915|pages=800–2|bibcode=2009Sci...323..800M|doi=10.1126/science.1166102|pmid=19197069|author=McNab, F.|author2=Varrone, A.|author3=Farde, L.|display-authors=etal}}</ref>。然而,同一训练方案的后续工作却未能再现这些有益影响。一份荟萃分析报告显示,持续至2011年的Klingberg 训练对智力和注意力的提升只有微乎其微的影响<ref>{{Cite journal|last=Hulme, C. & Melby-Lervåg, M.|year=2012|title=Current evidence does not support the claims made for CogMed working memory training|journal=Journal of Applied Research in Memory and Cognition|volume=1|issue=3|pages=197–200|doi=10.1016/j.jarmac.2012.06.006}}</ref>。<br />
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In another influential study, training with a working memory task (the dual [[n-back]] task) has improved performance on a fluid [[intelligence test]] in healthy young adults.<ref>{{Cite journal|author=Jaeggi, S.M.|author2=Buschkuehl, M.|author3= Jonides, J.|author4=Perrig, W. J.|title=Improving fluid intelligence with training on working memory |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=105 |issue=19 |pages=6829–33 |date=May 2008 |pmid=18443283 |pmc=2383929 |doi=10.1073/pnas.0801268105|bibcode=2008PNAS..105.6829J }}</ref> The improvement of fluid intelligence by training with the n-back task was replicated in 2010,<ref name="JaeggiStuder-Luethi2010">{{cite journal| last1=Jaeggi| first1=Susanne M.| last2=Studer-Luethi| first2=Barbara| last3=Buschkuehl|first3=Martin| last4=Su|first4=Yi-Fen|last5=Jonides|first5=John|last6=Perrig|first6=Walter J.|title=The relationship between n-back performance and matrix reasoning – implications for training and transfer|journal=Intelligence|volume=38|issue=6|year=2010|pages=625–635|issn=0160-2896|doi=10.1016/j.intell.2010.09.001}}</ref> but two studies published in 2012 failed to reproduce the effect.<ref name="RedickShipstead2013">{{cite journal|last1=Redick|first1=Thomas S.| last2=Shipstead| first2=Zach|last3=Harrison|first3=Tyler L.|last4=Hicks|first4=Kenny L.|last5=Fried|first5=David E.|last6=Hambrick|first6=David Z.|last7=Kane|first7=Michael J.|last8=Engle|first8=Randall W.|title=No evidence of intelligence improvement after working memory training: A randomized, placebo-controlled study|journal=Journal of Experimental Psychology: General|volume=142| issue=2|year=2013| pages=359–379| pmid=22708717|issn=1939-2222| doi=10.1037/a0029082}}</ref><ref name="ChooiThompson2012">{{cite journal| last1=Chooi| first1=Weng-Tink| last2=Thompson| first2=Lee A.| title=Working memory training does not improve intelligence in healthy young adults| journal=Intelligence| volume=40|issue=6| year=2012| pages=531–542| issn=0160-2896| doi=10.1016/j.intell.2012.07.004}}</ref> The combined evidence from about 30 experimental studies on the effectiveness of working-memory training has been evaluated by several meta-analyses.<ref>{{Cite journal|last1=Au|first1=Jacky|last2=Sheehan|first2=Ellen|last3=Tsai|first3=Nancy|last4=Duncan|first4=Greg J.|last5=Buschkuehl|first5=Martin|last6=Jaeggi|first6=Susanne M.|date=2014-08-08|title=Improving fluid intelligence with training on working memory: a meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=22|issue=2|pages=366–377|doi=10.3758/s13423-014-0699-x|pmid=25102926|issn=1069-9384|url=http://www.escholarship.org/uc/item/1mj701dj|type=Submitted manuscript}}</ref><ref>{{Cite journal|last1=Melby-Lervåg|first1=Monica|last2=Redick|first2=Thomas S.|last3=Hulme|first3=Charles|date=2016-07-29|title=Working Memory Training Does Not Improve Performance on Measures of Intelligence or Other Measures of "Far Transfer"|journal=Perspectives on Psychological Science|language=en|volume=11|issue=4|pages=512–534|doi=10.1177/1745691616635612|pmc=4968033|pmid=27474138}}</ref> The authors of these meta-analyses disagree in their conclusions as to whether or not working-memory training improves intelligence. Yet, these meta-analyses agree in their estimate of the size of the effect of working-memory training: If there is such an effect, it is likely to be small.<br />
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In another influential study, training with a working memory task (the dual n-back task) has improved performance on a fluid intelligence test in healthy young adults. The improvement of fluid intelligence by training with the n-back task was replicated in 2010, but two studies published in 2012 failed to reproduce the effect. The combined evidence from about 30 experimental studies on the effectiveness of working-memory training has been evaluated by several meta-analyses. The authors of these meta-analyses disagree in their conclusions as to whether or not working-memory training improves intelligence. Yet, these meta-analyses agree in their estimate of the size of the effect of working-memory training: If there is such an effect, it is likely to be small.<br />
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在另一项有影响力的研究中,工作记忆('''<font color="#ff8000">双 n-back 任务 The Dual n-back Task)</font>'''训练使健康青年在流体智力测试中的表现有所提升<ref>{{Cite journal|author=Jaeggi, S.M.|author2=Buschkuehl, M.|author3= Jonides, J.|author4=Perrig, W. J.|title=Improving fluid intelligence with training on working memory |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=105 |issue=19 |pages=6829–33 |date=May 2008 |pmid=18443283 |pmc=2383929 |doi=10.1073/pnas.0801268105|bibcode=2008PNAS..105.6829J }}</ref>。2010年时,通过 n-back 任务训练提高流体智力的实验被再次实施<ref name="JaeggiStuder-Luethi2010">{{cite journal| last1=Jaeggi| first1=Susanne M.| last2=Studer-Luethi| first2=Barbara| last3=Buschkuehl|first3=Martin| last4=Su|first4=Yi-Fen|last5=Jonides|first5=John|last6=Perrig|first6=Walter J.|title=The relationship between n-back performance and matrix reasoning – implications for training and transfer|journal=Intelligence|volume=38|issue=6|year=2010|pages=625–635|issn=0160-2896|doi=10.1016/j.intell.2010.09.001}}</ref>,但2012年发表的两项研究未能重现那一结果<ref name="RedickShipstead2013">{{cite journal|last1=Redick|first1=Thomas S.| last2=Shipstead| first2=Zach|last3=Harrison|first3=Tyler L.|last4=Hicks|first4=Kenny L.|last5=Fried|first5=David E.|last6=Hambrick|first6=David Z.|last7=Kane|first7=Michael J.|last8=Engle|first8=Randall W.|title=No evidence of intelligence improvement after working memory training: A randomized, placebo-controlled study|journal=Journal of Experimental Psychology: General|volume=142| issue=2|year=2013| pages=359–379| pmid=22708717|issn=1939-2222| doi=10.1037/a0029082}}</ref><ref name="ChooiThompson2012">{{cite journal| last1=Chooi| first1=Weng-Tink| last2=Thompson| first2=Lee A.| title=Working memory training does not improve intelligence in healthy young adults| journal=Intelligence| volume=40|issue=6| year=2012| pages=531–542| issn=0160-2896| doi=10.1016/j.intell.2012.07.004}}</ref>。在运用元分析对约30个关于工作记忆训练有效性的研究进行评估之后<ref>{{Cite journal|last1=Au|first1=Jacky|last2=Sheehan|first2=Ellen|last3=Tsai|first3=Nancy|last4=Duncan|first4=Greg J.|last5=Buschkuehl|first5=Martin|last6=Jaeggi|first6=Susanne M.|date=2014-08-08|title=Improving fluid intelligence with training on working memory: a meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=22|issue=2|pages=366–377|doi=10.3758/s13423-014-0699-x|pmid=25102926|issn=1069-9384|url=http://www.escholarship.org/uc/item/1mj701dj|type=Submitted manuscript}}</ref><ref>{{Cite journal|last1=Melby-Lervåg|first1=Monica|last2=Redick|first2=Thomas S.|last3=Hulme|first3=Charles|date=2016-07-29|title=Working Memory Training Does Not Improve Performance on Measures of Intelligence or Other Measures of "Far Transfer"|journal=Perspectives on Psychological Science|language=en|volume=11|issue=4|pages=512–534|doi=10.1177/1745691616635612|pmc=4968033|pmid=27474138}}</ref>,分析者并不认为训练可以提高智力。不过,这些元分析在某点上达成了一致: 训练大概率只会有很微弱的影响。<br />
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== 脑内 In the brain ==<br />
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=== 信息维持的神经机制 Neural mechanisms of maintaining information ===<br />
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The first insights into the neuronal and neurotransmitter basis of working memory came from animal research. The work of Jacobsen<ref>{{Cite journal|author=Jacobsen CF|title= Studies of cerebral function in primates |journal=Comparative Psychology Monographs |volume=13 |issue=3 |pages=1–68 |year=1938 |oclc=250695441 }}</ref> and Fulton in the 1930s first showed that lesions to the PFC impaired spatial working memory performance in monkeys. The later work of [[Joaquin Fuster]]<ref>{{Cite journal|author=Fuster JM |title=Unit activity in prefrontal cortex during delayed-response performance: neuronal correlates of transient memory |journal=Journal of Neurophysiology |volume=36 |issue=1 |pages=61–78 |date=January 1973 |pmid=4196203 |doi=10.1152/jn.1973.36.1.61 }}</ref> recorded the electrical activity of neurons in the PFC of monkeys while they were doing a delayed matching task. In that task, the monkey sees how the experimenter places a bit of food under one of two identical-looking cups. A shutter is then lowered for a variable delay period, screening off the cups from the monkey's view. After the delay, the shutter opens and the monkey is allowed to retrieve the food from under the cups. Successful retrieval in the first attempt – something the animal can achieve after some training on the task – requires holding the location of the food in memory over the delay period. Fuster found neurons in the PFC that fired mostly during the delay period, suggesting that they were involved in representing the food location while it was invisible. Later research has shown similar delay-active neurons also in the posterior [[parietal cortex]], the [[thalamus]], the [[Caudate nucleus|caudate]], and the [[globus pallidus]].<ref>{{Cite journal|vauthors=Ashby FG, Ell SW, Valentin VV, Casale MB |title=FROST: a distributed neurocomputational model of working memory maintenance |journal=Journal of Cognitive Neuroscience |volume=17 |issue=11 |pages=1728–43 |date=November 2005 |pmid=16269109 |doi=10.1162/089892905774589271|citeseerx=10.1.1.456.7179 }}</ref> The work of [[Patricia Goldman-Rakic|Goldman-Rakic]] and others showed that principal sulcal, dorsolateral PFC interconnects with all of these brain regions, and that neuronal microcircuits within PFC are able to maintain information in working memory through recurrent excitatory glutamate networks of pyramidal cells that continue to fire throughout the delay period.<ref>{{Cite journal|author=Goldman-Rakic PS|title= Cellular basis of working memory |journal=Neuron |volume=14 |issue= 3 |pages=447–485 |year=1995 | pmid = 7695894 | doi = 10.1016/0896-6273(95)90304-6 }}</ref> These circuits are tuned by lateral inhibition from GABAergic interneurons.<ref>{{Cite journal|vauthors=Rao SG, Williams GV, Goldman-Rakic PS |title= Destruction and creation of spatial tuning by disinhibition: GABA(A) blockade of prefrontal cortical neurons engaged by working memory |journal=Journal of Neuroscience |volume=20 |pages=485–494 |year=2000|pmid=10627624 |pmc= 6774140 |issue=1|doi= 10.1523/JNEUROSCI.20-01-00485.2000 }}</ref> The neuromodulatory arousal systems markedly alter PFC working memory function; for example, either too little or too much dopamine or norepinephrine impairs PFC network firing<ref>{{Cite journal|doi=10.1016/j.tics.2010.05.003|author1=Arnsten AFT |author2=Paspalas CD |author3=Gamo NJ |author4=Y. Y |author5=Wang M |title= Dynamic Network Connectivity: A new form of neuroplasticity|journal=Trends in Cognitive Sciences|volume=14 |pages=365–375 |year=2010|issue=8|pmid=20554470|pmc=2914830}}</ref> and working memory performance.<ref>{{Cite journal|doi=10.1146/annurev.neuro.051508.135535|vauthors=Robbins TW, Arnsten AF |title= The neuropsychopharmacology of fronto-executive function: monoaminergic modulation |journal=Annu Rev Neurosci|volume=32 |pages=267–287 |year=2009|pmid=19555290|pmc=2863127}}</ref><br />
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The first insights into the neuronal and neurotransmitter basis of working memory came from animal research. The work of Jacobsen and Fulton in the 1930s first showed that lesions to the PFC impaired spatial working memory performance in monkeys. The later work of Joaquin Fuster recorded the electrical activity of neurons in the PFC of monkeys while they were doing a delayed matching task. In that task, the monkey sees how the experimenter places a bit of food under one of two identical-looking cups. A shutter is then lowered for a variable delay period, screening off the cups from the monkey's view. After the delay, the shutter opens and the monkey is allowed to retrieve the food from under the cups. Successful retrieval in the first attempt – something the animal can achieve after some training on the task – requires holding the location of the food in memory over the delay period. Fuster found neurons in the PFC that fired mostly during the delay period, suggesting that they were involved in representing the food location while it was invisible. Later research has shown similar delay-active neurons also in the posterior parietal cortex, the thalamus, the caudate, and the globus pallidus. The work of Goldman-Rakic and others showed that principal sulcal, dorsolateral PFC interconnects with all of these brain regions, and that neuronal microcircuits within PFC are able to maintain information in working memory through recurrent excitatory glutamate networks of pyramidal cells that continue to fire throughout the delay period. These circuits are tuned by lateral inhibition from GABAergic interneurons. The neuromodulatory arousal systems markedly alter PFC working memory function; for example, either too little or too much dopamine or norepinephrine impairs PFC network firing and working memory performance.<br />
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最初,关于工作记忆神经元和神经递质基础的见解来自于对动物的研究。20世纪30年代,雅各布森 Jacobsen <ref>{{Cite journal|author=Jacobsen CF|title= Studies of cerebral function in primates |journal=Comparative Psychology Monographs |volume=13 |issue=3 |pages=1–68 |year=1938 |oclc=250695441 }}</ref>和富尔顿 Fulton在研究中首次证明了猴子的空间工作记忆能力会因PFC而减损。华金 · 福斯特 Joaquin Fuster <ref>{{Cite journal|author=Fuster JM |title=Unit activity in prefrontal cortex during delayed-response performance: neuronal correlates of transient memory |journal=Journal of Neurophysiology |volume=36 |issue=1 |pages=61–78 |date=January 1973 |pmid=4196203 |doi=10.1152/jn.1973.36.1.61 }}</ref>的后续工作记录了猴子在完成延迟匹配任务时 PFC 中神经元的电活动。在该任务中有两个相同的杯子,猴子看到实验人员把一点食物放在其中一个下面。然后一个挡板降下,暂时挡住猴子看向杯子的视线(延迟变量)。之后挡板打开,允许猴子从杯子下面取出食物。在第一次尝试中它成功地得到了食物——这是动物经过特定训练后应该能够完成的任务——要求动物在延迟期内维持对食物位置的记忆。Fuster发现在延迟期间,PFC中的大部分神经元被激活了,表明它们参与了在隔离期间对食物位置的记忆维持。后来的研究发现后'''<font color="#ff8000">顶叶皮层posterior parietal cortex</font>'''、'''<font color="#ff8000">丘脑thalamus</font>'''、'''<font color="#ff8000">尾状核caudate</font>'''和'''<font color="#ff8000">苍白球globus pallidus</font>'''也有类似的延迟活动神经元。<ref>{{Cite journal|vauthors=Ashby FG, Ell SW, Valentin VV, Casale MB |title=FROST: a distributed neurocomputational model of working memory maintenance |journal=Journal of Cognitive Neuroscience |volume=17 |issue=11 |pages=1728–43 |date=November 2005 |pmid=16269109 |doi=10.1162/089892905774589271|citeseerx=10.1.1.456.7179 }}</ref>高德马・拉齐克 Goldman-Rakic 等人的研究表明,脊髓背外侧的PFC与这些大脑区域相互连接,PFC内的神经元微回路凭借反复兴奋的锥体细胞谷氨酸网络来维持工作记忆中的信息——这些神经元网络在延迟期间是持续激活的<ref>{{Cite journal|author=Goldman-Rakic PS|title= Cellular basis of working memory |journal=Neuron |volume=14 |issue= 3 |pages=447–485 |year=1995 | pmid = 7695894 | doi = 10.1016/0896-6273(95)90304-6 }}</ref>。这些回路由GABA能中间神经元的侧抑制调节<ref>{{Cite journal|vauthors=Rao SG, Williams GV, Goldman-Rakic PS |title= Destruction and creation of spatial tuning by disinhibition: GABA(A) blockade of prefrontal cortical neurons engaged by working memory |journal=Journal of Neuroscience |volume=20 |pages=485–494 |year=2000|pmid=10627624 |pmc= 6774140 |issue=1|doi= 10.1523/JNEUROSCI.20-01-00485.2000 }}</ref>。神经调节性唤起系统对PFC工作记忆功能产生了显著影响; 例如,过多或过少的多巴胺或去甲肾上腺素会减损PFC神经网络放电功能<ref>{{Cite journal|doi=10.1016/j.tics.2010.05.003|author1=Arnsten AFT |author2=Paspalas CD |author3=Gamo NJ |author4=Y. Y |author5=Wang M |title= Dynamic Network Connectivity: A new form of neuroplasticity|journal=Trends in Cognitive Sciences|volume=14 |pages=365–375 |year=2010|issue=8|pmid=20554470|pmc=2914830}}</ref>和工作记忆表现<ref>{{Cite journal|doi=10.1146/annurev.neuro.051508.135535|vauthors=Robbins TW, Arnsten AF |title= The neuropsychopharmacology of fronto-executive function: monoaminergic modulation |journal=Annu Rev Neurosci|volume=32 |pages=267–287 |year=2009|pmid=19555290|pmc=2863127}}</ref>。<br />
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The research described above on persistent firing of certain neurons in the delay period of working memory tasks shows that the brain has a mechanism of keeping representations active without external input. Keeping representations active, however, is not enough if the task demands maintaining more than one chunk of information. In addition, the components and features of each chunk must be bound together to prevent them from being mixed up. For example, if a red triangle and a green square must be remembered at the same time, one must make sure that "red" is bound to "triangle" and "green" is bound to "square". One way of establishing such bindings is by having the neurons that represent features of the same chunk fire in synchrony, and those that represent features belonging to different chunks fire out of sync.<ref>{{Cite journal|date=August 2001|title=A cortical mechanism for binding in visual working memory|journal=Journal of Cognitive Neuroscience|volume=13|issue=6|pages=766–85|doi=10.1162/08989290152541430|pmid=11564321|vauthors=Raffone A, Wolters G}}</ref> In the example, neurons representing redness would fire in synchrony with neurons representing the triangular shape, but out of sync with those representing the square shape. So far, there is no direct evidence that working memory uses this binding mechanism, and other mechanisms have been proposed as well.<ref>{{Cite book|title=The unity of consciousness: Binding, integration, and dissociation|last2=Busby|first2=Richard S.|last3=Soto|first3=Rodolfo|publisher=Oxford University Press|year=2003|isbn=978-0-19-850857-1|location=Oxford|pages=168–90|chapter=Three forms of binding and their neural substrates: Alternatives to temporal synchrony|oclc=50747505|first1=Randall C.|last1=O'Reilly|editor1-first=Axel|editor1-last=Cleeremans|chapterurl=http://psycnet.apa.org/psycinfo/2003-88180-008}}</ref> It has been speculated that synchronous firing of neurons involved in working memory oscillate with frequencies in the [[theta rhythm|theta]] band (4 to 8&nbsp;Hz). Indeed, the power of theta frequency in the EEG increases with working memory load,<ref>{{Cite book|title=Handbook of binding and memory|publisher=Oxford University Press|year=2006|location=Oxford|pages=115–144|chapter=Binding principles in the theta frequency range|last1=Klimesch|first1=W.|editor1-first=H. D.|editor1-last=Zimmer|editor2-first=A.|editor2-last=Mecklinger|editor3-first=U.|editor3-last=Lindenberger}}</ref> and oscillations in the theta band measured over different parts of the skull become more coordinated when the person tries to remember the binding between two components of information.<ref>{{Cite journal|date=May 2007|title=Binding of verbal and spatial information in human working memory involves large-scale neural synchronization at theta frequency|journal=NeuroImage|volume=35|issue=4|pages=1654–62|doi=10.1016/j.neuroimage.2007.02.011|pmid=17379539|vauthors=Wu X, Chen X, Li Z, Han S, Zhang D}}</ref><br />
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The research described above on persistent firing of certain neurons in the delay period of working memory tasks shows that the brain has a mechanism of keeping representations active without external input. Keeping representations active, however, is not enough if the task demands maintaining more than one chunk of information. In addition, the components and features of each chunk must be bound together to prevent them from being mixed up. For example, if a red triangle and a green square must be remembered at the same time, one must make sure that "red" is bound to "triangle" and "green" is bound to "square". One way of establishing such bindings is by having the neurons that represent features of the same chunk fire in synchrony, and those that represent features belonging to different chunks fire out of sync. In the example, neurons representing redness would fire in synchrony with neurons representing the triangular shape, but out of sync with those representing the square shape. So far, there is no direct evidence that working memory uses this binding mechanism, and other mechanisms have been proposed as well. It has been speculated that synchronous firing of neurons involved in working memory oscillate with frequencies in the theta band (4 to 8&nbsp;Hz). Indeed, the power of theta frequency in the EEG increases with working memory load, and oscillations in the theta band measured over different parts of the skull become more coordinated when the person tries to remember the binding between two components of information.<br />
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上述关于工作记忆任务延迟期间某些神经元持续放电的研究表明,大脑有一种机制能使在无外部输入的情况下表征依旧保持活跃。但这不足以应对维护多个信息块的任务。此外,每个组块的组件和特性必须绑定在一起,以防止混淆。例如,如果必须同时记住一个红色三角形和一个绿色正方形,就必须确保“红色”与“三角形”绑定,而“绿色”与“正方形”绑定。实现该目标的一种方法是让表现同一组块特征的神经元同步激活,那些表现不同组块特征的神经元则不同步激活<ref>{{Cite journal|date=August 2001|title=A cortical mechanism for binding in visual working memory|journal=Journal of Cognitive Neuroscience|volume=13|issue=6|pages=766–85|doi=10.1162/08989290152541430|pmid=11564321|vauthors=Raffone A, Wolters G}}</ref>。在这个例子中,代表红色的神经元会与代表三角形的神经元同步激活,与代表正方形的神经元不同步激活。不过目前还没有直接的证据表明工作记忆使用这种结合机制,因此学界也提出了其他一些观点<ref>{{Cite book|title=The unity of consciousness: Binding, integration, and dissociation|last2=Busby|first2=Richard S.|last3=Soto|first3=Rodolfo|publisher=Oxford University Press|year=2003|isbn=978-0-19-850857-1|location=Oxford|pages=168–90|chapter=Three forms of binding and their neural substrates: Alternatives to temporal synchrony|oclc=50747505|first1=Randall C.|last1=O'Reilly|editor1-first=Axel|editor1-last=Cleeremans|chapterurl=http://psycnet.apa.org/psycinfo/2003-88180-008}}</ref>。据推测,工作记忆相关神经元的同步激活是在'''<font color="#ff8000">θ波段 theta band</font>''' (4ー8赫兹)振荡。脑电图θ频率的能量确实随工作记忆负荷的增加而增加<ref>{{Cite book|title=Handbook of binding and memory|publisher=Oxford University Press|year=2006|location=Oxford|pages=115–144|chapter=Binding principles in the theta frequency range|last1=Klimesch|first1=W.|editor1-first=H. D.|editor1-last=Zimmer|editor2-first=A.|editor2-last=Mecklinger|editor3-first=U.|editor3-last=Lindenberger}}</ref>,当受试者试图记住信息的两个组成部分之间的联系时,在头骨不同部位测量到的 θ 波段的振荡变得更加协调<ref>{{Cite journal|date=May 2007|title=Binding of verbal and spatial information in human working memory involves large-scale neural synchronization at theta frequency|journal=NeuroImage|volume=35|issue=4|pages=1654–62|doi=10.1016/j.neuroimage.2007.02.011|pmid=17379539|vauthors=Wu X, Chen X, Li Z, Han S, Zhang D}}</ref>。<br />
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=== 脑内定位 Localization in the brain ===<br />
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Localization of brain functions in humans has become much easier with the advent of [[brain imaging]] methods ([[Positron emission tomography|PET]] and [[fMRI]]). This research has confirmed that areas in the PFC are involved in working memory functions. During the 1990s much debate has centered on the different functions of the ventrolateral (i.e.,&nbsp;lower areas) and the [[Dorsolateral prefrontal cortex|dorsolateral (higher) areas of the PFC]]. A human lesion study provides additional evidence for the role of the [[dorsolateral prefrontal cortex]] in working memory.<ref>{{cite journal|last2=Koenigs|first2=Michael|last3=Grafman|first3=Jordan|year=2013|title=Dorsolateral prefrontal contributions to human working memory|journal=Cortex|volume=49|issue=5|pages=1195–1205|doi=10.1016/j.cortex.2012.05.022|pmid=22789779|last1=Barbey|first1=Aron K.|pmc=3495093}}</ref> One view was that the dorsolateral areas are responsible for spatial working memory and the ventrolateral areas for non-spatial working memory. Another view proposed a functional distinction, arguing that ventrolateral areas are mostly involved in pure maintenance of information, whereas dorsolateral areas are more involved in tasks requiring some processing of the memorized material. The debate is not entirely resolved but most of the evidence supports the functional distinction.<ref>{{Cite journal|author=Owen, A. M.|title=The functional organization of working memory processes within human lateral frontal cortex: the contribution of functional neuroimaging |journal=The European Journal of Neuroscience |volume=9 |issue=7 |pages=1329–39 |date=July 1997 |pmid=9240390 |doi=10.1111/j.1460-9568.1997.tb01487.x}}</ref><br />
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Localization of brain functions in humans has become much easier with the advent of brain imaging methods (PET and fMRI). This research has confirmed that areas in the PFC are involved in working memory functions. During the 1990s much debate has centered on the different functions of the ventrolateral (i.e.,&nbsp;lower areas) and the dorsolateral (higher) areas of the PFC. A human lesion study provides additional evidence for the role of the dorsolateral prefrontal cortex in working memory. One view was that the dorsolateral areas are responsible for spatial working memory and the ventrolateral areas for non-spatial working memory. Another view proposed a functional distinction, arguing that ventrolateral areas are mostly involved in pure maintenance of information, whereas dorsolateral areas are more involved in tasks requiring some processing of the memorized material. The debate is not entirely resolved but most of the evidence supports the functional distinction.<br />
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'''<font color="#ff8000">脑成像brain imaging</font>'''方法(PET和fMRI)的出现让人脑功能定位更加容易。一项研究证实PFC中的一些区域确实影响了工作记忆功能。在20世纪90年代,讨论大多集中在腹外侧区(即较低区域)和背外侧区(较高区域)的不同功能上。一项关于人体损伤的研究为背外侧脑前额叶外皮在工作记忆中发挥作用提供了额外的证据<ref>{{cite journal|last2=Koenigs|first2=Michael|last3=Grafman|first3=Jordan|year=2013|title=Dorsolateral prefrontal contributions to human working memory|journal=Cortex|volume=49|issue=5|pages=1195–1205|doi=10.1016/j.cortex.2012.05.022|pmid=22789779|last1=Barbey|first1=Aron K.|pmc=3495093}}</ref>。一种观点认为,背外侧区负责空间工作记忆,腹外侧区负责非空间工作记忆。另一种观点则是'''<font color="#ff8000">功能区分说functional distinction</font>''',认为腹外侧区域主要负责纯粹的信息维护,而背外侧区域则更倾向于负责记忆材料的处理。虽然分歧并没有彻底解决,但功能区分说还是得到了大多数证据的支持<ref>{{Cite journal|author=Owen, A. M.|title=The functional organization of working memory processes within human lateral frontal cortex: the contribution of functional neuroimaging |journal=The European Journal of Neuroscience |volume=9 |issue=7 |pages=1329–39 |date=July 1997 |pmid=9240390 |doi=10.1111/j.1460-9568.1997.tb01487.x}}</ref>。<br />
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Brain imaging has revealed that working memory functions are not limited to the PFC. A review of numerous studies<ref>{{Cite journal|vauthors=Smith EE, Jonides J |title=Storage and executive processes in the frontal lobes |journal=Science |volume=283 |issue=5408 |pages=1657–61 |date=March 1999 |pmid=10073923 |doi=10.1126/science.283.5408.1657|citeseerx=10.1.1.207.8961 }}</ref> shows areas of activation during working memory tasks scattered over a large part of the cortex. There is a tendency for spatial tasks to recruit more right-hemisphere areas, and for verbal and object working memory to recruit more left-hemisphere areas. The activation during verbal working memory tasks can be broken down into one component reflecting maintenance, in the left posterior parietal cortex, and a component reflecting subvocal rehearsal, in the left frontal cortex (Broca's area, known to be involved in speech production).<ref>{{Cite journal|author=Smith, E. E.|author2=Jonides, J.|author3=Marshuetz, C.|author4=Koeppe, R. A.|title=Components of verbal working memory: evidence from neuroimaging |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=95 |issue=3 |pages=876–82 |date=February 1998 |pmid=9448254 |pmc=33811 |doi=10.1073/pnas.95.3.876|bibcode=1998PNAS...95..876S }}</ref><br />
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Brain imaging has revealed that working memory functions are not limited to the PFC. A review of numerous studies shows areas of activation during working memory tasks scattered over a large part of the cortex. There is a tendency for spatial tasks to recruit more right-hemisphere areas, and for verbal and object working memory to recruit more left-hemisphere areas. The activation during verbal working memory tasks can be broken down into one component reflecting maintenance, in the left posterior parietal cortex, and a component reflecting subvocal rehearsal, in the left frontal cortex (Broca's area, known to be involved in speech production).<br />
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脑成像已经证明工作记忆功能并不局限于PFC。大量研究表明<ref>{{Cite journal|vauthors=Smith EE, Jonides J |title=Storage and executive processes in the frontal lobes |journal=Science |volume=283 |issue=5408 |pages=1657–61 |date=March 1999 |pmid=10073923 |doi=10.1126/science.283.5408.1657|citeseerx=10.1.1.207.8961 }}</ref>,工作记忆任务中的激活区域广泛分布于大脑皮层。其中,空间任务倾向于使用右半球区域,言语和物体工作记忆倾向于使用左半球区域。非文字工作记忆任务中的激活可以分解为在左后顶叶皮层反映维持的组件,以及在左额叶皮层的反映次声练习的组件(已知与语言产生有关的Broca区域)<ref>{{Cite journal|author=Smith, E. E.|author2=Jonides, J.|author3=Marshuetz, C.|author4=Koeppe, R. A.|title=Components of verbal working memory: evidence from neuroimaging |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=95 |issue=3 |pages=876–82 |date=February 1998 |pmid=9448254 |pmc=33811 |doi=10.1073/pnas.95.3.876|bibcode=1998PNAS...95..876S }}</ref><br />
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There is an emerging consensus that most working memory tasks recruit a network of PFC and parietal areas. A study has shown that during a working memory task the connectivity between these areas increases.<ref>{{Cite journal|author=Honey, G. D.|author2=Fu, C. H.|author3=Kim, J.|title=Effects of verbal working memory load on corticocortical connectivity modeled by path analysis of functional magnetic resonance imaging data |journal=NeuroImage |volume=17 |issue=2 |pages=573–82 |date=October 2002 |pmid=12377135 |doi=10.1016/S1053-8119(02)91193-6|display-authors=etal}}</ref> Another study has demonstrated that these areas are necessary for working memory, and not simply activated accidentally during working memory tasks, by temporarily blocking them through [[transcranial magnetic stimulation]] (TMS), thereby producing an impairment in task performance.<ref>{{Cite journal|author=Mottaghy, F. M.|title=Interfering with working memory in humans |journal=Neuroscience |volume=139 |issue=1 |pages=85–90 |date=April 2006 |pmid=16337091 |doi=10.1016/j.neuroscience.2005.05.037}}</ref><br />
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There is an emerging consensus that most working memory tasks recruit a network of PFC and parietal areas. A study has shown that during a working memory task the connectivity between these areas increases. Another study has demonstrated that these areas are necessary for working memory, and not simply activated accidentally during working memory tasks, by temporarily blocking them through transcranial magnetic stimulation (TMS), thereby producing an impairment in task performance.<br />
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人们逐渐达成共识,认为大多数工作记忆任务使用的是PFC顶叶区域组成的网络。一项研究表明,这些区域之间的连通性在工作记忆任务的执行过程中有所增加<ref>{{Cite journal|author=Honey, G. D.|author2=Fu, C. H.|author3=Kim, J.|title=Effects of verbal working memory load on corticocortical connectivity modeled by path analysis of functional magnetic resonance imaging data |journal=NeuroImage |volume=17 |issue=2 |pages=573–82 |date=October 2002 |pmid=12377135 |doi=10.1016/S1053-8119(02)91193-6|display-authors=etal}}</ref>。另一项研究表明,这些区域是工作记忆所必备的,并非是被意外激活的。通过经颅磁刺激(TMS)暂时阻止它们,从而导致任务性能受损<ref>{{Cite journal|author=Mottaghy, F. M.|title=Interfering with working memory in humans |journal=Neuroscience |volume=139 |issue=1 |pages=85–90 |date=April 2006 |pmid=16337091 |doi=10.1016/j.neuroscience.2005.05.037}}</ref>。<br />
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A current debate concerns the function of these brain areas. The PFC has been found to be active in a variety of tasks that require executive functions.<ref name="Kane MJ, Engle RW 2002 637–71" /> This has led some researchers to argue that the role of PFC in working memory is in controlling attention, selecting strategies, and manipulating information in working memory, but not in maintenance of information. The maintenance function is attributed to more posterior areas of the brain, including the parietal cortex.<ref>{{Cite journal|author=Curtis, C. E.|author2=D'Esposito, M.|title=Persistent activity in the prefrontal cortex during working memory |journal=Trends in Cognitive Sciences |volume=7 |issue=9 |pages=415–423 |date=September 2003 |pmid=12963473 |doi=10.1016/S1364-6613(03)00197-9|citeseerx=10.1.1.319.8928}}</ref><ref name="Postle">{{Cite journal|author=Postle BR |title=Working memory as an emergent property of the mind and brain |journal=Neuroscience |volume=139 |issue=1 |pages=23–38 |date=April 2006 |pmid=16324795 |pmc=1428794 |doi=10.1016/j.neuroscience.2005.06.005}}</ref> Other authors interpret the activity in parietal cortex as reflecting [[executive functions]], because the same area is also activated in other tasks requiring attention but not memory.<ref>{{Cite journal|author=Collette, F.|author2= Hogge, M.|author3= Salmon, E.|author4=Van der Linden, M.|title=Exploration of the neural substrates of executive functioning by functional neuroimaging |journal=Neuroscience |volume=139 |issue=1 |pages=209–21 |date=April 2006 |pmid=16324796 |doi=10.1016/j.neuroscience.2005.05.035|hdl= 2268/5937|hdl-access=free }}</ref><br />
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A current debate concerns the function of these brain areas. The PFC has been found to be active in a variety of tasks that require executive functions. Other authors interpret the activity in parietal cortex as reflecting executive functions, because the same area is also activated in other tasks requiring attention but not memory.<br />
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目前的争论集中于大脑各个区域功能的研究。研究发现,在许多需要执行功能的任务中,PFC都具有活性。<ref name="Kane MJ, Engle RW 2002 637–71" />这使得一些研究人员认为,PFC在工作记忆中的作用是控制注意力,选择策略以及操纵信息,而非信息维护。信息维护功能更多的由大脑后部区域负责——包括顶叶皮层<ref>{{Cite journal|author=Curtis, C. E.|author2=D'Esposito, M.|title=Persistent activity in the prefrontal cortex during working memory |journal=Trends in Cognitive Sciences |volume=7 |issue=9 |pages=415–423 |date=September 2003 |pmid=12963473 |doi=10.1016/S1364-6613(03)00197-9|citeseerx=10.1.1.319.8928}}</ref><ref name="Postle">{{Cite journal|author=Postle BR |title=Working memory as an emergent property of the mind and brain |journal=Neuroscience |volume=139 |issue=1 |pages=23–38 |date=April 2006 |pmid=16324795 |pmc=1428794 |doi=10.1016/j.neuroscience.2005.06.005}}</ref>。其他研究者把顶叶皮层的活动理解为对执行功能的反映,因为在其他需要注意力而不是记忆的任务中该区域同样被激活<ref>{{Cite journal|author=Collette, F.|author2= Hogge, M.|author3= Salmon, E.|author4=Van der Linden, M.|title=Exploration of the neural substrates of executive functioning by functional neuroimaging |journal=Neuroscience |volume=139 |issue=1 |pages=209–21 |date=April 2006 |pmid=16324796 |doi=10.1016/j.neuroscience.2005.05.035|hdl= 2268/5937|hdl-access=free }}</ref><br />
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A 2003 meta-analysis of 60 neuroimaging studies found left [[Frontal lobe|frontal]] cortex was involved in low-task demand verbal working memory and right [[Frontal lobe|frontal]] cortex for spatial working memory. Brodmann's areas (BAs) [[Brodmann area 6|6]], [[Brodmann area 8|8]], and [[Brodmann area 9|9]], in the [[Superior frontal gyrus|superior frontal cortex]] was involved when working memory must be continuously updated and when memory for temporal order had to be maintained. Right Brodmann [[Brodmann area 10|10]] and [[Brodmann area 47|47]] in the ventral frontal cortex were involved more frequently with demand for manipulation such as dual-task requirements or mental operations, and Brodmann 7 in the [[posterior parietal cortex]] was also involved in all types of executive function.<ref>{{Cite journal|title = Neuroimaging studies of working memory: a meta-analysis|journal = Cognitive, Affective & Behavioral Neuroscience|date = 2003-12-01|issn = 1530-7026|pmid = 15040547|pages = 255–274|volume = 3|issue = 4|first1 = Tor D.|last1 = Wager|first2 = Edward E.|last2 = Smith|doi=10.3758/cabn.3.4.255|doi-access = free}}</ref><br />
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A 2003 meta-analysis of 60 neuroimaging studies found left frontal cortex was involved in low-task demand verbal working memory and right frontal cortex for spatial working memory. Brodmann's areas (BAs) 6, 8, and 9, in the superior frontal cortex was involved when working memory must be continuously updated and when memory for temporal order had to be maintained. Right Brodmann 10 and 47 in the ventral frontal cortex were involved more frequently with demand for manipulation such as dual-task requirements or mental operations, and Brodmann 7 in the posterior parietal cortex was also involved in all types of executive function.<br />
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在2003年,一份对60项神经成像研究结果的元分析发现,左额叶皮层参与低任务需求的语言工作记忆,而右额叶皮层参与空间工作记忆。罗德曼大脑上额叶皮层区域(BAs)的6、8、9号参与需要不断更新的以及需要维持特定顺序的工作记忆。腹侧额叶皮层的右布罗德曼10和47号区域较频繁地参与需要双重任务或心理操作的工作记忆,其中后顶叶皮层的罗德曼7号区域参与了全部的执行功能<ref>{{Cite journal|title = Neuroimaging studies of working memory: a meta-analysis|journal = Cognitive, Affective & Behavioral Neuroscience|date = 2003-12-01|issn = 1530-7026|pmid = 15040547|pages = 255–274|volume = 3|issue = 4|first1 = Tor D.|last1 = Wager|first2 = Edward E.|last2 = Smith|doi=10.3758/cabn.3.4.255|doi-access = free}}</ref>。<br />
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Working memory has been suggested to involve two processes with different neuroanatomical locations in the frontal and parietal lobes.<ref name="Bledowski">{{Cite journal|author=Bledowski, C.|author2=Rahm, B.|author3=Rowe, J. B. |title=What 'works' in working memory? Separate systems for selection and updating of critical information |journal=The Journal of Neuroscience |volume=29 |issue=43 |pages=13735–41 |date=October 2009 |pmid=19864586 |doi=10.1523/JNEUROSCI.2547-09.2009 |pmc=2785708}}</ref> First, a selection operation that retrieves the most relevant item, and second an updating operation that changes the focus of attention made upon it. Updating the attentional focus has been found to involve the transient activation in the caudal [[superior frontal sulcus]] and [[posterior parietal cortex]], while increasing demands on selection selectively changes activation in the rostral superior frontal sulcus and posterior cingulate/[[precuneus]].<ref name="Bledowski" /><br />
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Working memory has been suggested to involve two processes with different neuroanatomical locations in the frontal and parietal lobes. First, a selection operation that retrieves the most relevant item, and second an updating operation that changes the focus of attention made upon it. Updating the attentional focus has been found to involve the transient activation in the caudal superior frontal sulcus and posterior parietal cortex, while increasing demands on selection selectively changes activation in the rostral superior frontal sulcus and posterior cingulate/precuneus.<br />
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我们一般认为,工作记忆包括两种过程——两类过程发生于额叶和顶叶两个不同位置<ref name="Bledowski">{{Cite journal|author=Bledowski, C.|author2=Rahm, B.|author3=Rowe, J. B. |title=What 'works' in working memory? Separate systems for selection and updating of critical information |journal=The Journal of Neuroscience |volume=29 |issue=43 |pages=13735–41 |date=October 2009 |pmid=19864586 |doi=10.1523/JNEUROSCI.2547-09.2009 |pmc=2785708}}</ref>。首先是检索最相关项的选择操作,其次是更改关注焦点的更新操作。更新操作包括'''<font color="#ff8000">额上沟superior frontal sulcus</font>'''尾部和'''<font color="#ff8000">后顶叶皮质posterior parietal cortex</font>'''的短暂激活,选择操作随选择的需求增加而选择性地发生额上沟和后扣带回/楔前叶激活<ref name="Bledowski" />。<br />
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Articulating the differential function of brain regions involved in working memory is dependent on tasks able to distinguish these functions.<ref name="Coltheart-2006">{{Cite journal | last1 = Coltheart | first1 = M. | title = What has functional neuroimaging told us about the mind (so far)? | journal = Cortex | volume = 42 | issue = 3 | pages = 323–31 |date=Apr 2006 | doi = 10.1016/S0010-9452(08)70358-7 | pmid = 16771037 }}</ref> Most brain imaging studies of working memory have used recognition tasks such as delayed recognition of one or several stimuli, or the n-back task, in which each new stimulus in a long series must be compared to the one presented n steps back in the series. The advantage of recognition tasks is that they require minimal movement (just pressing one of two keys), making fixation of the head in the scanner easier. Experimental research and research on individual differences in working memory, however, has used largely recall tasks (e.g.,&nbsp;the [[reading span task]], see below). It is not clear to what degree recognition and recall tasks reflect the same processes and the same capacity limitations.<br />
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Articulating the differential function of brain regions involved in working memory is dependent on tasks able to distinguish these functions. Most brain imaging studies of working memory have used recognition tasks such as delayed recognition of one or several stimuli, or the n-back task, in which each new stimulus in a long series must be compared to the one presented n steps back in the series. The advantage of recognition tasks is that they require minimal movement (just pressing one of two keys), making fixation of the head in the scanner easier. Experimental research and research on individual differences in working memory, however, has used largely recall tasks (e.g.,&nbsp;the reading span task, see below). It is not clear to what degree recognition and recall tasks reflect the same processes and the same capacity limitations.<br />
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要想阐明与工作记忆相关的大脑区域功能,首先需要区分这些功能的任务<ref name="Coltheart-2006">{{Cite journal | last1 = Coltheart | first1 = M. | title = What has functional neuroimaging told us about the mind (so far)? | journal = Cortex | volume = 42 | issue = 3 | pages = 323–31 |date=Apr 2006 | doi = 10.1016/S0010-9452(08)70358-7 | pmid = 16771037 }}</ref>。大多数关于工作记忆的脑成像研究都使用了识别任务,比如延迟识别一个或多个刺激,或 n-back 任务,即一个长系列中的每个新刺激都需与该系列中的一个n步后的刺激进行比较。识别任务的优势在于只需要最低限度的运动(只需二选一按键),这使头部扫描的定位更加容易。然而,关于工作记忆个体差异的实验研究大量使用的是回忆任务(例如阅读广度任务,见下文)。不过我们目前尚不清楚识别任务和回忆任务能在多大程度上反映相同过程和相同能力极限。<br />
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Brain imaging studies have been conducted with the reading span task or related tasks. Increased activation during these tasks was found in the PFC and, in several studies, also in the [[anterior cingulate cortex]] (ACC). People performing better on the task showed larger increase of activation in these areas, and their activation was correlated more over time, suggesting that their neural activity in these two areas was better coordinated, possibly due to stronger connectivity.<ref>{{Cite journal|author=Kondo, H.|author2=Osaka, N.|author3=Osaka, M.|title=Cooperation of the anterior cingulate cortex and dorsolateral prefrontal cortex for attention shifting |journal=NeuroImage |volume=23 |issue=2 |pages=670–9 |date=October 2004 |pmid=15488417 |doi=10.1016/j.neuroimage.2004.06.014}}</ref><ref>{{Cite journal|vauthors=Osaka N, Osaka M, Kondo H, Morishita M, Fukuyama H, Shibasaki H |title=The neural basis of executive function in working memory: an fMRI study based on individual differences |journal=NeuroImage |volume=21 |issue=2 |pages=623–31 |date=February 2004 |pmid=14980565 |doi=10.1016/j.neuroimage.2003.09.069}}</ref><br />
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Brain imaging studies have been conducted with the reading span task or related tasks. Increased activation during these tasks was found in the PFC and, in several studies, also in the anterior cingulate cortex (ACC). People performing better on the task showed larger increase of activation in these areas, and their activation was correlated more over time, suggesting that their neural activity in these two areas was better coordinated, possibly due to stronger connectivity.<br />
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脑成像研究已用于进行阅读广度任务或相关任务。任务过程中,PFC的活跃性增加,'''<font color="#ff8000">前扣带皮层anterior cingulate cortex </font>''' (ACC)的活性也有所增强。那些在任务中表现更好的人的这些区域活性显著提升,且随着时间的推移变得更强。这表明这两个区域的神经活动协调度更高——可能是因为区域间有更强的关联性<ref>{{Cite journal|author=Kondo, H.|author2=Osaka, N.|author3=Osaka, M.|title=Cooperation of the anterior cingulate cortex and dorsolateral prefrontal cortex for attention shifting |journal=NeuroImage |volume=23 |issue=2 |pages=670–9 |date=October 2004 |pmid=15488417 |doi=10.1016/j.neuroimage.2004.06.014}}</ref><ref>{{Cite journal|vauthors=Osaka N, Osaka M, Kondo H, Morishita M, Fukuyama H, Shibasaki H |title=The neural basis of executive function in working memory: an fMRI study based on individual differences |journal=NeuroImage |volume=21 |issue=2 |pages=623–31 |date=February 2004 |pmid=14980565 |doi=10.1016/j.neuroimage.2003.09.069}}</ref><br />
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=== 神经模型 Neural models ===<br />
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One approach to modeling the neurophysiology and the functioning of working memory is [[PBWM|prefrontal cortex basal ganglia working memory (PBWM)]]. In this model, the prefrontal cortex works hand-in-hand with the basal ganglia to accomplish the tasks of working memory. Many studies have shown this to be the case.<ref>{{Cite journal|last1=Baier|first1=B.|last2=Karnath|first2=H.-O.|last3=Dieterich|first3=M.|last4=Birklein|first4=F.|last5=Heinze|first5=C.|last6=Muller|first6=N. G.|date=2010-07-21|title=Keeping Memory Clear and Stable--The Contribution of Human Basal Ganglia and Prefrontal Cortex to Working Memory|journal=Journal of Neuroscience|volume=30|issue=29|pages=9788–9792|doi=10.1523/jneurosci.1513-10.2010|pmid=20660261|pmc=6632833|issn=0270-6474|doi-access=free}}</ref> One used ablation techniques in patients who had suffered from seizures and had damage to the prefrontal cortex and basal ganglia.<ref name=":2" /> Researchers found that such damage resulted in decreased capacity to carry out the executive function of working memory.<ref name=":2">{{Cite journal|last1=Voytek|first1=B.|last2=Knight|first2=R. T.|date=2010-10-04|title=Prefrontal cortex and basal ganglia contributions to visual working memory|journal=Proceedings of the National Academy of Sciences|volume=107|issue=42|pages=18167–18172|doi=10.1073/pnas.1007277107|pmid=20921401|issn=0027-8424|doi-access=free}}</ref> Additional research conducted on patients with brain alterations due to methamphetamine use found that training working memory increases volume in the basal ganglia.<ref>{{Cite journal|last1=Brooks|first1=S. J.|last2=Burch|first2=K. H.|last3=Maiorana|first3=S. A.|last4=Cocolas|first4=E.|last5=Schioth|first5=H. B.|last6=Nilsson|first6=E. K.|last7=Kamaloodien|first7=K.|last8=Stein|first8=D. J.|date=2016-02-01|title=Psychological intervention with working memory training increases basal ganglia volume: A VBM study of inpatient treatment for methamphetamine use|url=http://www.sciencedirect.com/science/article/pii/S2213158216301541|journal=NeuroImage: Clinical|language=en|volume=12|pages=478–491|doi=10.1016/j.nicl.2016.08.019|pmid=27625988|issn=2213-1582|doi-access=free}}</ref><br />
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One approach to modeling the neurophysiology and the functioning of working memory is prefrontal cortex basal ganglia working memory (PBWM). In this model, the prefrontal cortex works hand-in-hand with the basal ganglia to accomplish the tasks of working memory. Many studies have shown this to be the case. One used ablation techniques in patients who had suffered from seizures and had damage to the prefrontal cortex and basal ganglia. Researchers found that such damage resulted in decreased capacity to carry out the executive function of working memory .Additional research conducted on patients with brain alterations due to methamphetamine use found that training working memory increases volume in the basal ganglia.<br />
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'''<font color="#ff8000">前额叶皮质基底节工作记忆记忆模型 Prefrontal Cortex Basal Ganglia Working Memory (PBWM)</font>'''是模拟神经生理学和工作记忆功能模型的一种。<br />
在该模型中,脑前额叶外皮与基底神经节协力完成工作记忆任务,并得到许多研究证明支持<ref>{{Cite journal|last1=Baier|first1=B.|last2=Karnath|first2=H.-O.|last3=Dieterich|first3=M.|last4=Birklein|first4=F.|last5=Heinze|first5=C.|last6=Muller|first6=N. G.|date=2010-07-21|title=Keeping Memory Clear and Stable--The Contribution of Human Basal Ganglia and Prefrontal Cortex to Working Memory|journal=Journal of Neuroscience|volume=30|issue=29|pages=9788–9792|doi=10.1523/jneurosci.1513-10.2010|pmid=20660261|pmc=6632833|issn=0270-6474|doi-access=free}}</ref>,例如使用'''<font color="#ff8000">消融技术ablation techniques</font>'''治疗脑前额叶外皮和基底神经节受损、癫痫发作患者等。<ref name=":2" />研究人员发现,这种损害使得工作记忆的执行功能受损。<ref name=":2">{{Cite journal|last1=Voytek|first1=B.|last2=Knight|first2=R. T.|date=2010-10-04|title=Prefrontal cortex and basal ganglia contributions to visual working memory|journal=Proceedings of the National Academy of Sciences|volume=107|issue=42|pages=18167–18172|doi=10.1073/pnas.1007277107|pmid=20921401|issn=0027-8424|doi-access=free}}</ref>此外还有对因服用'''<font color="#ff8000">甲基苯丙胺 methamphetamine</font>'''而导致大脑改变的病人进行工作记忆训练后成功增加其基底神经节容量的案例<ref>{{Cite journal|last1=Brooks|first1=S. J.|last2=Burch|first2=K. H.|last3=Maiorana|first3=S. A.|last4=Cocolas|first4=E.|last5=Schioth|first5=H. B.|last6=Nilsson|first6=E. K.|last7=Kamaloodien|first7=K.|last8=Stein|first8=D. J.|date=2016-02-01|title=Psychological intervention with working memory training increases basal ganglia volume: A VBM study of inpatient treatment for methamphetamine use|url=http://www.sciencedirect.com/science/article/pii/S2213158216301541|journal=NeuroImage: Clinical|language=en|volume=12|pages=478–491|doi=10.1016/j.nicl.2016.08.019|pmid=27625988|issn=2213-1582|doi-access=free}}</ref>。<br />
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=== 神经生理学的压力效果 Effects of stress on neurophysiology ===<br />
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Working memory is impaired by acute and chronic psychological stress. This phenomenon was first discovered in animal studies by Arnsten and colleagues,<ref>{{Cite journal|doi=10.1126/science.280.5370.1711|author=Arnsten, A. F.|title=The biology of being frazzled |journal=Science |volume=280 |issue=5370 |pages=1711–2 |date=June 1998 |pmid=9660710}}</ref> who have shown that stress-induced [[catecholamine]] release in PFC rapidly decreases PFC neuronal firing and impairs working memory performance through feedforward, intracellular signaling pathways.<ref>{{Cite journal|author=Arnsten, AF |title=Stress signalling pathways that impair prefrontal cortex structure and function |journal=Nature Reviews Neuroscience |volume=10 |issue=6 |pages=410–22 |date=June 2009 |pmid=19455173|pmc=2907136 |doi=10.1038/nrn2648}}</ref> Exposure to chronic stress leads to more profound working memory deficits and additional architectural changes in PFC, including dendritic atrophy and spine loss,<ref>{{Cite journal|author=Radley, J. J.|author2= Rocher, A. B.|author3=Miller, M.|author4= Janssen, W. G.|author5=Liston, C.|author6=Hof, P. R.|author7=McEwen, B. S.|author8=Morrison, J. H.|title=Repeated stress induces dendritic spine loss in the rat medial prefrontal cortex |journal=Cereb Cortex |volume=16 |issue=3 |pages=313–20 |date=Mar 2006 |pmid=15901656 |doi=10.1093/cercor/bhi104|doi-access=free}}</ref> which can be prevented by inhibition of protein kinase C signaling.<ref>{{Cite journal|author=Hains, A. B.|author2=Vu, M. A.|author3=Maciejewski, P. K.|author4= van Dyck, C. H. |authorlink4=Christopher H. van Dyck |author5=Gottron, M.|author6= Arnsten, A. F. |title=Inhibition of protein kinase C signaling protects prefrontal cortex dendritic spines and cognition from the effects of chronic stress |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=42 |pages=17957–62 |date=Oct 2009 |pmid=19805148|pmc=2742406 |doi=10.1073/pnas.0908563106|bibcode=2009PNAS..10617957H }}</ref> [[fMRI]] research has extended this research to humans, and confirms that reduced working memory caused by acute stress links to reduced activation of the PFC, and stress increased levels of [[catecholamine]]s.<ref>{{Cite journal|vauthors=Qin S, Hermans EJ, van Marle HJ, Luo J, Fernández G |title=Acute psychological stress reduces working memory-related activity in the dorsolateral prefrontal cortex |journal=Biological Psychiatry |volume=66 |issue=1 |pages=25–32 |date=July 2009 |pmid=19403118 |doi=10.1016/j.biopsych.2009.03.006}}</ref> Imaging studies of medical students undergoing stressful exams have also shown weakened PFC functional connectivity, consistent with the animal studies.<ref>{{Cite journal|vauthors=Liston C, McEwen BS, Casey BJ |title=Psychosocial stress reversibly disrupts prefrontal processing and attentional control |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=3 |pages=912–7 |date=Jan 2009 |pmid=19139412|pmc=2621252 |doi=10.1073/pnas.0807041106|bibcode=2009PNAS..106..912L }}</ref> The marked effects of stress on PFC structure and function may help to explain how stress can cause or exacerbate mental illness.<br />
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Working memory is impaired by acute and chronic psychological stress. This phenomenon was first discovered in animal studies by Arnsten and colleagues, who have shown that stress-induced catecholamine release in PFC rapidly decreases PFC neuronal firing and impairs working memory performance through feedforward, intracellular signaling pathways. Exposure to chronic stress leads to more profound working memory deficits and additional architectural changes in PFC, including dendritic atrophy and spine loss, which can be prevented by inhibition of protein kinase C signaling. fMRI research has extended this research to humans, and confirms that reduced working memory caused by acute stress links to reduced activation of the PFC, and stress increased levels of catecholamines. Imaging studies of medical students undergoing stressful exams have also shown weakened PFC functional connectivity, consistent with the animal studies. The marked effects of stress on PFC structure and function may help to explain how stress can cause or exacerbate mental illness.<br />
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急性和慢性心理压力都会损害工作记忆。这最早由安斯登 Arnsten 和他的同事们<ref>{{Cite journal|doi=10.1126/science.280.5370.1711|author=Arnsten, A. F.|title=The biology of being frazzled |journal=Science |volume=280 |issue=5370 |pages=1711–2 |date=June 1998 |pmid=9660710}}</ref>在动物实验中发现。他们发现应激诱导PFC中'''<font color="#ff8000">儿茶酚胺 catecholamine</font>'''的释放可迅速降低PFC神经元的放电频率,并通过前馈和细胞内信号通路损害工作记忆<ref>{{Cite journal|author=Arnsten, AF |title=Stress signalling pathways that impair prefrontal cortex structure and function |journal=Nature Reviews Neuroscience |volume=10 |issue=6 |pages=410–22 |date=June 2009 |pmid=19455173|pmc=2907136 |doi=10.1038/nrn2648}}</ref>。长期暴露在压力下会导致更深层次的工作记忆缺陷和额外的PFC结构变化——包括树突萎缩和脊柱丧失<ref>{{Cite journal|author=Radley, J. J.|author2= Rocher, A. B.|author3=Miller, M.|author4= Janssen, W. G.|author5=Liston, C.|author6=Hof, P. R.|author7=McEwen, B. S.|author8=Morrison, J. H.|title=Repeated stress induces dendritic spine loss in the rat medial prefrontal cortex |journal=Cereb Cortex |volume=16 |issue=3 |pages=313–20 |date=Mar 2006 |pmid=15901656 |doi=10.1093/cercor/bhi104|doi-access=free}}</ref>——这些都可以通过抑制蛋白激酶C信号来预防<ref>{{Cite journal|author=Hains, A. B.|author2=Vu, M. A.|author3=Maciejewski, P. K.|author4= van Dyck, C. H. |authorlink4=Christopher H. van Dyck |author5=Gottron, M.|author6= Arnsten, A. F. |title=Inhibition of protein kinase C signaling protects prefrontal cortex dendritic spines and cognition from the effects of chronic stress |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=42 |pages=17957–62 |date=Oct 2009 |pmid=19805148|pmc=2742406 |doi=10.1073/pnas.0908563106|bibcode=2009PNAS..10617957H }}</ref>。功能磁共振成像研究已经将这项研究进一步扩展到人类,并证实了急性压力导致的工作记忆减少会降低PFC的活性,同时,压力还会导致儿茶酚胺水平提高<ref>{{Cite journal|vauthors=Qin S, Hermans EJ, van Marle HJ, Luo J, Fernández G |title=Acute psychological stress reduces working memory-related activity in the dorsolateral prefrontal cortex |journal=Biological Psychiatry |volume=66 |issue=1 |pages=25–32 |date=July 2009 |pmid=19403118 |doi=10.1016/j.biopsych.2009.03.006}}</ref>。在经历紧张的考试后,医学院学生的成像研究也表明其PFC功能减弱,与动物实验的结果一致<ref>{{Cite journal|vauthors=Liston C, McEwen BS, Casey BJ |title=Psychosocial stress reversibly disrupts prefrontal processing and attentional control |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=3 |pages=912–7 |date=Jan 2009 |pmid=19139412|pmc=2621252 |doi=10.1073/pnas.0807041106|bibcode=2009PNAS..106..912L }}</ref>。压力对PFC结构和功能的显著影响可能有助于解释为何压力会加重甚至导致精神疾病。<br />
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The more stress in one's life, the lower the efficiency of working memory in performing simple cognitive tasks. Students who performed exercises that reduced the intrusion of negative thoughts showed an increase in their working memory capacity. Mood states (positive or negative) can have an influence on the neurotransmitter dopamine, which in turn can affect problem solving.<ref>{{cite book|last=Revlin|first=Russell|title=Human Cognition : Theory and Practice.|year=2007|publisher=Worth Pub|location=New York, NY|isbn=978-0-7167-5667-5|page=147|edition=International}}</ref><br />
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The more stress in one's life, the lower the efficiency of working memory in performing simple cognitive tasks. Students who performed exercises that reduced the intrusion of negative thoughts showed an increase in their working memory capacity. Mood states (positive or negative) can have an influence on the neurotransmitter dopamine, which in turn can affect problem solving.<br />
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人在生活中的压力越大工作记忆在完成简单认知任务时的效率就会越低。接受过限制负面思想入侵练习的学生,其工作记忆容量明显有所增加。因此我们说,情绪状态(积极或消极)会影响神经递质多巴胺,进而影响问题解决效果<ref>{{cite book|last=Revlin|first=Russell|title=Human Cognition : Theory and Practice.|year=2007|publisher=Worth Pub|location=New York, NY|isbn=978-0-7167-5667-5|page=147|edition=International}}</ref>。<br />
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=== 神经生理学的酒精效果 Effects of alcohol on neurophysiology ===<br />
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Alcohol abuse can result in brain damage which impairs working memory.<ref name="pmid21466500">{{cite journal |vauthors=van Holst RJ, Schilt T |title=Drug-related decrease in neuropsychological functions of abstinent drug users |journal=Curr Drug Abuse Rev |volume=4 |issue=1 |pages=42–56 | date=March 2011 |pmid=21466500 |doi= 10.2174/1874473711104010042}}</ref> Alcohol has an effect on the [[Blood-oxygen-level dependent|blood-oxygen-level-dependent]] (BOLD) response. The BOLD response correlates increased blood oxygenation with brain activity, which makes this response a useful tool for measuring neuronal activity.<ref>{{cite journal | author = Jacobus J.|author2=Tapert S. F. | year = 2013 | title = Neurotoxic Effects of Alcohol in Adolescence | journal = [[Annual Review of Clinical Psychology]] | volume = 9 | issue = 1| pages = 703–721 | doi = 10.1146/annurev-clinpsy-050212-185610 | pmc = 3873326 | pmid=23245341}}</ref> The BOLD response affects regions of the brain such as the basal ganglia and thalamus when performing a working memory task. Adolescents who start drinking at a young age show a decreased BOLD response in these brain regions.<ref>{{cite journal | vauthors = Weiland BJ, Nigg JT, Welsh RC, Yau WY, Zubieta JK | displayauthors=etal | year = 2012 | title = Resiliency in adolescents at high risk for substance abuse: flexible adaptation via subthalamic nucleus and linkage to drinking and drug use in early adulthood | journal = Alcohol. Clin. Exp. Res. | volume = 36 | issue = 8| pages = 1355–64 | doi=10.1111/j.1530-0277.2012.01741.x| pmc = 3412943 | pmid=22587751}}</ref> Alcohol dependent young women in particular exhibit less of a BOLD response in parietal and frontal cortices when performing a spatial working memory task.<ref>{{cite journal | vauthors = Tapert SF, Brown GG, Kindermann SS, Cheung EH, Frank LR, Brown SA | year = 2001 | title = fMRI measurement of brain dysfunction in alcohol-dependent young women | journal = Alcohol. Clin. Exp. Res. | volume = 25 | issue = 2| pages = 236–45 | doi=10.1111/j.1530-0277.2001.tb02204.x | pmid=11236838}}</ref> Binge drinking, specifically, can also affect one's performance on working memory tasks, particularly visual working memory.<ref>{{cite journal | vauthors = Ferrett HL, Carey PD, Thomas KG, Tapert SF, Fein G | year = 2010 | title = Neuropsychological performance of South African treatment-naive adolescents with alcohol dependence | journal = Drug Alcohol Depend | volume = 110 | issue = 1–2| pages = 8–14 | doi=10.1016/j.drugalcdep.2010.01.019| pmc = 4456395 | pmid=20227839}}</ref><ref>{{cite journal | vauthors = Crego A, Holguin SR, Parada M, Mota N, Corral M, Cadaveira F | year = 2009 | title = Binge drinking affects attentional and visual working memory processing in young university students | journal = Alcohol. Clin. Exp. Res. | volume = 33 | issue = 11| pages = 1870–79 | doi=10.1111/j.1530-0277.2009.01025.x| pmid = 19673739 | hdl = 10347/16832 | hdl-access = free }}</ref> Additionally, there seems to be a gender difference in regards to how alcohol affects working memory. While women perform better on verbal working memory tasks after consuming alcohol compared to men, they appear to perform worse on spatial working memory tasks as indicated by less brain activity.<ref>{{cite journal | vauthors = Greenstein JE, Kassel JD, Wardle MC, Veilleux JC, Evatt DP, Heinz AJ, Yates MC | year = 2010 | title = The separate and combined effects of nicotine and alcohol on working memory capacity in nonabstinent smokers | journal = [[Experimental and Clinical Psychopharmacology]] | volume = 18 | issue = 2| pages = 120–128 | doi = 10.1037/a0018782 | pmid = 20384423 }}</ref><ref>{{cite journal | vauthors = Squeglia LM, Schweinsburg AD, Pulido C, Tapert SF | year = 2011 | title = Adolescent binge drinking linked to abnormal spatial working memory brain activation: Differential gender effects | journal = Alcoholism: Clinical and Experimental Research | volume = 35 | issue = 10| pages = 1831–1841 | doi = 10.1111/j.1530-0277.2011.01527.x | pmc = 3183294 | pmid=21762178}}</ref> Finally, age seems to be an additional factor. Older adults are more susceptible than others to the effects of alcohol on working memory.<ref>{{cite journal | vauthors = Boissoneault J, Sklar A, Prather R, Nixon SJ | year = 2014 | title = Acute effects of moderate alcohol on psychomotor, set shifting, and working memory function in older and younger social drinkers | journal = Journal of Studies on Alcohol and Drugs | volume = 75 | issue = 5| pages = 870–879 | doi = 10.15288/jsad.2014.75.870 | pmc = 4161706 | pmid=25208205}}</ref><br />
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Alcohol abuse can result in brain damage which impairs working memory. Alcohol has an effect on the blood-oxygen-level-dependent (BOLD) response. The BOLD response correlates increased blood oxygenation with brain activity, which makes this response a useful tool for measuring neuronal activity. The BOLD response affects regions of the brain such as the basal ganglia and thalamus when performing a working memory task. Adolescents who start drinking at a young age show a decreased BOLD response in these brain regions. Alcohol dependent young women in particular exhibit less of a BOLD response in parietal and frontal cortices when performing a spatial working memory task. Binge drinking, specifically, can also affect one's performance on working memory tasks, particularly visual working memory. Additionally, there seems to be a gender difference in regards to how alcohol affects working memory. While women perform better on verbal working memory tasks after consuming alcohol compared to men, they appear to perform worse on spatial working memory tasks as indicated by less brain activity. Finally, age seems to be an additional factor. Older adults are more susceptible than others to the effects of alcohol on working memory.<br />
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酗酒会损伤大脑,进而损害工作记忆<ref name="pmid21466500">{{cite journal |vauthors=van Holst RJ, Schilt T |title=Drug-related decrease in neuropsychological functions of abstinent drug users |journal=Curr Drug Abuse Rev |volume=4 |issue=1 |pages=42–56 | date=March 2011 |pmid=21466500 |doi= 10.2174/1874473711104010042}}</ref>。酒精会影响'''<font color="#ff8000">血氧水平依赖性 Blood-Oxygen-Level-Dependent(BOLD)</font>'''反应。BOLD反应把血氧含量增加与大脑活动联系起来,这使得其成为测量神经元活动的有效指标<ref>{{cite journal | author = Jacobus J.|author2=Tapert S. F. | year = 2013 | title = Neurotoxic Effects of Alcohol in Adolescence | journal = [[Annual Review of Clinical Psychology]] | volume = 9 | issue = 1| pages = 703–721 | doi = 10.1146/annurev-clinpsy-050212-185610 | pmc = 3873326 | pmid=23245341}}</ref>。在执行工作记忆任务时,BOLD反应影响大脑的基底神经节和丘脑等区域。从小就喝酒的青少年BOLD反应相应较低。特别的<ref>{{cite journal | vauthors = Weiland BJ, Nigg JT, Welsh RC, Yau WY, Zubieta JK | displayauthors=etal | year = 2012 | title = Resiliency in adolescents at high risk for substance abuse: flexible adaptation via subthalamic nucleus and linkage to drinking and drug use in early adulthood | journal = Alcohol. Clin. Exp. Res. | volume = 36 | issue = 8| pages = 1355–64 | doi=10.1111/j.1530-0277.2012.01741.x| pmc = 3412943 | pmid=22587751}}</ref>,有酒精依赖的年轻女性在执行空间工作记忆任务时顶叶和额叶皮层的BOLD反应较弱<ref>{{cite journal | vauthors = Tapert SF, Brown GG, Kindermann SS, Cheung EH, Frank LR, Brown SA | year = 2001 | title = fMRI measurement of brain dysfunction in alcohol-dependent young women | journal = Alcohol. Clin. Exp. Res. | volume = 25 | issue = 2| pages = 236–45 | doi=10.1111/j.1530-0277.2001.tb02204.x | pmid=11236838}}</ref>。酗酒工作记忆任务表现有显著影响——特别是视觉工作记忆<ref>{{cite journal | vauthors = Ferrett HL, Carey PD, Thomas KG, Tapert SF, Fein G | year = 2010 | title = Neuropsychological performance of South African treatment-naive adolescents with alcohol dependence | journal = Drug Alcohol Depend | volume = 110 | issue = 1–2| pages = 8–14 | doi=10.1016/j.drugalcdep.2010.01.019| pmc = 4456395 | pmid=20227839}}</ref><ref>{{cite journal | vauthors = Crego A, Holguin SR, Parada M, Mota N, Corral M, Cadaveira F | year = 2009 | title = Binge drinking affects attentional and visual working memory processing in young university students | journal = Alcohol. Clin. Exp. Res. | volume = 33 | issue = 11| pages = 1870–79 | doi=10.1111/j.1530-0277.2009.01025.x| pmid = 19673739 | hdl = 10347/16832 | hdl-access = free }}</ref>。此外,酒精对工作记忆的影响似乎也存在性别差异。与男性相比,女性酒后的非文字工作记忆任务完成得更好,但空间工作记忆任务完成得似乎更差(大脑活动迟缓)<ref>{{cite journal | vauthors = Greenstein JE, Kassel JD, Wardle MC, Veilleux JC, Evatt DP, Heinz AJ, Yates MC | year = 2010 | title = The separate and combined effects of nicotine and alcohol on working memory capacity in nonabstinent smokers | journal = [[Experimental and Clinical Psychopharmacology]] | volume = 18 | issue = 2| pages = 120–128 | doi = 10.1037/a0018782 | pmid = 20384423 }}</ref><ref>{{cite journal | vauthors = Squeglia LM, Schweinsburg AD, Pulido C, Tapert SF | year = 2011 | title = Adolescent binge drinking linked to abnormal spatial working memory brain activation: Differential gender effects | journal = Alcoholism: Clinical and Experimental Research | volume = 35 | issue = 10| pages = 1831–1841 | doi = 10.1111/j.1530-0277.2011.01527.x | pmc = 3183294 | pmid=21762178}}</ref>。最后,年龄似乎也是一个可考虑的因素。老年人更容易受到酒精的影响<ref>{{cite journal | vauthors = Boissoneault J, Sklar A, Prather R, Nixon SJ | year = 2014 | title = Acute effects of moderate alcohol on psychomotor, set shifting, and working memory function in older and younger social drinkers | journal = Journal of Studies on Alcohol and Drugs | volume = 75 | issue = 5| pages = 870–879 | doi = 10.15288/jsad.2014.75.870 | pmc = 4161706 | pmid=25208205}}</ref><br />
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== 基因 Genetics ==<br />
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=== 行为基因 Behavioral genetics ===<br />
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Individual differences in working-memory capacity are to some extent [[heritable]]; that is, about half of the variation between individuals is related to differences in their genes.<ref name=":1">{{Cite journal|last1=Engelhardt|first1=Laura E.|last2=Mann|first2=Frank D.|last3=Briley|first3=Daniel A.|last4=Church|first4=Jessica A.|last5=Harden|first5=K. Paige|last6=Tucker-Drob|first6=Elliot M.|title=Strong genetic overlap between executive functions and intelligence.|journal=Journal of Experimental Psychology: General|volume=145|issue=9|pages=1141–1159|doi=10.1037/xge0000195|pmc=5001920|pmid=27359131|year=2016}}</ref><ref name="Ando 615–624">{{Cite journal|last1=Ando|first1=Juko|last2=Ono|first2=Yutaka|last3=Wright|first3=Margaret J.|title=Genetic Structure of Spatial and Verbal Working Memory|journal=Behavior Genetics|language=en|volume=31|issue=6|pages=615–624|doi=10.1023/A:1013353613591|pmid=11838538|issn=0001-8244|year=2001}}</ref><ref>{{Cite journal|last1=Blokland|first1=Gabriëlla A. M.|last2=McMahon|first2=Katie L.|last3=Thompson|first3=Paul M.|last4=Martin|first4=Nicholas G.|last5=de Zubicaray|first5=Greig I.|last6=Wright|first6=Margaret J.|date=2011-07-27|title=Heritability of Working Memory Brain Activation|journal=Journal of Neuroscience|volume=31|issue=30|pages=10882–10890|doi=10.1523/jneurosci.5334-10.2011|pmid=21795540|pmc=3163233}}</ref> The genetic component of variability of working-memory capacity is largely shared with that of fluid intelligence.<ref name="Ando 615–624"/><ref name=":1" /><br />
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Individual differences in working-memory capacity are to some extent heritable; that is, about half of the variation between individuals is related to differences in their genes. The genetic component of variability of working-memory capacity is largely shared with that of fluid intelligence.<br />
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工作记忆能力的个体差异在某种程度上是遗传的,即个体间约一半的差异与基因差异有关<ref name=":1">{{Cite journal|last1=Engelhardt|first1=Laura E.|last2=Mann|first2=Frank D.|last3=Briley|first3=Daniel A.|last4=Church|first4=Jessica A.|last5=Harden|first5=K. Paige|last6=Tucker-Drob|first6=Elliot M.|title=Strong genetic overlap between executive functions and intelligence.|journal=Journal of Experimental Psychology: General|volume=145|issue=9|pages=1141–1159|doi=10.1037/xge0000195|pmc=5001920|pmid=27359131|year=2016}}</ref><ref name="Ando 615–624">{{Cite journal|last1=Ando|first1=Juko|last2=Ono|first2=Yutaka|last3=Wright|first3=Margaret J.|title=Genetic Structure of Spatial and Verbal Working Memory|journal=Behavior Genetics|language=en|volume=31|issue=6|pages=615–624|doi=10.1023/A:1013353613591|pmid=11838538|issn=0001-8244|year=2001}}</ref><ref>{{Cite journal|last1=Blokland|first1=Gabriëlla A. M.|last2=McMahon|first2=Katie L.|last3=Thompson|first3=Paul M.|last4=Martin|first4=Nicholas G.|last5=de Zubicaray|first5=Greig I.|last6=Wright|first6=Margaret J.|date=2011-07-27|title=Heritability of Working Memory Brain Activation|journal=Journal of Neuroscience|volume=31|issue=30|pages=10882–10890|doi=10.1523/jneurosci.5334-10.2011|pmid=21795540|pmc=3163233}}</ref>。工作记忆能力变异的遗传成分与流体智力的遗传成分大致相同<ref name="Ando 615–624"/><ref name=":1" /><br />
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=== 识别个别基因的尝试 Attempts to identify individual genes ===<br />
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Little is known about which genes are related to the functioning of working memory. Within the theoretical framework of the multi-component model, one candidate gene has been proposed, namely [[ROBO1]] for the hypothetical [[phonological loop]] component of working memory.<ref>{{Cite journal|last=Bates|first=Timothy|date=2011|title=Genetic Variance in a Component of the Language Acquisition Device: ROBO1 Polymorphisms Associated with Phonological Buffer Deficits|journal=Behavior Genetics|volume=41|issue=1|pages=50–7|doi=10.1007/s10519-010-9402-9|pmid=20949370}}</ref><br />
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Little is known about which genes are related to the functioning of working memory. Within the theoretical framework of the multi-component model, one candidate gene has been proposed, namely ROBO1 for the hypothetical phonological loop component of working memory.<br />
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我们对哪些基因与工作记忆的功能有关知之甚少。多成分模型的理论框架提出了一个候选基因——即工作记忆的语音回路ROBO1<ref>{{Cite journal|last=Bates|first=Timothy|date=2011|title=Genetic Variance in a Component of the Language Acquisition Device: ROBO1 Polymorphisms Associated with Phonological Buffer Deficits|journal=Behavior Genetics|volume=41|issue=1|pages=50–7|doi=10.1007/s10519-010-9402-9|pmid=20949370}}</ref>。<br />
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== 在学术成就方面的角色 Role in academic achievement ==<br />
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Working memory capacity is correlated with learning outcomes in literacy and numeracy. Initial evidence for this relation comes from the correlation between working-memory capacity and reading comprehension, as first observed by Daneman and Carpenter (1980)<ref>{{Cite journal|title = Individual differences in working memory and reading|journal = Journal of Verbal Learning and Verbal Behavior|date = 1980-08-01|pages = 450–466|volume = 19|issue = 4|doi = 10.1016/S0022-5371(80)90312-6|first1 = Meredyth|last1 = Daneman|first2 = Patricia A.|last2 = Carpenter}}</ref> and confirmed in a later meta-analytic review of several studies.<ref>{{Cite journal|last1=Daneman|first1=Meredyth|last2=Merikle|first2=Philip M.|title=Working memory and language comprehension: A meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=3|issue=4|pages=422–433|doi=10.3758/BF03214546|pmid=24213976|issn=1069-9384|year=1996|doi-access=free}}</ref> Subsequent work found that working memory performance in primary school children accurately predicted performance in mathematical problem solving.<ref>{{Cite journal|last1=Swanson|first1=H. Lee|last2=Beebe-Frankenberger|first2=Margaret|year=2004|title=The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties|journal=Journal of Educational Psychology|volume=96|issue=3|pages=471–491|doi=10.1037/0022-0663.96.3.471}}</ref> One longitudinal study showed that a child's working memory at 5 years old is a better predictor of academic success than IQ.<ref>{{Cite journal|vauthors=Alloway TP, Alloway RG |title=Investigating the predictive roles of working memory and IQ in academic attainment |journal=Journal of Experimental Child Psychology |volume=106|issue=1|pages= 20–9|year=2010|pmid=20018296 |doi=10.1016/j.jecp.2009.11.003|url=https://www.pure.ed.ac.uk/ws/files/11958608/Investigating_the_predictive_roles_of_working_memory_and_IQ_in_academic_attainment.pdf }}</ref><br />
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Working memory capacity is correlated with learning outcomes in literacy and numeracy. Initial evidence for this relation comes from the correlation between working-memory capacity and reading comprehension, as first observed by Daneman and Carpenter (1980) and confirmed in a later meta-analytic review of several studies. Subsequent work found that working memory performance in primary school children accurately predicted performance in mathematical problem solving. One longitudinal study showed that a child's working memory at 5 years old is a better predictor of academic success than IQ.<br />
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工作记忆容量与识字和算术能力的学习成果相关。1980年Daneman 和卡朋特 Carpenter首次从工作记忆容量和阅读理解的相关性研究中获得证据<ref>{{Cite journal|title = Individual differences in working memory and reading|journal = Journal of Verbal Learning and Verbal Behavior|date = 1980-08-01|pages = 450–466|volume = 19|issue = 4|doi = 10.1016/S0022-5371(80)90312-6|first1 = Meredyth|last1 = Daneman|first2 = Patricia A.|last2 = Carpenter}}</ref>——这在后来几项研究的元分析中也得到了证实<ref>{{Cite journal|last1=Daneman|first1=Meredyth|last2=Merikle|first2=Philip M.|title=Working memory and language comprehension: A meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=3|issue=4|pages=422–433|doi=10.3758/BF03214546|pmid=24213976|issn=1069-9384|year=1996|doi-access=free}}</ref>。随后的研究发现,小学生的工作记忆能力能够精确地反映在数学问题解决上<ref>{{Cite journal|last1=Swanson|first1=H. Lee|last2=Beebe-Frankenberger|first2=Margaret|year=2004|title=The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties|journal=Journal of Educational Psychology|volume=96|issue=3|pages=471–491|doi=10.1037/0022-0663.96.3.471}}</ref>。一项后续研究表明,孩子5岁时的工作记忆能力与智商相比,是我们预测其未来学术成就地更好依据<ref>{{Cite journal|vauthors=Alloway TP, Alloway RG |title=Investigating the predictive roles of working memory and IQ in academic attainment |journal=Journal of Experimental Child Psychology |volume=106|issue=1|pages= 20–9|year=2010|pmid=20018296 |doi=10.1016/j.jecp.2009.11.003|url=https://www.pure.ed.ac.uk/ws/files/11958608/Investigating_the_predictive_roles_of_working_memory_and_IQ_in_academic_attainment.pdf }}</ref>。<br />
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In a large-scale screening study, one in ten children in mainstream classrooms were identified with working memory deficits. The majority of them performed very poorly in academic achievements, independent of their IQ.<ref>{{Cite journal|vauthors=Alloway TP, Gathercole SE, Kirkwood H, Elliott J |title=The cognitive and behavioral characteristics of children with low working memory |journal=Child Development |volume=80 |issue=2 |pages=606–21 |year=2009 |pmid=19467014 |doi=10.1111/j.1467-8624.2009.01282.x|hdl=1893/978 |hdl-access=free }}</ref> Similarly, working memory deficits have been identified in national curriculum low-achievers as young as seven years of age.<ref>{{Cite journal|title = Working memory deficits in children with low achievements in the national curriculum at 7 years of age|journal = British Journal of Educational Psychology|date = 2000-06-01|issn = 2044-8279|pages = 177–194|volume = 70|issue = 2|doi = 10.1348/000709900158047|language = en|first1 = Susan E.|last1 = Gathercole|first2 = Susan J.|last2 = Pickering|pmid=10900777}}</ref> Without appropriate intervention, these children lag behind their peers. A recent study of 37 school-age children with significant learning disabilities has shown that working memory capacity at baseline measurement, but not IQ, predicts learning outcomes two years later.<ref>{{Cite journal|first1=Tracy Packiam |last1=Alloway |year=2009 |journal=European Journal of Psychological Assessment |volume=25 |issue=2 |pages=92–8 |doi=10.1027/1015-5759.25.2.92 |title=Working Memory, but Not IQ, Predicts Subsequent Learning in Children with Learning Difficulties|hdl=1893/1005 |hdl-access=free }}</ref> This suggests that working memory impairments are associated with low learning outcomes and constitute a high risk factor for educational underachievement for children. In children with learning disabilities such as [[dyslexia]], [[ADHD]], and developmental coordination disorder, a similar pattern is evident.<ref>{{cite book | last1 = Pickering | first1 = Susan J. | title = Working memory in dyslexia | editor1 = Tracy Packiam Alloway |editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Wagner | first1 = Richard K. | last2 = Muse | first2 = Andrea | title = Short-term memory deficits in developmental dyslexia | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Roodenrys | first1 = Steve | title = Working memory function in attention deficit hyperactivity disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Alloway | first1 = Tracy Packiam | title = Working memory skills in children with developmental coordination disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><br />
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In a large-scale screening study, one in ten children in mainstream classrooms were identified with working memory deficits. The majority of them performed very poorly in academic achievements, independent of their IQ. Similarly, working memory deficits have been identified in national curriculum low-achievers as young as seven years of age. Without appropriate intervention, these children lag behind their peers. A recent study of 37 school-age children with significant learning disabilities has shown that working memory capacity at baseline measurement, but not IQ, predicts learning outcomes two years later. This suggests that working memory impairments are associated with low learning outcomes and constitute a high risk factor for educational underachievement for children. In children with learning disabilities such as dyslexia, ADHD, and developmental coordination disorder, a similar pattern is evident.<br />
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在一项大规模的筛查研究中,大班教学模式中十分之一的儿童被认为患有工作记忆缺陷。他们中的大多数人在学术成就上乏善可陈——这与智商无关<ref>{{Cite journal|vauthors=Alloway TP, Gathercole SE, Kirkwood H, Elliott J |title=The cognitive and behavioral characteristics of children with low working memory |journal=Child Development |volume=80 |issue=2 |pages=606–21 |year=2009 |pmid=19467014 |doi=10.1111/j.1467-8624.2009.01282.x|hdl=1893/978 |hdl-access=free }}</ref>。同样,国家课程标准把最早在7岁就表现出工作记忆缺陷的儿童定性为低成就学生<ref>{{Cite journal|title = Working memory deficits in children with low achievements in the national curriculum at 7 years of age|journal = British Journal of Educational Psychology|date = 2000-06-01|issn = 2044-8279|pages = 177–194|volume = 70|issue = 2|doi = 10.1348/000709900158047|language = en|first1 = Susan E.|last1 = Gathercole|first2 = Susan J.|last2 = Pickering|pmid=10900777}}</ref>。如果没有适当的干预,这些孩子就会落后于同龄人。最近,一项针对37名具有显著学习障碍的学龄儿童的研究表明,基线测量的工作记忆能力(而非智商)可预测两年后的学习结果<ref>{{Cite journal|first1=Tracy Packiam |last1=Alloway |year=2009 |journal=European Journal of Psychological Assessment |volume=25 |issue=2 |pages=92–8 |doi=10.1027/1015-5759.25.2.92 |title=Working Memory, but Not IQ, Predicts Subsequent Learning in Children with Learning Difficulties|hdl=1893/1005 |hdl-access=free }}</ref>。这表明低分与工作记忆障碍有关,甚至成为导致教育失败的高风险因素。在有学习障碍的儿童中(如'''<font color="#ff8000">诵读困难dyslexia</font>'''、'''<font color="#ff8000">多动症ADHD</font>'''和失用症),类似模式是显而易见的<ref>{{cite book | last1 = Pickering | first1 = Susan J. | title = Working memory in dyslexia | editor1 = Tracy Packiam Alloway |editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Wagner | first1 = Richard K. | last2 = Muse | first2 = Andrea | title = Short-term memory deficits in developmental dyslexia | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Roodenrys | first1 = Steve | title = Working memory function in attention deficit hyperactivity disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Alloway | first1 = Tracy Packiam | title = Working memory skills in children with developmental coordination disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref>。<br />
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== 与注意力的关系 Relation to attention ==<br />
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There is some evidence that optimal working memory performance links to the neural ability to focus attention on task-relevant information and to ignore distractions,<ref>{{Cite journal|date=March 2009|title=Neural suppression of irrelevant information underlies optimal working memory performance|journal=The Journal of Neuroscience|volume=29|issue=10|pages=3059–66|doi=10.1523/JNEUROSCI.4621-08.2009|pmc=2704557|pmid=19279242|author=Zanto, T. P.|author2=Gazzaley, A.}}</ref> and that practice-related improvement in working memory is due to increasing these abilities.<ref>{{cite journal|last2=Zanto|first2=T.&nbsp;P.|last3=Rutman|first3=A.&nbsp;M.|last4=Clapp|first4=W.&nbsp;C.|last5=Gazzaley|first5=A.|year=2009|title=Practice-related improvement in working memory is modulated by changes in processing external interference|journal=Journal of Neurophysiology|volume=102|issue=3|pages=1779–89|doi=10.1152/jn.00179.2009|pmc=2746773|pmid=19587320|last1=Berry|first1=A.&nbsp;S.}}</ref> One line of research suggests a link between the working memory capacities of a person and their ability to control the orientation of attention to stimuli in the environment.<ref name="attention09">{{Cite journal|vauthors=Fukuda K, Vogel EK |title=Human variation in overriding attentional capture |journal=The Journal of Neuroscience |volume=29 |issue=27 |pages=8726–33 |date=July 2009 |pmid=19587279 |pmc=6664881 |doi=10.1523/JNEUROSCI.2145-09.2009}}</ref> Such control enables people to attend to information important for their current goals, and to ignore goal-irrelevant stimuli that tend to capture their attention due to their sensory [[salience (neuroscience)|saliency]] (such as an ambulance siren). The direction of attention according to one's goals is assumed to rely on "top-down" signals from the pre-frontal cortex (PFC) that biases processing in [[posterior cortex|posterior cortical areas]].<ref>{{Cite journal|vauthors=Desimone R, Duncan J |title=Neural mechanisms of selective visual attention |journal=Annual Review of Neuroscience |volume=18 |pages=193–222 |year=1995 |pmid=7605061 |doi=10.1146/annurev.ne.18.030195.001205}}</ref> Capture of attention by salient stimuli is assumed to be driven by "bottom-up" signals from subcortical structures and the primary sensory cortices.<ref>{{Cite journal|vauthors=Yantis S, Jonides J |title=Abrupt visual onsets and selective attention: voluntary versus automatic allocation |journal=Journal of Experimental Psychology. Human Perception and Performance |volume=16 |issue=1 |pages=121–34 |date=February 1990 |pmid=2137514 |url=http://content.apa.org/journals/xhp/16/1/121 |doi=10.1037/0096-1523.16.1.121|citeseerx=10.1.1.211.5016 }}</ref> The ability to override "bottom-up" capture of attention differs between individuals, and this difference has been found to correlate with their performance in a working-memory test for visual information.<ref name="attention09" /> Another study, however, found no correlation between the ability to override attentional capture and measures of more general working-memory capacity.<ref>{{Cite journal|last1=Mall|first1=Jonathan T.|last2=Morey|first2=Candice C.|last3=Wolff|first3=Michael J.|last4=Lehnert|first4=Franziska|date=2014-01-09|title=Visual selective attention is equally functional for individuals with low and high working memory capacity: Evidence from accuracy and eye movements|journal=Attention, Perception, & Psychophysics|language=en|volume=76|issue=7|pages=1998–2014|doi=10.3758/s13414-013-0610-2|pmid=24402698|issn=1943-3921|url=http://orca.cf.ac.uk/105362/1/Morey.%20Visual%20selective.pdf}}</ref><br />
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There is some evidence that optimal working memory performance links to the neural ability to focus attention on task-relevant information and to ignore distractions, and that practice-related improvement in working memory is due to increasing these abilities. One line of research suggests a link between the working memory capacities of a person and their ability to control the orientation of attention to stimuli in the environment. Such control enables people to attend to information important for their current goals, and to ignore goal-irrelevant stimuli that tend to capture their attention due to their sensory saliency (such as an ambulance siren). The direction of attention according to one's goals is assumed to rely on "top-down" signals from the pre-frontal cortex (PFC) that biases processing in posterior cortical areas. Capture of attention by salient stimuli is assumed to be driven by "bottom-up" signals from subcortical structures and the primary sensory cortices. The ability to override "bottom-up" capture of attention differs between individuals, and this difference has been found to correlate with their performance in a working-memory test for visual information. Another study, however, found no correlation between the ability to override attentional capture and measures of more general working-memory capacity.<br />
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有证据表明,较佳的工作记忆表现与能否忽略干扰集中注意力于任务相关信息的神经能力有关<ref>{{Cite journal|date=March 2009|title=Neural suppression of irrelevant information underlies optimal working memory performance|journal=The Journal of Neuroscience|volume=29|issue=10|pages=3059–66|doi=10.1523/JNEUROSCI.4621-08.2009|pmc=2704557|pmid=19279242|author=Zanto, T. P.|author2=Gazzaley, A.}}</ref>,也就是说训练之后的工作记忆之所以能够改善,是因为上述能力得到了改善<ref>{{cite journal|last2=Zanto|first2=T.&nbsp;P.|last3=Rutman|first3=A.&nbsp;M.|last4=Clapp|first4=W.&nbsp;C.|last5=Gazzaley|first5=A.|year=2009|title=Practice-related improvement in working memory is modulated by changes in processing external interference|journal=Journal of Neurophysiology|volume=102|issue=3|pages=1779–89|doi=10.1152/jn.00179.2009|pmc=2746773|pmid=19587320|last1=Berry|first1=A.&nbsp;S.}}</ref>。一项研究表明,工作记忆能力和面对环境刺激人能否控制注意力方向之间存在联系<ref name="attention09">{{Cite journal|vauthors=Fukuda K, Vogel EK |title=Human variation in overriding attentional capture |journal=The Journal of Neuroscience |volume=29 |issue=27 |pages=8726–33 |date=July 2009 |pmid=19587279 |pmc=6664881 |doi=10.1523/JNEUROSCI.2145-09.2009}}</ref>。因为这种控制会引导人关注相关的信息而忽略与目标无关的刺激——这些刺激往往因其感官显著性(如救护车警报器)而吸引人的注意力<ref>{{Cite journal|vauthors=Desimone R, Duncan J |title=Neural mechanisms of selective visual attention |journal=Annual Review of Neuroscience |volume=18 |pages=193–222 |year=1995 |pmid=7605061 |doi=10.1146/annurev.ne.18.030195.001205}}</ref>。个体的注意力方向被认为取决于前额叶皮质(PFC)“自上而下”发出的信号,这种信号偏好于在后皮质区处理任务<ref>{{Cite journal|vauthors=Yantis S, Jonides J |title=Abrupt visual onsets and selective attention: voluntary versus automatic allocation |journal=Journal of Experimental Psychology. Human Perception and Performance |volume=16 |issue=1 |pages=121–34 |date=February 1990 |pmid=2137514 |url=http://content.apa.org/journals/xhp/16/1/121 |doi=10.1037/0096-1523.16.1.121|citeseerx=10.1.1.211.5016 }}</ref>。皮层下结构和初级感觉皮层发出的“自下而上”的信号驱动着由显著刺激引发的注意力。<ref name="attention09" />然而,另一项研究发现,注意力过度集中对在工作记忆能力测量过程中没有起到预期作用<ref>{{Cite journal|last1=Mall|first1=Jonathan T.|last2=Morey|first2=Candice C.|last3=Wolff|first3=Michael J.|last4=Lehnert|first4=Franziska|date=2014-01-09|title=Visual selective attention is equally functional for individuals with low and high working memory capacity: Evidence from accuracy and eye movements|journal=Attention, Perception, & Psychophysics|language=en|volume=76|issue=7|pages=1998–2014|doi=10.3758/s13414-013-0610-2|pmid=24402698|issn=1943-3921|url=http://orca.cf.ac.uk/105362/1/Morey.%20Visual%20selective.pdf}}</ref><br />
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== 与神经系统疾病的关系 Relationship with neural disorders ==<br />
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An impairment of working memory functioning is normally seen in several neural disorders:<br />
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An impairment of working memory functioning is normally seen in several neural disorders:<br />
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工作记忆功能障碍通常见于以下神经系统疾病:<br />
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'''ADHD:''' Several authors<ref>Barkley; Castellanos and Tannock; Pennington and Ozonoff; Schachar (according to the source)</ref> have proposed that symptoms of [[ADHD]] arise from a primary deficit in a specific executive function (EF) domain such as working memory, response inhibition or a more general weakness in executive control.<ref name="WillcuttDoyle2005">{{cite journal|date=June 2005|title=Validity of the executive function theory of attention-deficit/hyperactivity disorder: a meta-analytic review|journal=Biol. Psychiatry|volume=57|issue=11|pages=1336–46|doi=10.1016/j.biopsych.2005.02.006|pmid=15950006|vauthors=Willcutt EG, Doyle AE, Nigg JT, Faraone SV, Pennington BF}}</ref> A meta-analytical review cites several studies that found significant lower group results for ADHD in spatial and verbal working memory tasks, and in several other EF tasks. However, the authors concluded that EF weaknesses neither are necessary nor sufficient to cause all cases of ADHD.<ref name="WillcuttDoyle2005" /><br />
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ADHD: Several authors have proposed that symptoms of ADHD arise from a primary deficit in a specific executive function (EF) domain such as working memory, response inhibition or a more general weakness in executive control. A meta-analytical review cites several studies that found significant lower group results for ADHD in spatial and verbal working memory tasks, and in several other EF tasks. However, the authors concluded that EF weaknesses neither are necessary nor sufficient to cause all cases of ADHD.<br />
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注意力缺陷多动障碍(ADHD): 一些研究者<ref>Barkley; Castellanos and Tannock; Pennington and Ozonoff; Schachar (according to the source)</ref>提出,ADHD 源于特定 '''<font color="#ff8000">执行功能(EF) Executive Function (EF)</font>'''领域——如工作记忆、反应抑制或执行控制方面——的原发性缺陷<ref name="WillcuttDoyle2005">{{cite journal|date=June 2005|title=Validity of the executive function theory of attention-deficit/hyperactivity disorder: a meta-analytic review|journal=Biol. Psychiatry|volume=57|issue=11|pages=1336–46|doi=10.1016/j.biopsych.2005.02.006|pmid=15950006|vauthors=Willcutt EG, Doyle AE, Nigg JT, Faraone SV, Pennington BF}}</ref>。引用了几项研究之后,研究人员得出一份元分析报告,发现在空间和语言工作记忆任务及其他几项EF任务中,ADHD群体有较低的成绩。然而,研究者的结论是EF缺陷既不必然也不足以引发所有的ADHD病例<ref name="WillcuttDoyle2005" /><br />
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Several [[neurotransmitters]], such as [[dopamine]] and [[glutamate]] may be both involved in ADHD and working memory. Both are associated with the [[frontal lobe|frontal]] brain, self-direction and self-regulation, but [[Causality|cause–effect]] have not been confirmed, so it is unclear whether working memory dysfunction leads to ADHD, or ADHD distractibility leads to poor functionality of working memory, or if there is some other connection.<ref>[http://guilfordjournals.com/doi/abs/10.1521/adhd.2008.16.6.8 Working Memory as a Core Deficit in ADHD: Preliminary Findings and Implications] – 2008</ref><ref name="Clark Blackwell 2007">{{cite journal|date=June 2007|title=Association between response inhibition and working memory in adult ADHD: a link to right frontal cortex pathology?|journal=Biol. Psychiatry|volume=61|issue=12|pages=1395–401|doi=10.1016/j.biopsych.2006.07.020|pmid=17046725|vauthors=Clark L, Blackwell AD, Aron AR, etal}}</ref><ref name="Roodenrys Koloski 2001">{{cite journal|last2=Koloski|first2=Natasha|last3=Grainger|first3=Jessica|year=2001|title=Working memory function in attention deficit hyperactivity disordered and reading disabled children|journal=British Journal of Developmental Psychology|volume=19|issue=3|pages=325–337|doi=10.1348/026151001166128|issn=0261-510X|last1=Roodenrys|first1=Steven}}</ref><br />
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Several neurotransmitters, such as dopamine and glutamate may be both involved in ADHD and working memory. Both are associated with the frontal brain, self-direction and self-regulation, but cause–effect have not been confirmed, so it is unclear whether working memory dysfunction leads to ADHD, or ADHD distractibility leads to poor functionality of working memory, or if there is some other connection.<br />
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多巴胺和谷氨酸盐等多种神经递质可能都与ADHD和工作记忆有关。两者都与额叶大脑、'''<font color="#ff8000">自我定向self-direction</font>'''和'''<font color="#ff8000">自我调节self-regulation</font>'''有关,但其中的因果关系尚未得到确认。所以目前不清楚是工作记忆功能障碍导致 ADHD,还是注意力分散导致ADHD工作记忆功能低下,亦或存在着其他联系<ref>[http://guilfordjournals.com/doi/abs/10.1521/adhd.2008.16.6.8 Working Memory as a Core Deficit in ADHD: Preliminary Findings and Implications] – 2008</ref><ref name="Clark Blackwell 2007">{{cite journal|date=June 2007|title=Association between response inhibition and working memory in adult ADHD: a link to right frontal cortex pathology?|journal=Biol. Psychiatry|volume=61|issue=12|pages=1395–401|doi=10.1016/j.biopsych.2006.07.020|pmid=17046725|vauthors=Clark L, Blackwell AD, Aron AR, etal}}</ref><ref name="Roodenrys Koloski 2001">{{cite journal|last2=Koloski|first2=Natasha|last3=Grainger|first3=Jessica|year=2001|title=Working memory function in attention deficit hyperactivity disordered and reading disabled children|journal=British Journal of Developmental Psychology|volume=19|issue=3|pages=325–337|doi=10.1348/026151001166128|issn=0261-510X|last1=Roodenrys|first1=Steven}}</ref>。<br />
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'''Parkinson's disease''':&nbsp;Patients with [[Parkinson's]] show signs of a reduced verbal function of working memory. They wanted to find if the reduction is due to a lack of ability to focus on relevant tasks, or a low amount of memory capacity. Twenty-one patients with Parkinson's were tested in comparison to the control group of 28 participants of the same age. The researchers found that both hypotheses were the reason working memory function is reduced which did not fully agree with their hypothesis that it is either one or the other.<ref>{{Cite journal|pmc=2929336|title=Visual working memory deficits in patients with Parkinson's disease are due to both reduced storage capacity and impaired ability to filter out irrelevant information|last=Lee|first=Eun-Young|date=5 August 2010|journal=Brain|volume=133|issue=9|pages=2677–2689|doi=10.1093/brain/awq197|pmid=20688815}}</ref><br />
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Parkinson's disease:&nbsp;Patients with Parkinson's show signs of a reduced verbal function of working memory. They wanted to find if the reduction is due to a lack of ability to focus on relevant tasks, or a low amount of memory capacity. Twenty-one patients with Parkinson's were tested in comparison to the control group of 28 participants of the same age. The researchers found that both hypotheses were the reason working memory function is reduced which did not fully agree with their hypothesis that it is either one or the other.<br />
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'''<font color="#ff8000">帕金森病 Parkinson's Disease</font>''': 帕金森病患者表现出工作记忆语言功能的减退。研究者想知道这种减少是因为缺乏专注于相关任务的能力,还是因为记忆容量太小。他们对21名帕金森病患者与28名同龄对照组进行了测试。研究人员发现二者都是工作记忆功能减退的原因,而非他们先前假设的原因在二者之一<ref>{{Cite journal|pmc=2929336|title=Visual working memory deficits in patients with Parkinson's disease are due to both reduced storage capacity and impaired ability to filter out irrelevant information|last=Lee|first=Eun-Young|date=5 August 2010|journal=Brain|volume=133|issue=9|pages=2677–2689|doi=10.1093/brain/awq197|pmid=20688815}}</ref>。<br />
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'''Alzheimer's disease''': As [[Alzheimer's disease]] becomes more serious, less working memory functions. There is one study that focuses on the neural connections and fluidity of working memory in mice brains. Half of the mice were given an injection that is similar to Alzheimer's effects, and the other half were not. Then they were expected to go through a maze that is a task to test working memory. The study help answer questions about how Alzheimer's can deteriorate the working memory and ultimately obliterate memory functions.<ref>{{Cite journal|last=Tiaotiao|first=Liu|date=December 2014|title=Functional connectivity in a rat model of Alzheimer's disease during a working memory task|journal=Current Alzheimer Research|volume=11|issue=10|pages=981–991|doi=10.2174/1567205011666141107125912 |pmid=25387338}}</ref><br />
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Alzheimer's disease: As Alzheimer's disease becomes more serious, less working memory functions. There is one study that focuses on the neural connections and fluidity of working memory in mice brains. Half of the mice were given an injection that is similar to Alzheimer's effects, and the other half were not. Then they were expected to go through a maze that is a task to test working memory. The study help answer questions about how Alzheimer's can deteriorate the working memory and ultimately obliterate memory functions.<br />
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'''<font color="#ff8000">阿尔茨海默病 Alzheimer's Disease</font>''': 工作记忆功能随着阿尔茨海默症病情的加重而降低。在一项针对老鼠大脑中的神经连接和工作记忆流动性的研究中,一半的老鼠注射了可以引发类阿尔茨海默症的药物,另一半则不注射药物。然后让它们穿越一个迷宫,即完成一个工作记忆测试任务。这项研究有助于回答阿尔兹海默症是如何损害工作记忆并最终消除记忆功能的<ref>{{Cite journal|last=Tiaotiao|first=Liu|date=December 2014|title=Functional connectivity in a rat model of Alzheimer's disease during a working memory task|journal=Current Alzheimer Research|volume=11|issue=10|pages=981–991|doi=10.2174/1567205011666141107125912 |pmid=25387338}}</ref>。<br />
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'''Huntington's disease''':&nbsp;A group of researchers hosted a study that researched the function and connectivity of working memory over a 30-month longitudinal experiment. It found that there were certain places in the brain where most connectivity was decreased in pre-[[Huntington disease]]d patients, in comparison to the control group that remained consistently functional.<ref>{{Cite journal|last=Poudel|first=Govinda R.|date=January 2015|title=Functional changes during working memory in Huntington's disease: 30-month longitudinal data from the IMAGE-HD study|journal=Brain Structure and Function|volume=220|issue=1|pages=501–512|pmid=24240602|doi=10.1007/s00429-013-0670-z}}</ref><br />
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Huntington's disease:&nbsp;A group of researchers hosted a study that researched the function and connectivity of working memory over a 30-month longitudinal experiment. It found that there were certain places in the brain where most connectivity was decreased in pre-Huntington diseased patients, in comparison to the control group that remained consistently functional.<br />
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'''<font color="#ff8000">亨廷顿氏病 Huntington's Disease</font>''': 一组研究人员进行了为期30个月的纵向实验,研究工作记忆的功能和关联性。研究发现,亨廷顿症患者大脑中特定部位的关联性降低,而对照组功能正常<ref>{{Cite journal|last=Poudel|first=Govinda R.|date=January 2015|title=Functional changes during working memory in Huntington's disease: 30-month longitudinal data from the IMAGE-HD study|journal=Brain Structure and Function|volume=220|issue=1|pages=501–512|pmid=24240602|doi=10.1007/s00429-013-0670-z}}</ref><br />
。<br />
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== 参见 See also ==<br />
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* [[多重记忆模型 Atkinson–Shiffrin memory model]]<br />
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* {{Section link|Prefrontal cortex|注意力和记忆 Attention and memory}}<br />
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* [[孤独症与工作记忆 Autism and working memory]]<br />
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* [[模糊痕迹理论 Fuzzy-trace theory]]<br />
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* [[中期记忆 Intermediate-term memory]]<br />
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* [[记忆与老化 Memory and aging]]<br />
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* [[PBWM|前额叶基底节工作记忆 Prefrontal cortex basal ganglia working memory (PBWM)]]<br />
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* [[意识结构 Cognitive architecture]]<br />
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* [[提姆・沙丽斯 Tim Shallice]]<br />
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== 参考文献 References ==<br />
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{{Reflist|33em}}<br />
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== 外部链接 External links ==<br />
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* [http://psych.colorado.edu/~miyake/MWM%20Chapter%201.pdf Models of Working Memory (Mechanisms of Active Maintenance and Executive Control)]<br />
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{{Memory}}<br />
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{{Dyslexia}}<br />
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[[Category:Memory processes]]<br />
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Category:Memory processes<br />
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分类: 记忆过程<br />
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[[Category:Problem solving]]<br />
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Category:Problem solving<br />
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分类: 解决问题<br />
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[[Category:Human behavior]]<br />
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Category:Human behavior<br />
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分类: 人类行为<br />
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<small>This page was moved from [[wikipedia:en:Working memory]]. Its edit history can be viewed at [[工作记忆/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%B7%A5%E4%BD%9C%E8%AE%B0%E5%BF%86&diff=21545工作记忆2021-02-04T02:08:19Z<p>Vicky:</p>
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<div>已由[[Xebec]]进行初步翻译。由和光同尘审校。<br />
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{{short description|Cognitive system for temporarily holding information}}<br />
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{{Use dmy dates|date=June 2020}}<br />
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'''Working memory''' is a cognitive system with a limited capacity that can [[Memory|hold information]] temporarily.<ref>{{Cite book|title=Models of working memory. Mechanisms of active maintenance and executive control|editor1=Miyake, A.|editor2=Shah, P.|publisher=Cambridge University Press|year=1999 |isbn=0-521-58325-X}}</ref> Working memory is important for reasoning and the guidance of decision-making and behavior.<ref name="Executive functions">{{cite journal | author = Diamond A | title = Executive functions | journal = Annu Rev Psychol | volume = 64 | pages = 135–168 | year = 2013 | pmid = 23020641 | pmc = 4084861 | doi = 10.1146/annurev-psych-113011-143750 | quote = WM (holding information in mind and manipulating it) is distinct from short-term memory (just holding information in mind). They cluster onto separate factors in factor analyses of children, adolescents, and adults (Alloway et al. 2004, Gathercole et al. 2004). They are linked to different neural subsystems. WM relies more on dorsolateral prefrontal cortex, whereas maintaining information in mind but not manipulating it [as long as the number of items is not huge (suprathreshold)] does not need involvement of dorsolateral prefrontal cortex (D’Esposito et al. 1999, Eldreth et al. 2006, Smith & Jonides 1999). Imaging studies show frontal activation only in ventrolateral prefrontal cortex for memory maintenance that is not suprathreshold.<br /><br />WM and short-term memory also show different developmental progressions; the latter develops earlier and faster.}}</ref><ref name="NHM-Cognitive Control">{{cite book|title=Molecular Neuropharmacology: A Foundation for Clinical Neuroscience|vauthors=Malenka RC, Nestler EJ, Hyman SE|publisher=McGraw-Hill Medical|year=2009|isbn=978-0-07-148127-4|veditors=Sydor A, Brown RY|edition=2nd|location=New York|pages=313–321|chapter=Chapter 13: Higher Cognitive Function and Behavioral Control|quote={{bull}} Executive function, the cognitive control of behavior, depends on the prefrontal cortex, which is highly developed in higher primates and especially humans.<br />{{bull}} Working memory is a short-term, capacity-limited cognitive buffer that stores information and permits its manipulation to guide decision-making and behavior.&nbsp;...<br /> working memory may be impaired in ADHD, the most common childhood psychiatric disorder seen in clinical settings&nbsp;... ADHD can be conceptualized as a disorder of executive function; specifically, ADHD is characterized by reduced ability to exert and maintain cognitive control of behavior. Compared with healthy individuals, those with ADHD have diminished ability to suppress inappropriate prepotent responses to stimuli (impaired response inhibition) and diminished ability to inhibit responses to irrelevant stimuli (impaired interference suppression).&nbsp;... Early results with structural MRI show thinning of the cerebral cortex in ADHD subjects compared with age-matched controls in prefrontal cortex and posterior parietal cortex, areas involved in working memory and attention.}}</ref> Working memory is often used synonymously with [[short-term memory]], but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information.<ref name="Executive functions" /><ref name="Cowan">{{Cite book | title = What are the differences between long-term, short-term, and working memory? | author=Cowan, Nelson | journal=Prog. Brain Res. | year=2008 | issue=169 | pages=323–338 |pmid=18394484 | doi=10.1016/S0079-6123(07)00020-9 | pmc=2657600 | volume=169| series=Progress in Brain Research | isbn=978-0-444-53164-3 }}</ref> Working memory is a theoretical concept central to [[cognitive psychology]], neuropsychology, and [[neuroscience]].<br />
<br />
Working memory is a cognitive system with a limited capacity that can hold information temporarily. Working memory is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct, assuming that working memory allows for the manipulation of stored information, whereas short-term memory only refers to the short-term storage of information. Working memory is a theoretical concept central to cognitive psychology, neuropsychology, and neuroscience.<br />
<br />
'''<font color="#ff8000">工作记忆 Working Memory</font>'''是一种能临时容纳有限信息的认知系统<ref>{{Cite book|title=Models of working memory. Mechanisms of active maintenance and executive control|editor1=Miyake, A.|editor2=Shah, P.|publisher=Cambridge University Press|year=1999 |isbn=0-521-58325-X}}</ref>,对推理、决策倾向和行为倾向有着重要影响<ref name="Executive functions">{{cite journal | author = Diamond A | title = Executive functions | journal = Annu Rev Psychol | volume = 64 | pages = 135–168 | year = 2013 | pmid = 23020641 | pmc = 4084861 | doi = 10.1146/annurev-psych-113011-143750 | quote = WM (holding information in mind and manipulating it) is distinct from short-term memory (just holding information in mind). They cluster onto separate factors in factor analyses of children, adolescents, and adults (Alloway et al. 2004, Gathercole et al. 2004). They are linked to different neural subsystems. WM relies more on dorsolateral prefrontal cortex, whereas maintaining information in mind but not manipulating it [as long as the number of items is not huge (suprathreshold)] does not need involvement of dorsolateral prefrontal cortex (D’Esposito et al. 1999, Eldreth et al. 2006, Smith & Jonides 1999). Imaging studies show frontal activation only in ventrolateral prefrontal cortex for memory maintenance that is not suprathreshold.<br /><br />WM and short-term memory also show different developmental progressions; the latter develops earlier and faster.}}</ref><ref name="NHM-Cognitive Control">{{cite book|title=Molecular Neuropharmacology: A Foundation for Clinical Neuroscience|vauthors=Malenka RC, Nestler EJ, Hyman SE|publisher=McGraw-Hill Medical|year=2009|isbn=978-0-07-148127-4|veditors=Sydor A, Brown RY|edition=2nd|location=New York|pages=313–321|chapter=Chapter 13: Higher Cognitive Function and Behavioral Control|quote={{bull}} Executive function, the cognitive control of behavior, depends on the prefrontal cortex, which is highly developed in higher primates and especially humans.<br />{{bull}} Working memory is a short-term, capacity-limited cognitive buffer that stores information and permits its manipulation to guide decision-making and behavior.&nbsp;...<br /> working memory may be impaired in ADHD, the most common childhood psychiatric disorder seen in clinical settings&nbsp;... ADHD can be conceptualized as a disorder of executive function; specifically, ADHD is characterized by reduced ability to exert and maintain cognitive control of behavior. Compared with healthy individuals, those with ADHD have diminished ability to suppress inappropriate prepotent responses to stimuli (impaired response inhibition) and diminished ability to inhibit responses to irrelevant stimuli (impaired interference suppression).&nbsp;... Early results with structural MRI show thinning of the cerebral cortex in ADHD subjects compared with age-matched controls in prefrontal cortex and posterior parietal cortex, areas involved in working memory and attention.}}</ref>。工作记忆常作为'''<font color="#ff8000">短期记忆 short-term Memory</font>'''的同义词,但一些理论学者认为,工作记忆能够调用存储的信息,而短期记忆仅指短期存储的信息,故二者不同<ref name="Executive functions" /><ref name="Cowan">{{Cite book | title = What are the differences between long-term, short-term, and working memory? | author=Cowan, Nelson | journal=Prog. Brain Res. | year=2008 | issue=169 | pages=323–338 |pmid=18394484 | doi=10.1016/S0079-6123(07)00020-9 | pmc=2657600 | volume=169| series=Progress in Brain Research | isbn=978-0-444-53164-3 }}</ref>。工作记忆是'''<font color="#ff8000">认知心理学 cognitive psychology </font>'''、'''<font color="#ff8000">神经心理学 neuropsychology </font>'''和'''<font color="#ff8000">神经科学 neuroscience </font>'''的核心概念之一。<br />
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== 历史 History ==<br />
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The term "working memory" was coined by [[George Armitage Miller|Miller]], [[Eugene Galanter|Galanter]], and [[Karl H. Pribram|Pribram]],<ref name="isbn0-03-010075-5">{{cite book |author1=Pribram, Karl H. |author2=Miller, George A. |author3=Galanter, Eugene |title=Plans and the structure of behavior |publisher=Holt, Rinehart and Winston |location=New York |year=1960 |pages=[https://archive.org/details/plansstructureo00mill/page/65 65] |isbn=978-0-03-010075-8 |oclc=190675 |url-access=registration |url=https://archive.org/details/plansstructureo00mill/page/65 }}</ref><ref>{{Cite journal|author=Baddeley A |title=Working memory: looking back and looking forward |journal=Nature Reviews Neuroscience |volume=4 |issue=10 |pages=829–39 |date=October 2003 |pmid=14523382 |doi=10.1038/nrn1201}}</ref> and was used in the 1960s in the context of theories that likened the mind to a computer. In 1968, [[Atkinson–Shiffrin memory model|Atkinson and Shiffrin]]<ref name="Atkinson Shiffrin 1968">{{cite book | last1 = Atkinson | first1 = R.C. | last2 = Shiffrin | first2 = R.M. | title = Human Memory: A Proposed System and its Control Processes | volume = 2 |pages = 89–195| editor1 = Kenneth W Spence |editor2= Janet T Spence | work = The psychology of learning and motivation | publisher = Academic Press | year = 1968 | isbn = 978-0-12-543302-0 |oclc = 185468704 |doi = 10.1016/S0079-7421(08)60422-3}}</ref> used the term to describe their "short-term store". What we now call working memory was formerly referred to variously as a "short-term store" or [[short-term memory]], primary memory, immediate memory, operant memory, and provisional memory.<ref name="Fuster 1997">{{cite book |author=Fuster, Joaquin M. |title=The prefrontal cortex: anatomy, physiology, and neuropsychology of the frontal lobe |publisher=Lippincott-Raven |location=Philadelphia |year=1997 |isbn=978-0-397-51849-4 |oclc=807338522 }}{{Page needed|date=September 2010}}</ref> Short-term memory is the ability to remember information over a brief period (in the order of seconds). Most theorists today use the concept of working memory to replace or include the older concept of short-term memory, marking a stronger emphasis on the notion of manipulating information rather than mere maintenance.<br />
<br />
The term "working memory" was coined by Miller, Galanter, and Pribram, and was used in the 1960s in the context of theories that likened the mind to a computer. In 1968, Atkinson and Shiffrin used the term to describe their "short-term store". What we now call working memory was formerly referred to variously as a "short-term store" or short-term memory, primary memory, immediate memory, operant memory, and provisional memory. Short-term memory is the ability to remember information over a brief period (in the order of seconds). Most theorists today use the concept of working memory to replace or include the older concept of short-term memory, marking a stronger emphasis on the notion of manipulating information rather than mere maintenance.<br />
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“'''<font color="#ff800">工作记忆 Working Memory</font>'''”这个术语由米勒 Miller、加兰特 Galanter和普里布拉姆 Pribram 提出<ref name="isbn0-03-010075-5">{{cite book |author1=Pribram, Karl H. |author2=Miller, George A. |author3=Galanter, Eugene |title=Plans and the structure of behavior |publisher=Holt, Rinehart and Winston |location=New York |year=1960 |pages=[https://archive.org/details/plansstructureo00mill/page/65 65] |isbn=978-0-03-010075-8 |oclc=190675 |url-access=registration |url=https://archive.org/details/plansstructureo00mill/page/65 }}</ref><ref>{{Cite journal|author=Baddeley A |title=Working memory: looking back and looking forward |journal=Nature Reviews Neuroscience |volume=4 |issue=10 |pages=829–39 |date=October 2003 |pmid=14523382 |doi=10.1038/nrn1201}}</ref>,在20世纪60年代被应用于把大脑比作计算机的理论研究之中。1968年,阿特金森 Atkinson和谢福林 Shiffrin <ref name="Atkinson Shiffrin 1968">{{cite book | last1 = Atkinson | first1 = R.C. | last2 = Shiffrin | first2 = R.M. | title = Human Memory: A Proposed System and its Control Processes | volume = 2 |pages = 89–195| editor1 = Kenneth W Spence |editor2= Janet T Spence | work = The psychology of learning and motivation | publisher = Academic Press | year = 1968 | isbn = 978-0-12-543302-0 |oclc = 185468704 |doi = 10.1016/S0079-7421(08)60422-3}}</ref>用该术语来表述“短期存储”。我们现在所说的工作记忆就是之前所谓的“短期存储”、“短期记忆”、“初级记忆”、“即时记忆”、“操作记忆”或“临时记忆”<ref name="Fuster 1997">{{cite book |author=Fuster, Joaquin M. |title=The prefrontal cortex: anatomy, physiology, and neuropsychology of the frontal lobe |publisher=Lippincott-Raven |location=Philadelphia |year=1997 |isbn=978-0-397-51849-4 |oclc=807338522 }}{{Page needed|date=September 2010}}</ref>。短期记忆是在短时间内(以秒为单位)记住信息的能力。如今,大多数理论学者会使用“工作记忆”这一概念取代或包含早期“短期记忆”的概念,这体现出对信息操纵观念的重视。<br />
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The earliest mention of experiments on the neural basis of working memory can be traced back to more than 100 years ago, when [[Eduard Hitzig|Hitzig]] and [[David Ferrier|Ferrier]] described [[ablation]] experiments of the [[prefrontal cortex]] (PFC); they concluded that the frontal cortex was important for cognitive rather than sensory processes.<ref name=Fuster1>{{Cite book|last1= Fuster|first1= Joaquin |title= The prefrontal cortex |page= 126 |url= https://books.google.com/books?id=zuZlvNICdhUC&pg=PT140 |edition= 4 |year= 2008 |publisher= Elsevier |location= Oxford, UK |isbn= 978-0-12-373644-4}}</ref> In 1935 and 1936, Carlyle Jacobsen and colleagues were the first to show the deleterious effect of prefrontal ablation on delayed response.<ref name=Fuster1 /><ref name=Benton>{{Cite book|last1= Benton|first1= A.&nbsp;L.|editor1-first= Harvey,&nbsp;S.|editor1-last= Levin|editor2-first= Howard,&nbsp;M.|editor2-last= Eisenberg|editor3-first= Arthur,&nbsp;L.|editor3-last= Benton|title= Frontal lobe function and dysfunction|chapter-url= https://books.google.com/books?id=9b1htO0V0rwC&pg=PA19&lpg=PA19&dq=Jacobsen++prefrontal+ablation&q=Jacobsen%20%20prefrontal%20ablation|year= 1991|publisher= Oxford University Press|location= New York|isbn= 978-0-19-506284-7|page= 19|chapter= The prefrontal region:Its early history}}</ref><br />
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The earliest mention of experiments on the neural basis of working memory can be traced back to more than 100 years ago, when Hitzig and Ferrier described ablation experiments of the prefrontal cortex (PFC); they concluded that the frontal cortex was important for cognitive rather than sensory processes. In 1935 and 1936, Carlyle Jacobsen and colleagues were the first to show the deleterious effect of prefrontal ablation on delayed response.<br />
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关于工作记忆神经学基础的实验最早可追溯到100多年前希齐格 Hitzig 和费里尔 Ferrier 对前额叶皮质消融实验的研究(PFC)。'''<font color="#ff8000">额叶皮层 frontal cortex</font>'''对认知程序比对感官程序更重要是当时研究得出的一大结论<ref name=Fuster1>{{Cite book|last1= Fuster|first1= Joaquin |title= The prefrontal cortex |page= 126 |url= https://books.google.com/books?id=zuZlvNICdhUC&pg=PT140 |edition= 4 |year= 2008 |publisher= Elsevier |location= Oxford, UK |isbn= 978-0-12-373644-4}}</ref>。在1935年和1936年, 卡莱尔 · 雅各布森 Carlyle Jacobsen及其同事们首次披露了前额叶切除对延时反映的不良影响<ref name=Fuster1 /><ref name=Benton>{{Cite book|last1= Benton|first1= A.&nbsp;L.|editor1-first= Harvey,&nbsp;S.|editor1-last= Levin|editor2-first= Howard,&nbsp;M.|editor2-last= Eisenberg|editor3-first= Arthur,&nbsp;L.|editor3-last= Benton|title= Frontal lobe function and dysfunction|chapter-url= https://books.google.com/books?id=9b1htO0V0rwC&pg=PA19&lpg=PA19&dq=Jacobsen++prefrontal+ablation&q=Jacobsen%20%20prefrontal%20ablation|year= 1991|publisher= Oxford University Press|location= New York|isbn= 978-0-19-506284-7|page= 19|chapter= The prefrontal region:Its early history}}</ref><br />
。<br />
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== 理论 Theories ==<br />
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Numerous models have been proposed for how working memory functions, both anatomically and cognitively. Of those, the two that have been most influential are summarized below.<br />
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Numerous models have been proposed for how working memory functions, both anatomically and cognitively. Of those, the two that have been most influential are summarized below.<br />
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基于解剖学和认识学,人们设计出工作记忆运行的神经模型,其中最有影响力的两个模型概括如下:<br />
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=== 多组件模型 The multicomponent model ===<br />
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{{Main|Baddeley's model of working memory}}<br />
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[[File:Baddeley and Hitch's Working Memory Model.png|thumb|300px|巴德利 Baddeley和希池 Hitch 的工作记忆模型]]<br />
[图1:巴德利 Baddeley和希池 Hitch 的工作记忆模型]<br />
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In 1974, [[Alan Baddeley|Baddeley]] and [[Graham Hitch|Hitch]]<ref name="Baddeley Hitch 1974">{{cite book | last1 = Baddeley | first1 = Alan D. | last2 = Hitch | first2 = Graham | title = Working Memory | volume = 2 | editor = Gordon H. Bower | work = The psychology of learning and motivation | publisher = Academic Press | year = 1974 | pages = 47–89 | isbn = 978-0-12-543308-2 |oclc = 777285348 |doi= 10.1016/S0079-7421(08)60452-1}}</ref> introduced the [[Baddeley's model of working memory|multicomponent model of working memory]]. The theory proposed a model containing three components: the central executive, the phonological loop, and the visuospatial sketchpad with the central executive functioning as a control center of sorts, directing info between the phonological and visuospatial components.<ref name="Levin 2011">{{Cite book|title = Working Memory : Capacity, Developments and Improvement Techniques|last = Levin|first = E.S.|publisher = [[Nova Science Publishers, Inc.]]|year = 2011|location = New York}}</ref> The [[Baddeley's model of working memory#Central executive|central executive]] is responsible for, among other things, directing [[attention]] to relevant information, suppressing irrelevant information and inappropriate actions, and coordinating cognitive processes when more than one task is simultaneously performed. A "central executive" is responsible for supervising the integration of information and for coordinating subordinate systems responsible for the short-term maintenance of information. One subordinate system, the [[phonological loop]] (PL), stores phonological information (that is, the sound of language) and prevents its decay by continuously refreshing it in a [[memory rehearsal|rehearsal]] loop. It can, for example, maintain a seven-digit telephone number for as long as one repeats the number to oneself again and again.<ref>{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = New York|pages = 281–282|edition = 9}}</ref> The other subordinate system, the [[Baddeley's model of working memory#Visuospatial sketchpad|visuospatial sketchpad]], stores visual and spatial information. It can be used, for example, for constructing and manipulating visual images and for representing mental maps. The sketchpad can be further broken down into a visual subsystem (dealing with such phenomena as shape, colour, and texture), and a spatial subsystem (dealing with location).<br />
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In 1974, Baddeley and Hitch introduced the multicomponent model of working memory. The theory proposed a model containing three components: the central executive, the phonological loop, and the visuospatial sketchpad with the central executive functioning as a control center of sorts, directing info between the phonological and visuospatial components. The central executive is responsible for, among other things, directing attention to relevant information, suppressing irrelevant information and inappropriate actions, and coordinating cognitive processes when more than one task is simultaneously performed. A "central executive" is responsible for supervising the integration of information and for coordinating subordinate systems responsible for the short-term maintenance of information. One subordinate system, the phonological loop (PL), stores phonological information (that is, the sound of language) and prevents its decay by continuously refreshing it in a rehearsal loop. It can, for example, maintain a seven-digit telephone number for as long as one repeats the number to oneself again and again. The other subordinate system, the visuospatial sketchpad, stores visual and spatial information. It can be used, for example, for constructing and manipulating visual images and for representing mental maps. The sketchpad can be further broken down into a visual subsystem (dealing with such phenomena as shape, colour, and texture), and a spatial subsystem (dealing with location).<br />
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1974年,Baddeley和Hitch<ref name="Baddeley Hitch 1974">{{cite book | last1 = Baddeley | first1 = Alan D. | last2 = Hitch | first2 = Graham | title = Working Memory | volume = 2 | editor = Gordon H. Bower | work = The psychology of learning and motivation | publisher = Academic Press | year = 1974 | pages = 47–89 | isbn = 978-0-12-543308-2 |oclc = 777285348 |doi= 10.1016/S0079-7421(08)60452-1}}</ref>提出了'''<font color="#ff8000">工作记忆多组件模型 Multicomponent Model of Working Memory</font>'''——该模型由三个组件构成:'''<font color="#ff8000">中央执行器 Central Executive</font>'''、'''<font color="#ff8000">语音回路(PL) Phonological Loop (PL)</font>'''、'''<font color="#ff8000">视觉绘板 Visuospatial Sketchpad</font>'''<ref name="Levin 2011">{{Cite book|title = Working Memory : Capacity, Developments and Improvement Techniques|last = Levin|first = E.S.|publisher = [[Nova Science Publishers, Inc.]]|year = 2011|location = New York}}</ref>。其中,中央执行器作为某种控制中心,负责疏通语音回路和视觉绘板之间的信息传递通道,引导相关信息,抑制无关信息及不当行为,保持认知程序在执行多任务时的协调。中央执行器还会监督信息的整合以及协调各个负责短期信息维护的子系统。语音回路(PL)组件用于存储语音信息并通过不断刷新防止其受损,例如,只要不断重复一个7位数的电话号码它就可以被很好地储存<ref>{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = New York|pages = 281–282|edition = 9}}</ref>。而视觉绘板组件则负责存储视觉和空间信息,例如构建、操控视觉图像及展现精神世界。视觉绘板还可进一步分为'''<font color="#ff8000">视觉子系统visual subsystem</font>'''(处理形状、颜色和纹理等)和'''<font color="#ff8000">空间子系统spatial subsystem</font>'''(处理位置)。<br />
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In 2000, Baddeley extended the model by adding a fourth component, the [[Baddeley's model of working memory#Episodic buffer|episodic buffer]], which holds representations that integrate phonological, visual, and spatial information, and possibly information not covered by the subordinate systems (e.g.,&nbsp;semantic information, musical information). The episodic buffer is also the link between working memory and long-term memory.<ref name="Weiten 2013 281–282">{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = Belmont, CA|pages = 281–282|edition = 9}}</ref> The component is episodic because it is assumed to bind information into a unitary episodic representation. The episodic buffer resembles Tulving's concept of [[episodic memory]], but it differs in that the episodic buffer is a temporary store.<ref>{{cite journal | url=http://nbu.bg/cogs/events/2002/materials/Markus/ep_bufer.pdf | title=The episodic buffer: a new component of working memory? | author=Baddeley, A. D. | journal=Trends Cogn. Sci. | year=2000 | volume=4 | issue=11 | pages=417–423 | doi=10.1016/S1364-6613(00)01538-2 | pmid=11058819}}</ref><br />
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In 2000, Baddeley extended the model by adding a fourth component, the episodic buffer, which holds representations that integrate phonological, visual, and spatial information, and possibly information not covered by the subordinate systems (e.g.,&nbsp;semantic information, musical information). The episodic buffer is also the link between working memory and long-term memory. The component is episodic because it is assumed to bind information into a unitary episodic representation. The episodic buffer resembles Tulving's concept of episodic memory, but it differs in that the episodic buffer is a temporary store.<br />
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2000年,Baddeley 增加了第四个组件'''<font color="#ff8000">情景缓冲区 Episodic Buffer</font>''',这进一步扩展了该模型。情景缓冲区可以整合语音、视觉、空间信息,及可能未被子系统涵盖的信息(例如语义、音乐)。它同时是工作记忆和长期记忆之间的枢纽<ref name="Weiten 2013 281–282">{{Cite book|title = Variations in psychology|last = Weiten|first = W.|publisher = Wadsworth|year = 2013|location = Belmont, CA|pages = 281–282|edition = 9}}</ref>。该组件的基本原理是把信息绑定到单一情节,因此它的运行是情节性的。情景缓冲区与图尔文 Tulving'''<font color="#ff8000">情景记忆 Episodic Memory</font>'''的概念类似,不同之处在于情景缓冲区是临时存储<ref>{{cite journal | url=http://nbu.bg/cogs/events/2002/materials/Markus/ep_bufer.pdf | title=The episodic buffer: a new component of working memory? | author=Baddeley, A. D. | journal=Trends Cogn. Sci. | year=2000 | volume=4 | issue=11 | pages=417–423 | doi=10.1016/S1364-6613(00)01538-2 | pmid=11058819}}</ref><br />
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=== 作为长期记忆一部分的工作记忆 Working memory as part of long-term memory ===<br />
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{{Annotated image|caption=The central executive of working memory is retrieving memory from long-term memory.|image=WorkingMemory Label Free.jpg|width=320|height=179|image-width=320|image-left=0|image-top=0|annotations={{Annotation|130|15|Central Executive|font-weight=bold|font-size=10}}<br />
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{{Annotation|10|160|Long-term Memory|font-weight=bold|font-size=10}}}}[[Anders Ericsson]] and [[Walter Kintsch]]<ref>{{cite journal|year=1995|title=Long-term working memory.|journal=Psychological Review|volume=102|issue=2|pages=211–245|doi=10.1037/0033-295X.102.2.211|pmid=7740089|author=Ericsson, K. A.|author2=Kintsch, W.|lastauthoramp=y}}</ref> have introduced the notion of "long-term working memory", which they define as a set of "retrieval structures" in long-term memory that enable seamless access to the information relevant for everyday tasks. In this way, parts of long-term memory effectively function as working memory. In a similar vein, [[Nelson Cowan|Cowan]] does not regard working memory as a separate system from [[long-term memory]]. Representations in working memory are a subset of representations in long-term memory. Working memory is organized into two embedded levels. The first consists of long-term memory representations that are activated. There can be many of these—there is theoretically no limit to the activation of representations in long-term memory. The second level is called the focus of attention. The focus is regarded as having a limited capacity and holds up to four of the activated representations.<ref name="Cowan 1995">{{cite book |author=Cowan, Nelson |title=Attention and memory: an integrated framework |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=1995 |isbn=978-0-19-506760-6 |oclc=30475237 }}{{Page needed|date=September 2010}}</ref><br />
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Anders Ericsson and Walter Kintsch have introduced the notion of "long-term working memory", which they define as a set of "retrieval structures" in long-term memory that enable seamless access to the information relevant for everyday tasks. In this way, parts of long-term memory effectively function as working memory. In a similar vein, Cowan does not regard working memory as a separate system from long-term memory. Representations in working memory are a subset of representations in long-term memory. Working memory is organized into two embedded levels. The first consists of long-term memory representations that are activated. There can be many of these—there is theoretically no limit to the activation of representations in long-term memory. The second level is called the focus of attention. The focus is regarded as having a limited capacity and holds up to four of the activated representations.<br />
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{{Annotated image|caption=The central executive of working memory is retrieving memory from long-term memory.|image=WorkingMemory Label Free.jpg|width=320|height=179|image-width=320|image-left=0|image-top=0|annotations={{Annotation|130|15|Central Executive|font-weight=bold|font-size=10}}<br />
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{{Annotation|10|160|Long-term Memory|font-weight=bold|font-size=10}}}}安德斯 · 埃里克森 Anders Ericsson 和沃尔特 · 金奇 Walter Kintsch <ref>{{cite journal|year=1995|title=Long-term working memory.|journal=Psychological Review|volume=102|issue=2|pages=211–245|doi=10.1037/0033-295X.102.2.211|pmid=7740089|author=Ericsson, K. A.|author2=Kintsch, W.|lastauthoramp=y}}</ref>引入了“'''<font color="#ff8000">长期工作记忆 Long-term Working Memory</font>'''”这一概念,即一组能让人从'''<font color="#ff8000">长期记忆 Long-term Memory</font>'''中无缝获取日常所需信息的“检索结构” 。也就是说,一部分长期记忆有效地发挥了工作记忆的作用。同样,考恩 Cowan 并不认为工作记忆完全独立于长期记忆的。工作记忆的表征是长期记忆表征的一个子集。工作记忆被处理成两个嵌入层次。第一层为被激活的长期记忆表征(可能会很多,毕竟理论上长期记忆表征的激活是没有上限的)。第二层叫做注意力'''<font color="#ff8000">焦点focus</font>''',焦点被认为是一种有限能力,可容纳四个激活的表征<ref name="Cowan 1995">{{cite book |author=Cowan, Nelson |title=Attention and memory: an integrated framework |publisher=Oxford University Press |location=Oxford [Oxfordshire] |year=1995 |isbn=978-0-19-506760-6 |oclc=30475237 }}{{Page needed|date=September 2010}}</ref>。<br />
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Oberauer has extended Cowan's model by adding a third component, a more narrow focus of attention that holds only one chunk at a time. The one-element focus is embedded in the four-element focus and serves to select a single chunk for processing. For example, four digits can be held in mind at the same time in Cowan's "focus of attention". When the individual wishes to perform a process on each of these digits—for example, adding the number two to each digit—separate processing is required for each digit since most individuals cannot perform several mathematical processes in parallel.<ref>{{Cite journal|title = Attention, working memory, and long-term memory in multimedia learning: A integrated perspective based on process models of working memory|last = Schweppe|first = J.|date = 2014|journal = Educational Psychology Review|doi = 10.1007/s10648-013-9242-2|issue = 2|volume = 26|page = 289}}</ref> Oberauer's attentional component selects one of the digits for processing and then shifts the attentional focus to the next digit, continuing until all digits have been processed.<ref>{{Cite journal|author=Oberauer K |title=Access to information in working memory: exploring the focus of attention |journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |volume=28 |issue=3 |pages=411–21 |date=May 2002 |pmid=12018494 |doi=10.1037/0278-7393.28.3.411|citeseerx=10.1.1.163.4979 }}</ref><br />
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Oberauer has extended Cowan's model by adding a third component, a more narrow focus of attention that holds only one chunk at a time. The one-element focus is embedded in the four-element focus and serves to select a single chunk for processing. For example, four digits can be held in mind at the same time in Cowan's "focus of attention". When the individual wishes to perform a process on each of these digits—for example, adding the number two to each digit—separate processing is required for each digit since most individuals cannot perform several mathematical processes in parallel. Oberauer's attentional component selects one of the digits for processing and then shifts the attentional focus to the next digit, continuing until all digits have been processed.<br />
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奥伯奥尔 Oberauer 在Cowan模型的基础上又添加了一个组件——一个更窄的注意力焦点,一次只能容纳一个'''<font color="#ff8000">组块chunk</font>'''。单元素焦点系统嵌在四元素焦点系统之中,用于挑选要处理的单个块。例如,根据Cowan 的“注意力焦点”理论,四个数字可以同时出现在脑海中。当个体要加工所有数字时(例如,将数字2加到每个数字)必须要先对每个数字进行独立加工(因为大多数人不能同时处理多个数学问题)<ref>{{Cite journal|title = Attention, working memory, and long-term memory in multimedia learning: A integrated perspective based on process models of working memory|last = Schweppe|first = J.|date = 2014|journal = Educational Psychology Review|doi = 10.1007/s10648-013-9242-2|issue = 2|volume = 26|page = 289}}</ref>。此时Oberauer 的注意力组件将选择其中一个数字进行处理,结束后就把焦点转到下一个数字,直到处理完毕<ref>{{Cite journal|author=Oberauer K |title=Access to information in working memory: exploring the focus of attention |journal=Journal of Experimental Psychology: Learning, Memory, and Cognition |volume=28 |issue=3 |pages=411–21 |date=May 2002 |pmid=12018494 |doi=10.1037/0278-7393.28.3.411|citeseerx=10.1.1.163.4979 }}</ref>。<br />
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== 容量 Capacity ==<br />
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Working memory is widely acknowledged as having limited capacity. An early quantification of the capacity limit associated with short-term memory was the "[[The Magical Number Seven, Plus or Minus Two|magical number seven]]" suggested by Miller in 1956.<ref name="miller">{{Cite journal|author=Miller GA |title=The magical number seven plus or minus two: some limits on our capacity for processing information |journal=Psychological Review |volume=63 |issue=2 |pages=81–97 |date=March 1956 |pmid=13310704 |doi=10.1037/h0043158|citeseerx=10.1.1.308.8071 }} Republished: {{Cite journal|author=Miller GA |title=The magical number seven, plus or minus two: some limits on our capacity for processing information. 1956 |journal=Psychological Review |volume=101 |issue=2 |pages=343–52 |date=April 1994 |pmid=8022966 |doi=10.1037/0033-295X.101.2.343}}</ref> He claimed that the information-processing capacity of young adults is around seven elements, which he called "chunks", regardless of whether the elements are digits, letters, words, or other units. Later research revealed this number depends on the category of chunks used (e.g., span may be around seven for digits, six for letters, and five for words), and even on features of the [[chunking (psychology)|chunks]] within a category. For instance, span is lower for long than short words. In general, memory span for verbal contents (digits, letters, words, etc.) depends on the phonological complexity of the content (i.e., the number of phonemes, the number of syllables),<ref>{{Cite journal|last=Service|first=Elisabet|date=1998-05-01|title=The Effect of Word Length on Immediate Serial Recall Depends on Phonological Complexity, Not Articulatory Duration|journal=The Quarterly Journal of Experimental Psychology Section A|volume=51|issue=2|pages=283–304|doi=10.1080/713755759|issn=0272-4987}}</ref> and on the lexical status of the contents (whether the contents are words known to the person or not).<ref>{{Cite journal|first1=Charles |last1=Hulme |first2=Steven |last2=Roodenrys |first3=Gordon |last3=Brown |first4=Robin |last4=Mercer |date=November 1995 |title=The role of long-term memory mechanisms in memory span |journal=British Journal of Psychology |volume=86 |issue=4 |pages=527–36 |doi=10.1111/j.2044-8295.1995.tb02570.x}}</ref> Several other factors affect a person's measured span, and therefore it is difficult to pin down the capacity of short-term or working memory to a number of chunks. Nonetheless, Cowan proposed that working memory has a capacity of about four chunks in young adults (and fewer in children and old adults).<ref>{{Cite journal|first1=Nelson |last1=Cowan |year=2001 |title=The magical number 4 in short-term memory: A reconsideration of mental storage capacity |journal=Behavioral and Brain Sciences |volume=24 |issue=1 |pages=87–185 |doi=10.1017/S0140525X01003922 |pmid=11515286|doi-access=free }}</ref><br />
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Working memory is widely acknowledged as having limited capacity. An early quantification of the capacity limit associated with short-term memory was the "magical number seven" suggested by Miller in 1956. He claimed that the information-processing capacity of young adults is around seven elements, which he called "chunks", regardless of whether the elements are digits, letters, words, or other units. Later research revealed this number depends on the category of chunks used (e.g., span may be around seven for digits, six for letters, and five for words), and even on features of the chunks within a category. For instance, span is lower for long than short words. In general, memory span for verbal contents (digits, letters, words, etc.) depends on the phonological complexity of the content (i.e., the number of phonemes, the number of syllables), and on the lexical status of the contents (whether the contents are words known to the person or not). Several other factors affect a person's measured span, and therefore it is difficult to pin down the capacity of short-term or working memory to a number of chunks. Nonetheless, Cowan proposed that working memory has a capacity of about four chunks in young adults (and fewer in children and old adults).<br />
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工作记忆通常被认为容量有限。1956年,米勒 Miller提出了“'''<font color="#ff8000">神奇数字7 The Magical Number Seven</font>'''”来量化短期记忆<ref name="miller">{{Cite journal|author=Miller GA |title=The magical number seven plus or minus two: some limits on our capacity for processing information |journal=Psychological Review |volume=63 |issue=2 |pages=81–97 |date=March 1956 |pmid=13310704 |doi=10.1037/h0043158|citeseerx=10.1.1.308.8071 }} Republished: {{Cite journal|author=Miller GA |title=The magical number seven, plus or minus two: some limits on our capacity for processing information. 1956 |journal=Psychological Review |volume=101 |issue=2 |pages=343–52 |date=April 1994 |pmid=8022966 |doi=10.1037/0033-295X.101.2.343}}</ref>。他认为年轻人的信息处理能力容量大约是7个元素,称之为组块。组块内容可以是数字、字母、单词等。后续的研究发现,这个数字的大小取决于所用组块的类别(例如,数字对应7个,字母对应6个,单词对应5个)甚至取决于该类别中组块的特征。例如,长词的组块数会低于短词的组块数。一般而言,口头内容(数字、字母、单词)的记忆规模取决于内容的音系复杂度(即音素、音节的量)<ref>{{Cite journal|last=Service|first=Elisabet|date=1998-05-01|title=The Effect of Word Length on Immediate Serial Recall Depends on Phonological Complexity, Not Articulatory Duration|journal=The Quarterly Journal of Experimental Psychology Section A|volume=51|issue=2|pages=283–304|doi=10.1080/713755759|issn=0272-4987}}</ref>以及所用词汇状态(内容所用单词是否为主体所知)<ref>{{Cite journal|first1=Charles |last1=Hulme |first2=Steven |last2=Roodenrys |first3=Gordon |last3=Brown |first4=Robin |last4=Mercer |date=November 1995 |title=The role of long-term memory mechanisms in memory span |journal=British Journal of Psychology |volume=86 |issue=4 |pages=527–36 |doi=10.1111/j.2044-8295.1995.tb02570.x}}</ref>。除此之外,还有其他若干因素也会影响人的记忆规模,因此难以确定短期记忆或工作记忆的组块数。尽管如此,Cowan还是认为年轻人的工作记忆容量大约是4个组块(儿童和老年人则更少)<ref>{{Cite journal|first1=Nelson |last1=Cowan |year=2001 |title=The magical number 4 in short-term memory: A reconsideration of mental storage capacity |journal=Behavioral and Brain Sciences |volume=24 |issue=1 |pages=87–185 |doi=10.1017/S0140525X01003922 |pmid=11515286|doi-access=free }}</ref><br />
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Whereas most adults can repeat about seven digits in correct order, some individuals have shown impressive enlargements of their digit span—up to 80 digits. This feat is possible by extensive training on an encoding strategy by which the digits in a list are grouped (usually in groups of three to five) and these groups are encoded as a single unit (a chunk). For this to succeed, participants must be able to recognize the groups as some known string of digits. One person studied by Ericsson and his colleagues, for example, used an extensive knowledge of racing times from the history of sports in the process of coding chunks: several such chunks could then be combined into a higher-order chunk, forming a hierarchy of chunks. In this way, only some chunks at the highest level of the hierarchy must be retained in working memory, and for retrieval the chunks are unpacked. That is, the chunks in working memory act as retrieval cues that point to the digits they contain. Practicing memory skills such as these does not expand working memory capacity proper: it is the capacity to transfer (and retrieve) information from long-term memory that is improved, according to Ericsson and Kintsch (1995; see also Gobet & Simon, 2000<ref name="Gobet F 2000 551–70">{{Cite journal|date=November 2000|title=Some shortcomings of long-term working memory|journal=British Journal of Psychology|volume=91|issue=Pt 4|pages=551–70|doi=10.1348/000712600161989|pmid=11104178|author=Gobet F|url=http://bura.brunel.ac.uk/handle/2438/807|type=Submitted manuscript}}</ref>).<br />
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Whereas most adults can repeat about seven digits in correct order, some individuals have shown impressive enlargements of their digit span—up to 80 digits. This feat is possible by extensive training on an encoding strategy by which the digits in a list are grouped (usually in groups of three to five) and these groups are encoded as a single unit (a chunk). For this to succeed, participants must be able to recognize the groups as some known string of digits. One person studied by Ericsson and his colleagues, for example, used an extensive knowledge of racing times from the history of sports in the process of coding chunks: several such chunks could then be combined into a higher-order chunk, forming a hierarchy of chunks. In this way, only some chunks at the highest level of the hierarchy must be retained in working memory, and for retrieval the chunks are unpacked. That is, the chunks in working memory act as retrieval cues that point to the digits they contain. Practicing memory skills such as these does not expand working memory capacity proper: it is the capacity to transfer (and retrieve) information from long-term memory that is improved, according to Ericsson and Kintsch (1995; see also Gobet & Simon, 2000).<br />
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大多数成年人能够正确地重复7个数字,但有些个体的记忆规模则得到了显著扩充——高达80个数字。这可以通过编码策略培训来实现。按编码策略将列表中的数字分组(通常分3到5组)并将这些组编码为一个独立单元(一个组块)。要实现这一点,参与者必须要将组识别为某些已知的数字字符串。例如,埃里克森 Ericsson 和他同事的一位研究对象利用了体育史中各大比赛的时间来编写代码组块: 几个这样的组块可组合成一个更高级的组块,形成组块层次结构。如此,只要层次结构最高级别的组块保持在工作记忆中即可——当然这些组块是可检索的。也就是说,工作记忆中的组块是提取数字内容的指向性线索。埃里克森 Ericsson 和 金茨 Kintsch (1995; 参见 Gobet & Simon,2000<ref name="Gobet F 2000 551–70">{{Cite journal|date=November 2000|title=Some shortcomings of long-term working memory|journal=British Journal of Psychology|volume=91|issue=Pt 4|pages=551–70|doi=10.1348/000712600161989|pmid=11104178|author=Gobet F|url=http://bura.brunel.ac.uk/handle/2438/807|type=Submitted manuscript}}</ref>)认为,练习这种记忆技巧并不能真正提高工作记忆容量,所提高的是从长期记忆中传递(和检索)信息的能力。<br />
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=== 测量和关联 Measures and correlates ===<br />
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Working memory capacity can be tested by a variety of tasks. A commonly used measure is a dual-task paradigm, combining a [[memory span]] measure with a concurrent processing task, sometimes referred to as "complex span". Daneman and Carpenter invented the first version of this kind of task, the "[[reading span]]", in 1980.<ref>{{Cite journal|first1=Meredyth |last1=Daneman |first2=Patricia A. |last2=Carpenter |date=August 1980 |title=Individual differences in working memory and reading |journal=Journal of Verbal Learning & Verbal Behavior |volume=19 |issue=4 |pages=450–66 |doi=10.1016/S0022-5371(80)90312-6}}</ref> Subjects read a number of sentences (usually between two and six) and tried to remember the last word of each sentence. At the end of the list of sentences, they repeated back the words in their correct order. Other tasks that do not have this dual-task nature have also been shown to be good measures of working memory capacity.<ref>{{Cite journal|last2=Süss|first2=H.-M.|last3=Schulze|first3=R.|last4=Wilhelm|first4=O.|last5=Wittmann|first5=W.&nbsp;W.|date=December 2000|title=Working memory capacity—facets of a cognitive ability construct|journal=Personality and Individual Differences|volume=29|issue=6|pages=1017–45|doi=10.1016/S0191-8869(99)00251-2|first1=K.|last1=Oberauer}}</ref> Whereas Daneman and Carpenter believed that the combination of "storage" (maintenance) and processing is needed to measure working memory capacity, we know now that the capacity of working memory can be measured with short-term memory tasks that have no additional processing component.<ref>{{Cite journal|last1=Unsworth|first1=Nash|last2=Engle|first2=Randall W.|title=On the division of short-term and working memory: An examination of simple and complex span and their relation to higher order abilities.|journal=Psychological Bulletin|volume=133|issue=6|pages=1038–1066|doi=10.1037/0033-2909.133.6.1038|pmid=17967093|year=2007}}</ref><ref>{{Cite journal|last=Colom, R. Abad, F. J. Quiroga, M. A. Shih, P. C. Flores-Mendoza, C.|year=2008|title=Working memory and intelligence are highly related constructs, but why?|journal=Intelligence|volume=36|issue=6|pages=584–606|doi=10.1016/j.intell.2008.01.002}}</ref> Conversely, working memory capacity can also be measured with certain processing tasks that don't involve maintenance of information.<ref>{{Cite journal|last=Oberauer, K. Süß, H.-M. Wilhelm, O. Wittmann, W. W.|year=2003|title=The multiple faces of working memory - storage, processing, supervision, and coordination|doi=10.1016/s0160-2896(02)00115-0|journal=Intelligence|volume=31|issue=2|pages=167–193|url=https://www.zora.uzh.ch/id/eprint/97155/1/intelligence.pdf}}</ref><ref>{{Cite journal|last=Chuderski|first=Adam|date=2013-09-25|title=The relational integration task explains fluid reasoning above and beyond other working memory tasks|journal=Memory & Cognition|language=en|volume=42|issue=3|pages=448–463|doi=10.3758/s13421-013-0366-x|issn=0090-502X|pmc=3969517|pmid=24222318}}</ref> The question of what features a task must have to qualify as a good measure of working memory capacity is a topic of ongoing research.<br />
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Working memory capacity can be tested by a variety of tasks. A commonly used measure is a dual-task paradigm, combining a memory span measure with a concurrent processing task, sometimes referred to as "complex span". Daneman and Carpenter invented the first version of this kind of task, the "reading span", in 1980. Subjects read a number of sentences (usually between two and six) and tried to remember the last word of each sentence. At the end of the list of sentences, they repeated back the words in their correct order. Other tasks that do not have this dual-task nature have also been shown to be good measures of working memory capacity. Whereas Daneman and Carpenter believed that the combination of "storage" (maintenance) and processing is needed to measure working memory capacity, we know now that the capacity of working memory can be measured with short-term memory tasks that have no additional processing component. Conversely, working memory capacity can also be measured with certain processing tasks that don't involve maintenance of information. The question of what features a task must have to qualify as a good measure of working memory capacity is a topic of ongoing research.<br />
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我们可以通过一系列任务来测量工作记忆的容量。其中一个方法是双任务范例,它将'''<font color="#ff8000">记忆广度测度 memory span measure</font>'''与'''<font color="#ff8000">并发处理任务concurrent processing task</font>'''(有时称为“复杂规模”)结合起来。1980年,丹曼 Daneman 和 卡朋特 Carpenter 发明了该方法的第一个版本——“阅读广度”<ref>{{Cite journal|first1=Meredyth |last1=Daneman |first2=Patricia A. |last2=Carpenter |date=August 1980 |title=Individual differences in working memory and reading |journal=Journal of Verbal Learning & Verbal Behavior |volume=19 |issue=4 |pages=450–66 |doi=10.1016/S0022-5371(80)90312-6}}</ref>。受试者阅读大量的句子(通常2至6个),并努力记住每个句子的最后一个单词。阅读完后他们按照自己认为正确的顺序复述单词<ref>{{Cite journal|last1=Unsworth|first1=Nash|last2=Engle|first2=Randall W.|title=On the division of short-term and working memory: An examination of simple and complex span and their relation to higher order abilities.|journal=Psychological Bulletin|volume=133|issue=6|pages=1038–1066|doi=10.1037/0033-2909.133.6.1038|pmid=17967093|year=2007}}</ref><ref>{{Cite journal|last=Colom, R. Abad, F. J. Quiroga, M. A. Shih, P. C. Flores-Mendoza, C.|year=2008|title=Working memory and intelligence are highly related constructs, but why?|journal=Intelligence|volume=36|issue=6|pages=584–606|doi=10.1016/j.intell.2008.01.002}}</ref>。其他一些不具备双任务性质的任务同样也是测量工作记忆容量的好办法<ref>{{Cite journal|last2=Süss|first2=H.-M.|last3=Schulze|first3=R.|last4=Wilhelm|first4=O.|last5=Wittmann|first5=W.&nbsp;W.|date=December 2000|title=Working memory capacity—facets of a cognitive ability construct|journal=Personality and Individual Differences|volume=29|issue=6|pages=1017–45|doi=10.1016/S0191-8869(99)00251-2|first1=K.|last1=Oberauer}}</ref>。Daneman 和Carpenter 相信“存储”(维护)和加工的结合是测量工作记忆容量所必须的,现在我们知道工作记忆的容量既可以用没有额外处理组件的短时记忆任务来测量,也可以用不涉及信息维护的某些处理任务来衡量<ref>{{Cite journal|last=Oberauer, K. Süß, H.-M. Wilhelm, O. Wittmann, W. W.|year=2003|title=The multiple faces of working memory - storage, processing, supervision, and coordination|doi=10.1016/s0160-2896(02)00115-0|journal=Intelligence|volume=31|issue=2|pages=167–193|url=https://www.zora.uzh.ch/id/eprint/97155/1/intelligence.pdf}}</ref><ref>{{Cite journal|last=Chuderski|first=Adam|date=2013-09-25|title=The relational integration task explains fluid reasoning above and beyond other working memory tasks|journal=Memory & Cognition|language=en|volume=42|issue=3|pages=448–463|doi=10.3758/s13421-013-0366-x|issn=0090-502X|pmc=3969517|pmid=24222318}}</ref>。至于用于测量工作记忆容量的好的任务方案应当具备哪些特征,这仍是一个待研究的课题。<br />
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Measures of working-memory capacity are strongly related to performance in other complex cognitive tasks, such as reading comprehension, problem solving, and with measures of [[intelligence quotient]].<ref>{{Cite journal|vauthors=Conway AR, Kane MJ, Engle RW |title=Working memory capacity and its relation to general intelligence |journal=Trends in Cognitive Sciences |volume=7 |issue=12 |pages=547–52 |date=December 2003 |pmid=14643371 |doi=10.1016/j.tics.2003.10.005|citeseerx=10.1.1.538.4967 }}</ref><br />
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Measures of working-memory capacity are strongly related to performance in other complex cognitive tasks, such as reading comprehension, problem solving, and with measures of intelligence quotient.<br />
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工作记忆容量的测量与其他复杂认知任务中的表现有密切联系,例如'''<font color="#ff8000">阅读理解 reading comprehension</font>'''、'''<font color="#ff8000">问题解决 problem solving</font>'''和'''<font color="#ff8000">智商测量intelligence quotient</font>'''。<ref>{{Cite journal|vauthors=Conway AR, Kane MJ, Engle RW |title=Working memory capacity and its relation to general intelligence |journal=Trends in Cognitive Sciences |volume=7 |issue=12 |pages=547–52 |date=December 2003 |pmid=14643371 |doi=10.1016/j.tics.2003.10.005|citeseerx=10.1.1.538.4967 }}</ref>。<br />
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Some researchers have argued<ref>{{Cite journal|author=Engle, R. W.|author2=Tuholski, S. W.|author3=Laughlin, J. E.|author4=Conway, A. R. |title=Working memory, short-term memory, and general fluid intelligence: a latent-variable approach |journal=Journal of Experimental Psychology: General |volume=128 |issue=3 |pages=309–31 |date=September 1999 |pmid=10513398 |doi=10.1037/0096-3445.128.3.309|url=https://semanticscholar.org/paper/cf15817ee5f9c1536ee4da2c4c018555600ca91b}}</ref> that working-memory capacity reflects the efficiency of executive functions, most notably the ability to maintain multiple task-relevant representations in the face of distracting irrelevant information; and that such tasks seem to reflect individual differences in the ability to focus and maintain attention, particularly when other events are serving to capture attention. Both working memory and executive functions rely strongly, though not exclusively, on frontal brain areas.<ref name="Kane MJ, Engle RW 2002 637–71">{{Cite journal|doi=10.3758/BF03196323|author=Kane, M. J.|author2=Engle, R. W.|title=The role of prefrontal cortex in working-memory capacity, executive attention, and general fluid intelligence: an individual-differences perspective |journal=Psychonomic Bulletin & Review |volume=9 |issue=4 |pages=637–71 |date=December 2002 |pmid=12613671 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=12613671|doi-access=free }}</ref><br />
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Some researchers have argued that working-memory capacity reflects the efficiency of executive functions, most notably the ability to maintain multiple task-relevant representations in the face of distracting irrelevant information; and that such tasks seem to reflect individual differences in the ability to focus and maintain attention, particularly when other events are serving to capture attention. Both working memory and executive functions rely strongly, though not exclusively, on frontal brain areas.<br />
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一些研究人员认为<ref>{{Cite journal|author=Engle, R. W.|author2=Tuholski, S. W.|author3=Laughlin, J. E.|author4=Conway, A. R. |title=Working memory, short-term memory, and general fluid intelligence: a latent-variable approach |journal=Journal of Experimental Psychology: General |volume=128 |issue=3 |pages=309–31 |date=September 1999 |pmid=10513398 |doi=10.1037/0096-3445.128.3.309|url=https://semanticscholar.org/paper/cf15817ee5f9c1536ee4da2c4c018555600ca91b}}</ref>,工作记忆容量能够反映执行功能的效率,其中最具代表性的是面对不相关信息时协调多个任务相关表征的能力; 且这样的任务似乎也反映出在集中注意力和保持注意力方面的个体能力差异(特别是当其他事件能吸引注意力时)。工作记忆和执行功能都非常依赖(但不限于)额叶大脑区域<ref name="Kane MJ, Engle RW 2002 637–71">{{Cite journal|doi=10.3758/BF03196323|author=Kane, M. J.|author2=Engle, R. W.|title=The role of prefrontal cortex in working-memory capacity, executive attention, and general fluid intelligence: an individual-differences perspective |journal=Psychonomic Bulletin & Review |volume=9 |issue=4 |pages=637–71 |date=December 2002 |pmid=12613671 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=12613671|doi-access=free }}</ref><br />
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Other researchers have argued that the capacity of working memory is better characterized as the ability to mentally form relations between elements, or to grasp relations in given information. This idea has been advanced, among others, by Graeme Halford, who illustrated it by our limited ability to understand statistical interactions between variables.<ref>{{Cite journal|author=Halford, G. S.|author2=Baker, R.|author3=McCredden, J. E.|author4=Bain, J. D. |title=How many variables can humans process? |journal=Psychological Science |volume=16 |issue=1 |pages=70–76 |date=January 2005 |pmid=15660854 |doi=10.1111/j.0956-7976.2005.00782.x}}</ref> These authors asked people to compare written statements about the relations between several variables to graphs illustrating the same or a different relation, as in the following sentence: "If the cake is from France, then it has more sugar if it is made with chocolate than if it is made with cream, but if the cake is from Italy, then it has more sugar if it is made with cream than if it is made of chocolate". This statement describes a relation between three variables (country, ingredient, and amount of sugar), which is the maximum most individuals can understand. The capacity limit apparent here is obviously not a memory limit (all relevant information can be seen continuously) but a limit to how many relationships are discerned simultaneously.<br />
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Other researchers have argued that the capacity of working memory is better characterized as the ability to mentally form relations between elements, or to grasp relations in given information. This idea has been advanced, among others, by Graeme Halford, who illustrated it by our limited ability to understand statistical interactions between variables. These authors asked people to compare written statements about the relations between several variables to graphs illustrating the same or a different relation, as in the following sentence: "If the cake is from France, then it has more sugar if it is made with chocolate than if it is made with cream, but if the cake is from Italy, then it has more sugar if it is made with cream than if it is made of chocolate". This statement describes a relation between three variables (country, ingredient, and amount of sugar), which is the maximum most individuals can understand. The capacity limit apparent here is obviously not a memory limit (all relevant information can be seen continuously) but a limit to how many relationships are discerned simultaneously.<br />
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另一些研究人员主张,用个体构建元素间关系或获取信息的能力来测量工作记忆容量更佳。格雷姆 · 哈尔福德Graeme Halford用我们理解变量之间统计交互作用的有限能力来解释这个想法<ref>{{Cite journal|author=Halford, G. S.|author2=Baker, R.|author3=McCredden, J. E.|author4=Bain, J. D. |title=How many variables can humans process? |journal=Psychological Science |volume=16 |issue=1 |pages=70–76 |date=January 2005 |pmid=15660854 |doi=10.1111/j.0956-7976.2005.00782.x}}</ref>。这些发起人要求人们把陈述几个变量之间关系的书面表达与相应的图示(说明相同或不同关系)进行比较,例如: ”如果蛋糕来自法国,那么用巧克力做的比用奶油做的含糖量高。但如果蛋糕来自意大利,那么用奶油做的比用巧克力做的含糖量高”。这个陈述描述了三个变量之间的关系(国家、成分和糖量)——这是大多数人理解能力的上限。这里的容量限制显然不是记忆量限制(所有相关信息都可完整看到),而是可同时识别关系量的限制。<br />
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=== 工作记忆容量的试验研究 Experimental studies of working-memory capacity ===<br />
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There are several hypotheses about the nature of the capacity limit. One is that a limited pool of cognitive resources is needed to keep representations active and thereby available for processing, and for carrying out processes.<ref name=":0">{{Cite journal|author=Just, M. A.|author2=Carpenter, P. A. |title=A capacity theory of comprehension: individual differences in working memory |journal=Psychological Review |volume=99 |issue=1 |pages=122–49 |date=January 1992 |pmid=1546114 |doi=10.1037/0033-295X.99.1.122|url=http://repository.cmu.edu/cgi/viewcontent.cgi?article=1730&context=psychology }}</ref> Another hypothesis is that memory traces in working memory decay within a few seconds, unless refreshed through rehearsal, and because the speed of rehearsal is limited, we can maintain only a limited amount of information.<ref>{{Cite journal|doi=10.3758/BF03198549|author=Towse, J. N.|author2=Hitch, G. J.|author3=Hutton, U.|title=On the interpretation of working memory span in adults |journal=Memory & Cognition |volume=28 |issue=3 |pages=341–8 |date=April 2000 |pmid=10881551|doi-access=free }}</ref> Yet another idea is that representations held in working memory interfere with each other.<ref>{{Cite journal|vauthors=Waugh NC, Norman DA |title=Primary Memory |journal=Psychological Review |volume=72 |issue= 2|pages=89–104 |date=March 1965 |pmid=14282677 |doi=10.1037/h0021797}}</ref><br />
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There are several hypotheses about the nature of the capacity limit. One is that a limited pool of cognitive resources is needed to keep representations active and thereby available for processing, and for carrying out processes. Another hypothesis is that memory traces in working memory decay within a few seconds, unless refreshed through rehearsal, and because the speed of rehearsal is limited, we can maintain only a limited amount of information. Yet another idea is that representations held in working memory interfere with each other.<br />
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关于'''<font color="#ff8000">容量极限capacity limit</font>'''的性质有几种假设。一种观点认为其性质是一种有限认知资源池,作为激活记忆表征以及处理记忆表征的前提<ref name=":0">{{Cite journal|author=Just, M. A.|author2=Carpenter, P. A. |title=A capacity theory of comprehension: individual differences in working memory |journal=Psychological Review |volume=99 |issue=1 |pages=122–49 |date=January 1992 |pmid=1546114 |doi=10.1037/0033-295X.99.1.122|url=http://repository.cmu.edu/cgi/viewcontent.cgi?article=1730&context=psychology }}</ref>,另一种观点认为工作记忆若不反复刷新将会在几秒内衰退。又因为刷新速率是有限的,所以我们只能维持一定的信息量<ref>{{Cite journal|doi=10.3758/BF03198549|author=Towse, J. N.|author2=Hitch, G. J.|author3=Hutton, U.|title=On the interpretation of working memory span in adults |journal=Memory & Cognition |volume=28 |issue=3 |pages=341–8 |date=April 2000 |pmid=10881551|doi-access=free }}</ref>。还有观点认为容量极限是工作记忆中的表征互相干涉的结果<ref>{{Cite journal|vauthors=Waugh NC, Norman DA |title=Primary Memory |journal=Psychological Review |volume=72 |issue= 2|pages=89–104 |date=March 1965 |pmid=14282677 |doi=10.1037/h0021797}}</ref>。<br />
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====衰变理论 Decay theories====<br />
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The assumption that the contents of short-term or working memory [[decay theory|decay]] over time, unless decay is prevented by rehearsal, goes back to the early days of experimental research on short-term memory.<ref>{{Cite journal|last=Brown, J.|year=1958|title=Some tests of the decay theory of immediate memory|journal=Quarterly Journal of Experimental Psychology|volume=10|pages=12–21|doi=10.1080/17470215808416249}}</ref><ref>{{Cite journal|author1=Peterson, L. R. |author2=Peterson, M. J.|year=1959|title=Short-term retention of individual verbal items|journal=Journal of Experimental Psychology|volume=58|issue=3|pages=193–198|doi=10.1037/h0049234|pmid=14432252|citeseerx=10.1.1.227.1807}}</ref> It is also an important assumption in the multi-component theory of working memory.<ref>{{Cite book|title=Working memory|author1=Baddeley, A. D.|publisher=Clarendon|year=1986|location=Oxford}}</ref> The most elaborate decay-based theory of working memory to date is the "time-based resource sharing model".<ref>{{Cite journal|date=March 2004|title=Time constraints and resource sharing in adults' working memory spans|journal=Journal of Experimental Psychology: General|volume=133|issue=1|pages=83–100|doi=10.1037/0096-3445.133.1.83|pmid=14979753|vauthors=Barrouillet P, Bernardin S, Camos V|citeseerx=10.1.1.379.9208}}</ref> This theory assumes that representations in working memory decay unless they are refreshed. Refreshing them requires an attentional mechanism that is also needed for any concurrent processing task. When there are small time intervals in which the processing task does not require attention, this time can be used to refresh memory traces. The theory therefore predicts that the amount of forgetting depends on the temporal density of attentional demands of the processing task—this density is called "cognitive load". The cognitive load depends on two variables, the rate at which the processing task requires individual steps to be carried out, and the duration of each step. For example, if the processing task consists of adding digits, then having to add another digit every half second places a higher cognitive load on the system than having to add another digit every two seconds. In a series of experiments, Barrouillet and colleagues have shown that memory for lists of letters depends neither on the number of processing steps nor the total time of processing but on cognitive load.<ref>{{citation|title=Time and cognitive load in working memory|date=May 2007|journal=J Exp Psychol Learn Mem Cogn|vauthors=Barrouillet P, Bernardin S, Portrat S, Vergauwe E, Camos V|volume=33|issue=3|pages=570–585|doi=10.1037/0278-7393.33.3.570|pmid=17470006|url=https://archive-ouverte.unige.ch/unige:88299}}</ref><br />
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The assumption that the contents of short-term or working memory decay over time, unless decay is prevented by rehearsal, goes back to the early days of experimental research on short-term memory. It is also an important assumption in the multi-component theory of working memory. The most elaborate decay-based theory of working memory to date is the "time-based resource sharing model". This theory assumes that representations in working memory decay unless they are refreshed. Refreshing them requires an attentional mechanism that is also needed for any concurrent processing task. When there are small time intervals in which the processing task does not require attention, this time can be used to refresh memory traces. The theory therefore predicts that the amount of forgetting depends on the temporal density of attentional demands of the processing task—this density is called "cognitive load". The cognitive load depends on two variables, the rate at which the processing task requires individual steps to be carried out, and the duration of each step. For example, if the processing task consists of adding digits, then having to add another digit every half second places a higher cognitive load on the system than having to add another digit every two seconds. In a series of experiments, Barrouillet and colleagues have shown that memory for lists of letters depends neither on the number of processing steps nor the total time of processing but on cognitive load.<br />
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该理论假设短期记忆或工作记忆的内容会随着时间的推移而'''<font color="#ff8000">衰退 decay</font>''',这种衰退只能通过不断刷新来遏制。这种理论来自短期记忆的早期研究<ref>{{Cite journal|last=Brown, J.|year=1958|title=Some tests of the decay theory of immediate memory|journal=Quarterly Journal of Experimental Psychology|volume=10|pages=12–21|doi=10.1080/17470215808416249}}</ref><ref>{{Cite journal|author1=Peterson, L. R. |author2=Peterson, M. J.|year=1959|title=Short-term retention of individual verbal items|journal=Journal of Experimental Psychology|volume=58|issue=3|pages=193–198|doi=10.1037/h0049234|pmid=14432252|citeseerx=10.1.1.227.1807}}</ref>。它同样是工作记忆多元理论中的一个重要假设<ref>{{Cite book|title=Working memory|author1=Baddeley, A. D.|publisher=Clarendon|year=1986|location=Oxford}}</ref>。迄今为止,基于衰减假设的最详尽的工作记忆理论是“'''<font color="#ff8000">基于时间的资源共享模型 time-based resource sharing model” </font>'''<ref>{{Cite journal|date=March 2004|title=Time constraints and resource sharing in adults' working memory spans|journal=Journal of Experimental Psychology: General|volume=133|issue=1|pages=83–100|doi=10.1037/0096-3445.133.1.83|pmid=14979753|vauthors=Barrouillet P, Bernardin S, Camos V|citeseerx=10.1.1.379.9208}}</ref>。该理论假设工作记忆中的表征不断衰退,需要持续刷新来维持。而刷新需要注意力机制——对于任何平行任务都是必需的——的保障。当任务进程中存在不需要注意力的微小时间间隔时,刷新记忆路径的任务可以在此时完成。因此,该理论推测遗忘量取决于任务进程所需即时注意力的密度,这种密度叫做“认知负荷”。认知负荷取决于两个变量,一是任务进程中各个步骤执行的速率,二是每个步骤的持续时间。例如,如果处理的任务内容是数字添加,那么每半秒添加一个数字会比每两秒添加一个数字给系统带来的认知负荷更大。在一系列的实验中,巴鲁耶 Barrouillet 及其同事证明字母列表的记忆并不取决于处理步骤的数量或者处理的总时间,而是取决于认知负荷<ref>{{citation|title=Time and cognitive load in working memory|date=May 2007|journal=J Exp Psychol Learn Mem Cogn|vauthors=Barrouillet P, Bernardin S, Portrat S, Vergauwe E, Camos V|volume=33|issue=3|pages=570–585|doi=10.1037/0278-7393.33.3.570|pmid=17470006|url=https://archive-ouverte.unige.ch/unige:88299}}</ref>。<br />
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==== 资源理论 Resource theories====<br />
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Resource theories assume that the capacity of working memory is a limited resource that must be shared between all representations that need to be maintained in working memory simultaneously.<ref>{{Cite journal|last1=Ma|first1=W. J.|author2=Husain, M.|author3=Bays, P. M.|year=2014|title=Changing concepts of working memory|journal=Nature Reviews Neuroscience|volume=17|issue=3|pages=347–356|doi=10.1038/nn.3655|pmid=24569831|pmc=4159388}}</ref> Some resource theorists also assume that maintenance and concurrent processing share the same resource;<ref name=":0" /> this can explain why maintenance is typically impaired by a concurrent processing demand. Resource theories have been very successful in explaining data from tests of working memory for simple visual features, such as colors or orientations of bars. An ongoing debate is whether the resource is a continuous quantity that can be subdivided among any number of items in working memory, or whether it consists of a small number of discrete "slots", each of which can be assigned to one memory item, so that only a limited number of about 3 items can be maintained in working memory at all.<ref>{{Cite journal|last1=van den Berg|first1=Ronald|last2=Awh|first2=Edward|last3=Ma|first3=Wei Ji|title=Factorial comparison of working memory models.|journal=Psychological Review|volume=121|issue=1|pages=124–149|doi=10.1037/a0035234|pmc=4159389|pmid=24490791|year=2014}}</ref><br />
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Resource theories assume that the capacity of working memory is a limited resource that must be shared between all representations that need to be maintained in working memory simultaneously. Some resource theorists also assume that maintenance and concurrent processing share the same resource;<br />
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'''<font color="#ff8000">资源理论 resource theories</font>'''认为工作记忆容量是一种由储存于工作记忆中的全部表征所共享的有限资源<ref>{{Cite journal|last1=Ma|first1=W. J.|author2=Husain, M.|author3=Bays, P. M.|year=2014|title=Changing concepts of working memory|journal=Nature Reviews Neuroscience|volume=17|issue=3|pages=347–356|doi=10.1038/nn.3655|pmid=24569831|pmc=4159388}}</ref>。一些资源理论学者同时还假设维护和并行处理会占用同样的资源;<br />
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==== 干涉理论 Interference theories====<br />
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Several forms of [[Interference theory|interference]] have been discussed by theorists. One of the oldest ideas is that new items simply replace older ones in working memory. Another form of interference is retrieval competition. For example, when the task is to remember a list of 7 words in their order, we need to start recall with the first word. While trying to retrieve the first word, the second word, which is represented in proximity, is accidentally retrieved as well, and the two compete for being recalled. Errors in serial recall tasks are often confusions of neighboring items on a memory list (so-called transpositions), showing that retrieval competition plays a role in limiting our ability to recall lists in order, and probably also in other working memory tasks. A third form of interference is the distortion of representations by superposition: When multiple representations are added on top of each other, each of them is blurred by the presence of all the others.<ref>{{Cite journal|last1=Oberauer|first1=Klaus|last2=Lewandowsky|first2=Stephan|last3=Farrell|first3=Simon|last4=Jarrold|first4=Christopher|last5=Greaves|first5=Martin|date=2012-06-20|title=Modeling working memory: An interference model of complex span|journal=Psychonomic Bulletin & Review|language=en|volume=19|issue=5|pages=779–819|doi=10.3758/s13423-012-0272-4|pmid=22715024|issn=1069-9384|url=http://doc.rero.ch/record/320568/files/13423_2012_Article_272.pdf}}</ref> A fourth form of interference assumed by some authors is feature overwriting.<ref>{{Cite journal|doi=10.1016/j.jml.2006.08.009 |title=A formal model of capacity limits in working memory |date=November 2006 |first1=Klaus |last1=Oberauer |first2=Reinhold |last2=Kliegl |journal=Journal of Memory and Language |volume=55 |issue=4 |pages=601–26|doi-access=free }}</ref><ref>{{Cite journal|doi=10.1007/s00221-010-2501-2 |pmid=21132280 |title=Distractor frequency influences performance in vibrotactile working memory |year=2011 |first1=T. |last1=Bancroft |first2=P. |last2=Servos |journal=Experimental Brain Research |volume=208 |issue=4 |pages=529–32}}</ref> The idea is that each word, digit, or other item in working memory is represented as a bundle of features, and when two items share some features, one of them steals the features from the other. The more items are held in working memory, and the more their features overlap, the more each of them will be degraded by the loss of some features.<br />
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Several forms of interference have been discussed by theorists. One of the oldest ideas is that new items simply replace older ones in working memory. Another form of interference is retrieval competition. For example, when the task is to remember a list of 7 words in their order, we need to start recall with the first word. While trying to retrieve the first word, the second word, which is represented in proximity, is accidentally retrieved as well, and the two compete for being recalled. Errors in serial recall tasks are often confusions of neighboring items on a memory list (so-called transpositions), showing that retrieval competition plays a role in limiting our ability to recall lists in order, and probably also in other working memory tasks. A third form of interference is the distortion of representations by superposition: When multiple representations are added on top of each other, each of them is blurred by the presence of all the others. A fourth form of interference assumed by some authors is feature overwriting. The idea is that each word, digit, or other item in working memory is represented as a bundle of features, and when two items share some features, one of them steals the features from the other. The more items are held in working memory, and the more their features overlap, the more each of them will be degraded by the loss of some features.<br />
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理论家们讨论过多种形式的干涉。最初的观点之一是,新事物只是单纯地取代了工作记忆中的旧事物。另一种干涉形式是'''<font color="#ff8000">检索竞争 retrieval competition</font>'''。例如当任务是按照一定顺序记住7个单词时,我们需要从第一个单词开始回忆。而在试图检索第一个单词时,我们往往会意外地检索到第二个单词,至于我们最终会回忆起哪个单词,这就得看它们竞争的结果了。回忆中出现的错误通常表现为记忆列表中相邻项目的混淆(即所谓的换位) ,这表明检索竞争限制了我们按照正确顺序回忆列表的能力,这种限制也可能发生在其他工作记忆任务中。另一种形式的干涉是叠表征的变形: 当多重表征叠加在一起时,每一表征都因其他表征的相互作用而模糊不清<ref>{{Cite journal|last1=Oberauer|first1=Klaus|last2=Lewandowsky|first2=Stephan|last3=Farrell|first3=Simon|last4=Jarrold|first4=Christopher|last5=Greaves|first5=Martin|date=2012-06-20|title=Modeling working memory: An interference model of complex span|journal=Psychonomic Bulletin & Review|language=en|volume=19|issue=5|pages=779–819|doi=10.3758/s13423-012-0272-4|pmid=22715024|issn=1069-9384|url=http://doc.rero.ch/record/320568/files/13423_2012_Article_272.pdf}}</ref>。一些人认为特征覆盖也是一种干涉形式<ref>{{Cite journal|doi=10.1016/j.jml.2006.08.009 |title=A formal model of capacity limits in working memory |date=November 2006 |first1=Klaus |last1=Oberauer |first2=Reinhold |last2=Kliegl |journal=Journal of Memory and Language |volume=55 |issue=4 |pages=601–26|doi-access=free }}</ref><ref>{{Cite journal|doi=10.1007/s00221-010-2501-2 |pmid=21132280 |title=Distractor frequency influences performance in vibrotactile working memory |year=2011 |first1=T. |last1=Bancroft |first2=P. |last2=Servos |journal=Experimental Brain Research |volume=208 |issue=4 |pages=529–32}}</ref>。该观点认为工作记忆中的每个单词、数字或其他项目都被表现为一系列特征,当两个项目共享某些特征时,其中一个就会窃取另一个的特征。工作记忆中保存的条目越多则重叠的特征越多,因此每个条目丢失的特征越多,减损也就越多。<br />
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==== 极限 Limitations ====<br />
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None of these hypotheses can explain the experimental data entirely. The resource hypothesis, for example, was meant to explain the trade-off between maintenance and processing: The more information must be maintained in working memory, the slower and more error prone concurrent processes become, and with a higher demand on concurrent processing memory suffers. This trade-off has been investigated by tasks like the reading-span task described above. It has been found that the amount of trade-off depends on the similarity of the information to be remembered and the information to be processed. For example, remembering numbers while processing spatial information, or remembering spatial information while processing numbers, impair each other much less than when material of the same kind must be remembered and processed.<ref>{{Cite journal|doi=10.1016/j.jml.2006.07.009 |title=The relationship between processing and storage in working memory span: Not two sides of the same coin |date=February 2007 |first1=Yukio |last1=Maehara |first2=Satoru |last2=Saito |journal=Journal of Memory and Language |volume=56 |issue=2 |pages=212–228}}</ref> Also, remembering words and processing digits, or remembering digits and processing words, is easier than remembering and processing materials of the same category.<ref>{{Cite journal|doi=10.1076/anec.6.2.99.784 |title=Selection from Working Memory: on the Relationship between Processing and Storage Components |date=June 1999 |last1=Li |first1=Karen Z.H. |journal=Aging, Neuropsychology, and Cognition |volume=6 |issue=2 |pages=99–116}}</ref> These findings are also difficult to explain for the decay hypothesis, because decay of memory representations should depend only on how long the processing task delays rehearsal or recall, not on the content of the processing task. A further problem for the decay hypothesis comes from experiments in which the recall of a list of letters was delayed, either by instructing participants to recall at a slower pace, or by instructing them to say an irrelevant word once or three times in between recall of each letter. Delaying recall had virtually no effect on recall accuracy.<ref>{{Cite journal|doi=10.3758/BF03196705|vauthors=Lewandowsky S, Duncan M, Brown GD |title=Time does not cause forgetting in short-term serial recall |journal=Psychonomic Bulletin & Review |volume=11 |issue=5 |pages=771–90 |date=October 2004 |pmid=15732687 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=15732687|doi-access=free }}</ref><ref>{{Cite journal|vauthors=Oberauer K, Lewandowsky S |title=Forgetting in immediate serial recall: decay, temporal distinctiveness, or interference? |journal=Psychological Review |volume=115 |issue=3 |pages=544–76 |date=July 2008 |pmid=18729591 |doi=10.1037/0033-295X.115.3.544|url=https://api.research-repository.uwa.edu.au/files/1546099/11204_PID11204.pdf }}</ref> The [[interference theory]] seems to fare best with explaining why the similarity between memory contents and the contents of concurrent processing tasks affects how much they impair each other. More similar materials are more likely to be confused, leading to retrieval competition.<br />
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None of these hypotheses can explain the experimental data entirely. The resource hypothesis, for example, was meant to explain the trade-off between maintenance and processing: The more information must be maintained in working memory, the slower and more error prone concurrent processes become, and with a higher demand on concurrent processing memory suffers. This trade-off has been investigated by tasks like the reading-span task described above. It has been found that the amount of trade-off depends on the similarity of the information to be remembered and the information to be processed. For example, remembering numbers while processing spatial information, or remembering spatial information while processing numbers, impair each other much less than when material of the same kind must be remembered and processed. Also, remembering words and processing digits, or remembering digits and processing words, is easier than remembering and processing materials of the same category. These findings are also difficult to explain for the decay hypothesis, because decay of memory representations should depend only on how long the processing task delays rehearsal or recall, not on the content of the processing task. A further problem for the decay hypothesis comes from experiments in which the recall of a list of letters was delayed, either by instructing participants to recall at a slower pace, or by instructing them to say an irrelevant word once or three times in between recall of each letter. Delaying recall had virtually no effect on recall accuracy. The interference theory seems to fare best with explaining why the similarity between memory contents and the contents of concurrent processing tasks affects how much they impair each other. More similar materials are more likely to be confused, leading to retrieval competition.<br />
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这些假说都不能完全解释实验数据。例如,资源理论旨在解释维护和加工之间的平衡: 工作记忆中需要保存的信息越多,并发进程就变得越慢、越容易出错,且对并发加工记忆的要求也越高。先前叙述的阅读广度任务等被应用于此现象的研究。研究发现,平衡量取决于所要记忆或处理的信息的相似性。例如,在处理空间信息时去记忆数字,或者在处理数字时去记忆空间信息,这些任务的偏差程度要低于记忆并处理同类材料所造成的损失<ref>{{Cite journal|doi=10.1016/j.jml.2006.07.009 |title=The relationship between processing and storage in working memory span: Not two sides of the same coin |date=February 2007 |first1=Yukio |last1=Maehara |first2=Satoru |last2=Saito |journal=Journal of Memory and Language |volume=56 |issue=2 |pages=212–228}}</ref>。此外,记忆单词时处理数字,或记忆数字时处理单词,也要比记忆和处理同一类别材料更容易<ref>{{Cite journal|doi=10.1076/anec.6.2.99.784 |title=Selection from Working Memory: on the Relationship between Processing and Storage Components |date=June 1999 |last1=Li |first1=Karen Z.H. |journal=Aging, Neuropsychology, and Cognition |volume=6 |issue=2 |pages=99–116}}</ref>。这些发现同样也很难解释衰退假说,因为记忆表征的衰退应该只取决任务处理进程中刷新延迟的时间,而不取决于任务处理的内容。'''<font color="#ff8000">衰退假说 decay theories</font>'''的另一个问题来自于延迟回忆字母列表的实验——通过要求参与者以较慢的速度回忆或在回忆每个字母的间隔说一个不相关单词一至三次来实现延迟效果。但延迟回忆对回忆准确率几乎没有影响<ref>{{Cite journal|doi=10.3758/BF03196705|vauthors=Lewandowsky S, Duncan M, Brown GD |title=Time does not cause forgetting in short-term serial recall |journal=Psychonomic Bulletin & Review |volume=11 |issue=5 |pages=771–90 |date=October 2004 |pmid=15732687 |url=http://pbr.psychonomic-journals.org/cgi/pmidlookup?view=long&pmid=15732687|doi-access=free }}</ref><ref>{{Cite journal|vauthors=Oberauer K, Lewandowsky S |title=Forgetting in immediate serial recall: decay, temporal distinctiveness, or interference? |journal=Psychological Review |volume=115 |issue=3 |pages=544–76 |date=July 2008 |pmid=18729591 |doi=10.1037/0033-295X.115.3.544|url=https://api.research-repository.uwa.edu.au/files/1546099/11204_PID11204.pdf }}</ref>。'''<font color="#ff8000">干扰理论 interference theories</font>'''似乎最好地解释了为何记忆内容相似或并发进程内容相似就会造成记忆效果减损。材料越相似就越容易混淆,进而引起检索竞争。<br />
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== 发展 Development ==<br />
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The capacity of working memory increases gradually over childhood<ref name="ReferenceA">{{cite journal | doi = 10.1037/0012-1649.40.2.177 | last1 = Gathercole | first1 = S. E. | last2 = Pickering | first2 = S. J. | last3 = Ambridge | first3 = B. | last4 = Wearing | first4 = H. | year = 2004 | title = The structure of working memory from 4 to 15 years of age | journal = Developmental Psychology | volume = 40 | issue = 2| pages = 177–190 | pmid = 14979759 | citeseerx = 10.1.1.529.2727 }}</ref> and declines gradually in old age.<ref>{{cite journal | doi = 10.1037/0894-4105.8.4.535 | last1 = Salthouse | first1 = T. A. | year = 1994 | title = The aging of working memory | journal = Neuropsychology | volume = 8 | issue = 4| pages = 535–543 }}</ref><br />
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The capacity of working memory increases gradually over childhood and declines gradually in old age.<br />
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工作记忆的容量在儿童时期逐渐增加,在老年时期逐渐下降<ref name="ReferenceA">{{cite journal | doi = 10.1037/0012-1649.40.2.177 | last1 = Gathercole | first1 = S. E. | last2 = Pickering | first2 = S. J. | last3 = Ambridge | first3 = B. | last4 = Wearing | first4 = H. | year = 2004 | title = The structure of working memory from 4 to 15 years of age | journal = Developmental Psychology | volume = 40 | issue = 2| pages = 177–190 | pmid = 14979759 | citeseerx = 10.1.1.529.2727 }}</ref> and declines gradually in old age.<ref>{{cite journal | doi = 10.1037/0894-4105.8.4.535 | last1 = Salthouse | first1 = T. A. | year = 1994 | title = The aging of working memory | journal = Neuropsychology | volume = 8 | issue = 4| pages = 535–543 }}</ref>。<br />
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=== 儿童期 Childhood ===<br />
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{{Main|Neo-Piagetian theories of cognitive development}}<br />
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Measures of performance on tests of working memory increase continuously between early childhood and adolescence, while the structure of correlations between different tests remains largely constant. theorists have argued that the growth of working-memory capacity is a major driving force of cognitive development. This hypothesis has received substantial empirical support from studies showing that the capacity of working memory is a strong predictor of cognitive abilities in childhood.<ref>Jarrold, C., & Bayliss, D. M. (2007). Variation in working memory due to typical and atypical development. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake & J. N. Towse (Eds.), Variation in working memory (pp. 137–161). New York: Oxford University Press.</ref> Particularly strong evidence for a role of working memory for development comes from a longitudinal study showing that working-memory capacity at one age predicts reasoning ability at a later age.<ref>{{cite journal | doi = 10.1111/j.1467-9280.2007.01895.x | last1 = Kail | first1 = R. | year = 2007 | title = Longitudinal evidence that increases in processing speed and working memory enhance children's reasoning | journal = Psychological Science | volume = 18 | issue = 4| pages = 312–313 | pmid = 17470254 }}</ref> Studies in the Neo-Piagetian tradition have added to this picture by analyzing the complexity of cognitive tasks in terms of the number of items or relations that have to be considered simultaneously for a solution. Across a broad range of tasks, children manage task versions of the same level of complexity at about the same age, consistent with the view that working memory capacity limits the complexity they can handle at a given age.<ref>{{cite journal | doi = 10.1016/S0010-0285(02)00002-6 | last1 = Andrews | first1 = G. | last2 = Halford | first2 = G. S. | year = 2002 | title = A cognitive complexity metric applied to cognitive development | journal = Cognitive Psychology | volume = 45 | issue = 2| pages = 153–219 | pmid = 12528901 }}</ref> Although neuroscience studies support the notion that children rely on prefrontal cortex for performing various working memory tasks, an [[fMRI]] meta-analysis on children compared to adults performing the n back task revealed lack of consistent prefrontal cortex activation in children, while posterior regions including the [[insular cortex]] and [[cerebellum]] remain intact.<ref name= "cf">Yaple, Z., Arsalidou, M (2018). N-back working memory task: Meta-analysis of normative fMRI studies with children, Child Development, 89(6), 2010-2022.</ref><br />
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Measures of performance on tests of working memory increase continuously between early childhood and adolescence, while the structure of correlations between different tests remains largely constant. theorists have argued that the growth of working-memory capacity is a major driving force of cognitive development. This hypothesis has received substantial empirical support from studies showing that the capacity of working memory is a strong predictor of cognitive abilities in childhood. Particularly strong evidence for a role of working memory for development comes from a longitudinal study showing that working-memory capacity at one age predicts reasoning ability at a later age. Studies in the Neo-Piagetian tradition have added to this picture by analyzing the complexity of cognitive tasks in terms of the number of items or relations that have to be considered simultaneously for a solution. Across a broad range of tasks, children manage task versions of the same level of complexity at about the same age, consistent with the view that working memory capacity limits the complexity they can handle at a given age. Although neuroscience studies support the notion that children rely on prefrontal cortex for performing various working memory tasks, an fMRI meta-analysis on children compared to adults performing the n back task revealed lack of consistent prefrontal cortex activation in children, while posterior regions including the insular cortex and cerebellum remain intact.<br />
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从儿童到青少年这段时间里,人们在针对工作记忆的测试中表现会越来越好,而不同测试之间的相关性结构基本保持不变。理论学者认为工作记忆容量的增长是认知发展的主要驱动力之一。这一假设得到了大量研究的支持,研究表明工作记忆能力是童年认知能力的一个强预测因子<ref>Jarrold, C., & Bayliss, D. M. (2007). Variation in working memory due to typical and atypical development. In A. R. A. Conway, C. Jarrold, M. J. Kane, A. Miyake & J. N. Towse (Eds.), Variation in working memory (pp. 137–161). New York: Oxford University Press.</ref>。工作记忆对认知发展起作用的有力证明来自一项追踪研究。该研究表明,根据人在某一年龄上的工作记忆能力可以预测其之后的推理能力<ref>{{cite journal | doi = 10.1111/j.1467-9280.2007.01895.x | last1 = Kail | first1 = R. | year = 2007 | title = Longitudinal evidence that increases in processing speed and working memory enhance children's reasoning | journal = Psychological Science | volume = 18 | issue = 4| pages = 312–313 | pmid = 17470254 }}</ref>。 对新皮亚杰传统的的研究也支持了这一观点。该研究分析了认知任务复杂性(情境下需要同时考虑的项目及关系的数量)的问题。在一系列任务之中,相同年龄段的儿童可处理难度近似的任务,这与特定年龄下的工作记忆容量会限制人能够处理的问题的复杂度的观点一致<ref>{{cite journal | doi = 10.1016/S0010-0285(02)00002-6 | last1 = Andrews | first1 = G. | last2 = Halford | first2 = G. S. | year = 2002 | title = A cognitive complexity metric applied to cognitive development | journal = Cognitive Psychology | volume = 45 | issue = 2| pages = 153–219 | pmid = 12528901 }}</ref>。虽然神经科学研究认为儿童依靠脑前额叶皮层来完成各种工作记忆任务,但一项功能性磁共振成象元在分析对比了儿童和成人在n back任务中的表现之后,发现儿童相对来说较难做到持续激活脑前额叶皮层,反而是后部区域包括到叶皮质和小脑都表现正常<ref name= "cf">Yaple, Z., Arsalidou, M (2018). N-back working memory task: Meta-analysis of normative fMRI studies with children, Child Development, 89(6), 2010-2022.</ref>。<br />
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=== 老化 Aging ===<br />
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Working memory is among the cognitive functions most sensitive to decline in [[old age]].<ref name="Hertzog 2003">{{cite journal |vauthors=Hertzog C, Dixon RA, Hultsch DF, MacDonald SW |title=Latent change models of adult cognition: are changes in processing speed and working memory associated with changes in episodic memory? |journal=Psychol Aging |volume=18 |issue=4 |pages=755–69 |date=December 2003 |pmid=14692862 |doi=10.1037/0882-7974.18.4.755 }}</ref><ref name="Park, D. C. 2002">{{cite journal |vauthors=Park DC, Lautenschlager G, Hedden T, Davidson NS, Smith AD, Smith PK |title=Models of visuospatial and verbal memory across the adult life span |journal=Psychol Aging |volume=17 |issue=2 |pages=299–320 |date=June 2002 |pmid=12061414 |doi= 10.1037/0882-7974.17.2.299 }}</ref> Several explanations have been offered for this decline in psychology. One is the processing speed theory of cognitive aging by Tim Salthouse.<ref>{{cite journal | doi = 10.1037/0033-295X.103.3.403 | last1 = Salthouse | first1 = T. A. | year = 1996 | title = The processing speed theory of adult age differences in cognition | journal = Psychological Review | volume = 103 | issue = 3| pages = 403–428 | pmid = 8759042 | citeseerx = 10.1.1.464.585 }}</ref> Drawing on the finding of general slowing of cognitive processes as people grow older, Salthouse argues that slower processing leaves more time for working-memory contents to decay, thus reducing effective capacity. However, the decline of working-memory capacity cannot be entirely attributed to slowing because capacity declines more in old age than speed.<ref name="Park, D. C. 2002" /><ref>{{cite journal | doi = 10.1016/0010-0277(95)00689-3 | last1 = Mayr | first1 = U. | last2 = Kliegl | first2 = R. | last3 = Krampe | first3 = R. T. | year = 1996 | title = Sequential and coordinative processing dynamics in figural transformation across the life span | journal = Cognition | volume = 59 | issue = 1| pages = 61–90 | pmid = 8857471 }}</ref> Another proposal is the inhibition hypothesis advanced by [[Lynn Hasher]] and Rose Zacks.<ref>Hasher, L., & Zacks, R.&nbsp;T. (1988). Working memory, comprehension, and aging: A review and new view. In G. H. Bower (Ed.), ''The psychology of learning and motivation'', ''Vol. 22'', (pp. 193–225). New York: Academic Press.</ref> This theory assumes a general deficit in old age in the ability to inhibit irrelevant, or no-longer relevant, information. Therefore, working memory tends to be cluttered with irrelevant contents that reduce the effective capacity for relevant content. The assumption of an inhibition deficit in old age has received much empirical support<ref>Hasher, L., Zacks, R.&nbsp;T., & May, C.&nbsp;P. (1999). Inhibitory control, circadian arousal, and age. In D.&nbsp;Gopher & A.&nbsp;Koriat (Eds.), ''Attention and Performance'' (pp. 653–675). Cambridge, MA: MIT Press.</ref> but, so far, it is not clear whether the decline in inhibitory ability fully explains the decline of working-memory capacity. An explanation on the neural level of the decline of working memory and other cognitive functions in old age has been proposed by West.<ref>{{cite journal | doi = 10.1037/0033-2909.120.2.272 | last1 = West | first1 = R.&nbsp;L. | year = 1996 | title = An application of prefrontal cortex function theory to cognitive aging | journal = Psychological Bulletin | volume = 120 | issue = 2| pages = 272–292 | pmid = 8831298 }}</ref> She argued that working memory depends to a large degree on the [[pre-frontal cortex]], which deteriorates more than other brain regions as we grow old. Age related decline in working memory can be briefly reversed using low intensity transcranial stimulation, synchronizing rhythms in bilateral frontal and left temporal lobe areas.<ref>{{Cite news|url=https://www.theguardian.com/science/2019/apr/08/scientists-use-electrical-pulses-reverse-memory-decline-ageing|title=Scientists reverse memory decline using electrical pulses|last=Devlin, H.|date=2019-04-08|work=The Guardian|access-date=2019-04-09|language=en-GB|issn=0261-3077}}</ref><br />
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Working memory is among the cognitive functions most sensitive to decline in old age. Several explanations have been offered for this decline in psychology. One is the processing speed theory of cognitive aging by Tim Salthouse. Drawing on the finding of general slowing of cognitive processes as people grow older, Salthouse argues that slower processing leaves more time for working-memory contents to decay, thus reducing effective capacity. However, the decline of working-memory capacity cannot be entirely attributed to slowing because capacity declines more in old age than speed. Another proposal is the inhibition hypothesis advanced by Lynn Hasher and Rose Zacks. This theory assumes a general deficit in old age in the ability to inhibit irrelevant, or no-longer relevant, information. Therefore, working memory tends to be cluttered with irrelevant contents that reduce the effective capacity for relevant content. The assumption of an inhibition deficit in old age has received much empirical support but, so far, it is not clear whether the decline in inhibitory ability fully explains the decline of working-memory capacity. An explanation on the neural level of the decline of working memory and other cognitive functions in old age has been proposed by West. She argued that working memory depends to a large degree on the pre-frontal cortex, which deteriorates more than other brain regions as we grow old. Age related decline in working memory can be briefly reversed using low intensity transcranial stimulation, synchronizing rhythms in bilateral frontal and left temporal lobe areas.<br />
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人进入老年期后,一系列认知功能都会有所衰退,其中最严重的就是工作记忆<ref name="Hertzog 2003">{{cite journal |vauthors=Hertzog C, Dixon RA, Hultsch DF, MacDonald SW |title=Latent change models of adult cognition: are changes in processing speed and working memory associated with changes in episodic memory? |journal=Psychol Aging |volume=18 |issue=4 |pages=755–69 |date=December 2003 |pmid=14692862 |doi=10.1037/0882-7974.18.4.755 }}</ref><ref name="Park, D. C. 2002">{{cite journal |vauthors=Park DC, Lautenschlager G, Hedden T, Davidson NS, Smith AD, Smith PK |title=Models of visuospatial and verbal memory across the adult life span |journal=Psychol Aging |volume=17 |issue=2 |pages=299–320 |date=June 2002 |pmid=12061414 |doi= 10.1037/0882-7974.17.2.299 }}</ref>。心理学对此有几种解释。一个是提姆 · 萨尔特豪斯 Tim Salthouse 提出的关于认知老化的'''<font color="#ff8000">加工速度理论 processing speed theory</font>'''<ref>{{cite journal | doi = 10.1037/0033-295X.103.3.403 | last1 = Salthouse | first1 = T. A. | year = 1996 | title = The processing speed theory of adult age differences in cognition | journal = Psychological Review | volume = 103 | issue = 3| pages = 403–428 | pmid = 8759042 | citeseerx = 10.1.1.464.585 }}</ref>。普遍而言,人的认知过程随着年龄增长而滞缓。所以Salthouse 认为工作记忆会有更多的衰减机会,从而使其有效容量降低。然而,工作记忆容量的下降不能完全归因于此,因为老年时期记忆容量的下降速度比速度本身下降的更快<ref name="Park, D. C. 2002" /><ref>{{cite journal | doi = 10.1016/0010-0277(95)00689-3 | last1 = Mayr | first1 = U. | last2 = Kliegl | first2 = R. | last3 = Krampe | first3 = R. T. | year = 1996 | title = Sequential and coordinative processing dynamics in figural transformation across the life span | journal = Cognition | volume = 59 | issue = 1| pages = 61–90 | pmid = 8857471 }}</ref>。另一个是琳恩·哈什尔 Lynn Hasher 和 罗丝·扎克 Rose Zacks 提出的'''<font color="#ff8000">抑制假说 inhibition hypothesis</font>'''<ref>Hasher, L., & Zacks, R.&nbsp;T. (1988). Working memory, comprehension, and aging: A review and new view. In G. H. Bower (Ed.), ''The psychology of learning and motivation'', ''Vol. 22'', (pp. 193–225). New York: Academic Press.</ref>。该理论假设老年人排除不相关信息的能力不足。因此,工作记忆往往会被不相关内容所干扰,从而降低记忆内容的有效容量。老年抑制能力缺失的假设得到了大量研究的支持<ref>Hasher, L., Zacks, R.&nbsp;T., & May, C.&nbsp;P. (1999). Inhibitory control, circadian arousal, and age. In D.&nbsp;Gopher & A.&nbsp;Koriat (Eds.), ''Attention and Performance'' (pp. 653–675). Cambridge, MA: MIT Press.</ref>,但抑制能力的下降能否完全解释为何工作记忆能力下降,目前为止还不清楚。韦斯特 West对老年工作记忆及其他认知功能的衰退则提出了一种神经层面的解释<ref>{{cite journal | doi = 10.1037/0033-2909.120.2.272 | last1 = West | first1 = R.&nbsp;L. | year = 1996 | title = An application of prefrontal cortex function theory to cognitive aging | journal = Psychological Bulletin | volume = 120 | issue = 2| pages = 272–292 | pmid = 8831298 }}</ref>。她认为前额叶皮层对工作记忆有着很大的影响,而随着年龄的增长,前额叶皮与其他大脑区域相比更容易衰退。由衰老引发的工作记忆衰退可通过低强度经颅刺激同步化额叶或左侧颞叶节律来短期逆转<ref>{{Cite news|url=https://www.theguardian.com/science/2019/apr/08/scientists-use-electrical-pulses-reverse-memory-decline-ageing|title=Scientists reverse memory decline using electrical pulses|last=Devlin, H.|date=2019-04-08|work=The Guardian|access-date=2019-04-09|language=en-GB|issn=0261-3077}}</ref>。<br />
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== 训练 Training ==<br />
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{{further|Working memory training|Neurobiological effects of physical exercise#Cognitive control and memory}}<br />
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Torkel Klingberg was the first to investigate whether intensive training of working memory has beneficial effects on other cognitive functions. His pioneering study suggested that working memory can be improved by training in ADHD patients through computerized programs.<ref>{{Cite journal|author=Klingberg, T.|author2=Forssberg, H.|author3=Westerberg, H. |title=Training of working memory in children with ADHD |journal=Journal of Clinical and Experimental Neuropsychology |volume=24 |issue=6 |pages=781–91 |date=September 2002 |pmid=12424652 |doi=10.1076/jcen.24.6.781.8395|citeseerx=10.1.1.326.5165}}</ref> This study has found that a period of [[working memory training]] increases a range of cognitive abilities and increases IQ test scores. Another study of the same group<ref>{{Cite journal|date=January 2004|title=Increased prefrontal and parietal activity after training of working memory|journal=Nature Neuroscience|volume=7|issue=1|pages=75–9|doi=10.1038/nn1165|pmid=14699419|vauthors=Olesen PJ, Westerberg H, Klingberg T}}</ref> has shown that, after training, measured brain activity related to working memory increased in the prefrontal cortex, an area that many researchers have associated with working memory functions. It has been shown in one study that working memory training increases the density of [[prefrontal cortex|prefrontal]] and [[parietal cortex|parietal]] [[dopamine receptor]]s (specifically, [[DRD1]]) in test persons.<ref>{{Cite journal|date=February 2009|title=Changes in cortical dopamine D1 receptor binding associated with cognitive training|journal=Science|volume=323|issue=5915|pages=800–2|bibcode=2009Sci...323..800M|doi=10.1126/science.1166102|pmid=19197069|author=McNab, F.|author2=Varrone, A.|author3=Farde, L.|display-authors=etal}}</ref> However, subsequent work with the same training program has failed to replicate the beneficial effects of training on cognitive performance. A meta-analytic summary of research with Klingberg's training program up to 2011 shows that this training has at best a negligible effect on tests of intelligence and of attention<ref>{{Cite journal|last=Hulme, C. & Melby-Lervåg, M.|year=2012|title=Current evidence does not support the claims made for CogMed working memory training|journal=Journal of Applied Research in Memory and Cognition|volume=1|issue=3|pages=197–200|doi=10.1016/j.jarmac.2012.06.006}}</ref>.<br />
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Torkel Klingberg was the first to investigate whether intensive training of working memory has beneficial effects on other cognitive functions. His pioneering study suggested that working memory can be improved by training in ADHD patients through computerized programs. This study has found that a period of working memory training increases a range of cognitive abilities and increases IQ test scores. Another study of the same group has shown that, after training, measured brain activity related to working memory increased in the prefrontal cortex, an area that many researchers have associated with working memory functions. It has been shown in one study that working memory training increases the density of prefrontal and parietal dopamine receptors (specifically, DRD1) in test persons. However, subsequent work with the same training program has failed to replicate the beneficial effects of training on cognitive performance. A meta-analytic summary of research with Klingberg's training program up to 2011 shows that this training has at best a negligible effect on tests of intelligence and of attention.<br />
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托克尔 · 克林伯格 Torkel Klingberg 是第一个研究工作记忆强化训练是否对其他认知功能有益的人。他实施的开创性研究表明ADHD患者在经过电脑程序训练后工作记忆得到改善<ref>{{Cite journal|author=Klingberg, T.|author2=Forssberg, H.|author3=Westerberg, H. |title=Training of working memory in children with ADHD |journal=Journal of Clinical and Experimental Neuropsychology |volume=24 |issue=6 |pages=781–91 |date=September 2002 |pmid=12424652 |doi=10.1076/jcen.24.6.781.8395|citeseerx=10.1.1.326.5165}}</ref>。该研究发现,'''<font color="#ff8000">工作记忆训练 Working Memory Training</font>'''可以提高人的一系列认知能力及 IQ 测试成绩。针对同一群体的另一项研究<ref>{{Cite journal|date=January 2004|title=Increased prefrontal and parietal activity after training of working memory|journal=Nature Neuroscience|volume=7|issue=1|pages=75–9|doi=10.1038/nn1165|pmid=14699419|vauthors=Olesen PJ, Westerberg H, Klingberg T}}</ref>表明,训练之后脑前额叶外皮层——被许多研究人员认为与工作记忆功能相关——的大脑活动测度有所增加。还有一项研究表明,工作记忆训练能增加受试者前额叶和顶叶多巴胺受体(特别是 DRD1)的密度<ref>{{Cite journal|date=February 2009|title=Changes in cortical dopamine D1 receptor binding associated with cognitive training|journal=Science|volume=323|issue=5915|pages=800–2|bibcode=2009Sci...323..800M|doi=10.1126/science.1166102|pmid=19197069|author=McNab, F.|author2=Varrone, A.|author3=Farde, L.|display-authors=etal}}</ref>。然而,同一训练方案的后续工作却未能再现这些有益影响。一份荟萃分析报告显示,持续至2011年的Klingberg 训练对智力和注意力的提升只有微乎其微的影响<ref>{{Cite journal|last=Hulme, C. & Melby-Lervåg, M.|year=2012|title=Current evidence does not support the claims made for CogMed working memory training|journal=Journal of Applied Research in Memory and Cognition|volume=1|issue=3|pages=197–200|doi=10.1016/j.jarmac.2012.06.006}}</ref>。<br />
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In another influential study, training with a working memory task (the dual [[n-back]] task) has improved performance on a fluid [[intelligence test]] in healthy young adults.<ref>{{Cite journal|author=Jaeggi, S.M.|author2=Buschkuehl, M.|author3= Jonides, J.|author4=Perrig, W. J.|title=Improving fluid intelligence with training on working memory |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=105 |issue=19 |pages=6829–33 |date=May 2008 |pmid=18443283 |pmc=2383929 |doi=10.1073/pnas.0801268105|bibcode=2008PNAS..105.6829J }}</ref> The improvement of fluid intelligence by training with the n-back task was replicated in 2010,<ref name="JaeggiStuder-Luethi2010">{{cite journal| last1=Jaeggi| first1=Susanne M.| last2=Studer-Luethi| first2=Barbara| last3=Buschkuehl|first3=Martin| last4=Su|first4=Yi-Fen|last5=Jonides|first5=John|last6=Perrig|first6=Walter J.|title=The relationship between n-back performance and matrix reasoning – implications for training and transfer|journal=Intelligence|volume=38|issue=6|year=2010|pages=625–635|issn=0160-2896|doi=10.1016/j.intell.2010.09.001}}</ref> but two studies published in 2012 failed to reproduce the effect.<ref name="RedickShipstead2013">{{cite journal|last1=Redick|first1=Thomas S.| last2=Shipstead| first2=Zach|last3=Harrison|first3=Tyler L.|last4=Hicks|first4=Kenny L.|last5=Fried|first5=David E.|last6=Hambrick|first6=David Z.|last7=Kane|first7=Michael J.|last8=Engle|first8=Randall W.|title=No evidence of intelligence improvement after working memory training: A randomized, placebo-controlled study|journal=Journal of Experimental Psychology: General|volume=142| issue=2|year=2013| pages=359–379| pmid=22708717|issn=1939-2222| doi=10.1037/a0029082}}</ref><ref name="ChooiThompson2012">{{cite journal| last1=Chooi| first1=Weng-Tink| last2=Thompson| first2=Lee A.| title=Working memory training does not improve intelligence in healthy young adults| journal=Intelligence| volume=40|issue=6| year=2012| pages=531–542| issn=0160-2896| doi=10.1016/j.intell.2012.07.004}}</ref> The combined evidence from about 30 experimental studies on the effectiveness of working-memory training has been evaluated by several meta-analyses.<ref>{{Cite journal|last1=Au|first1=Jacky|last2=Sheehan|first2=Ellen|last3=Tsai|first3=Nancy|last4=Duncan|first4=Greg J.|last5=Buschkuehl|first5=Martin|last6=Jaeggi|first6=Susanne M.|date=2014-08-08|title=Improving fluid intelligence with training on working memory: a meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=22|issue=2|pages=366–377|doi=10.3758/s13423-014-0699-x|pmid=25102926|issn=1069-9384|url=http://www.escholarship.org/uc/item/1mj701dj|type=Submitted manuscript}}</ref><ref>{{Cite journal|last1=Melby-Lervåg|first1=Monica|last2=Redick|first2=Thomas S.|last3=Hulme|first3=Charles|date=2016-07-29|title=Working Memory Training Does Not Improve Performance on Measures of Intelligence or Other Measures of "Far Transfer"|journal=Perspectives on Psychological Science|language=en|volume=11|issue=4|pages=512–534|doi=10.1177/1745691616635612|pmc=4968033|pmid=27474138}}</ref> The authors of these meta-analyses disagree in their conclusions as to whether or not working-memory training improves intelligence. Yet, these meta-analyses agree in their estimate of the size of the effect of working-memory training: If there is such an effect, it is likely to be small.<br />
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In another influential study, training with a working memory task (the dual n-back task) has improved performance on a fluid intelligence test in healthy young adults. The improvement of fluid intelligence by training with the n-back task was replicated in 2010, but two studies published in 2012 failed to reproduce the effect. The combined evidence from about 30 experimental studies on the effectiveness of working-memory training has been evaluated by several meta-analyses. The authors of these meta-analyses disagree in their conclusions as to whether or not working-memory training improves intelligence. Yet, these meta-analyses agree in their estimate of the size of the effect of working-memory training: If there is such an effect, it is likely to be small.<br />
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在另一项有影响力的研究中,工作记忆('''<font color="#ff8000">双 n-back 任务 The Dual n-back Task)</font>'''训练使健康青年在流体智力测试中的表现有所提升<ref>{{Cite journal|author=Jaeggi, S.M.|author2=Buschkuehl, M.|author3= Jonides, J.|author4=Perrig, W. J.|title=Improving fluid intelligence with training on working memory |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=105 |issue=19 |pages=6829–33 |date=May 2008 |pmid=18443283 |pmc=2383929 |doi=10.1073/pnas.0801268105|bibcode=2008PNAS..105.6829J }}</ref>。2010年时,通过 n-back 任务训练提高流体智力的实验被再次实施<ref name="JaeggiStuder-Luethi2010">{{cite journal| last1=Jaeggi| first1=Susanne M.| last2=Studer-Luethi| first2=Barbara| last3=Buschkuehl|first3=Martin| last4=Su|first4=Yi-Fen|last5=Jonides|first5=John|last6=Perrig|first6=Walter J.|title=The relationship between n-back performance and matrix reasoning – implications for training and transfer|journal=Intelligence|volume=38|issue=6|year=2010|pages=625–635|issn=0160-2896|doi=10.1016/j.intell.2010.09.001}}</ref>,但2012年发表的两项研究未能重现那一结果<ref name="RedickShipstead2013">{{cite journal|last1=Redick|first1=Thomas S.| last2=Shipstead| first2=Zach|last3=Harrison|first3=Tyler L.|last4=Hicks|first4=Kenny L.|last5=Fried|first5=David E.|last6=Hambrick|first6=David Z.|last7=Kane|first7=Michael J.|last8=Engle|first8=Randall W.|title=No evidence of intelligence improvement after working memory training: A randomized, placebo-controlled study|journal=Journal of Experimental Psychology: General|volume=142| issue=2|year=2013| pages=359–379| pmid=22708717|issn=1939-2222| doi=10.1037/a0029082}}</ref><ref name="ChooiThompson2012">{{cite journal| last1=Chooi| first1=Weng-Tink| last2=Thompson| first2=Lee A.| title=Working memory training does not improve intelligence in healthy young adults| journal=Intelligence| volume=40|issue=6| year=2012| pages=531–542| issn=0160-2896| doi=10.1016/j.intell.2012.07.004}}</ref>。在运用元分析对约30个关于工作记忆训练有效性的研究进行评估之后<ref>{{Cite journal|last1=Au|first1=Jacky|last2=Sheehan|first2=Ellen|last3=Tsai|first3=Nancy|last4=Duncan|first4=Greg J.|last5=Buschkuehl|first5=Martin|last6=Jaeggi|first6=Susanne M.|date=2014-08-08|title=Improving fluid intelligence with training on working memory: a meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=22|issue=2|pages=366–377|doi=10.3758/s13423-014-0699-x|pmid=25102926|issn=1069-9384|url=http://www.escholarship.org/uc/item/1mj701dj|type=Submitted manuscript}}</ref><ref>{{Cite journal|last1=Melby-Lervåg|first1=Monica|last2=Redick|first2=Thomas S.|last3=Hulme|first3=Charles|date=2016-07-29|title=Working Memory Training Does Not Improve Performance on Measures of Intelligence or Other Measures of "Far Transfer"|journal=Perspectives on Psychological Science|language=en|volume=11|issue=4|pages=512–534|doi=10.1177/1745691616635612|pmc=4968033|pmid=27474138}}</ref>,分析者并不认为训练可以提高智力。不过,这些元分析在某点上达成了一致: 训练大概率只会有很微弱的影响。<br />
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== 脑内 In the brain ==<br />
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=== 信息维持的神经机制 Neural mechanisms of maintaining information ===<br />
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The first insights into the neuronal and neurotransmitter basis of working memory came from animal research. The work of Jacobsen<ref>{{Cite journal|author=Jacobsen CF|title= Studies of cerebral function in primates |journal=Comparative Psychology Monographs |volume=13 |issue=3 |pages=1–68 |year=1938 |oclc=250695441 }}</ref> and Fulton in the 1930s first showed that lesions to the PFC impaired spatial working memory performance in monkeys. The later work of [[Joaquin Fuster]]<ref>{{Cite journal|author=Fuster JM |title=Unit activity in prefrontal cortex during delayed-response performance: neuronal correlates of transient memory |journal=Journal of Neurophysiology |volume=36 |issue=1 |pages=61–78 |date=January 1973 |pmid=4196203 |doi=10.1152/jn.1973.36.1.61 }}</ref> recorded the electrical activity of neurons in the PFC of monkeys while they were doing a delayed matching task. In that task, the monkey sees how the experimenter places a bit of food under one of two identical-looking cups. A shutter is then lowered for a variable delay period, screening off the cups from the monkey's view. After the delay, the shutter opens and the monkey is allowed to retrieve the food from under the cups. Successful retrieval in the first attempt – something the animal can achieve after some training on the task – requires holding the location of the food in memory over the delay period. Fuster found neurons in the PFC that fired mostly during the delay period, suggesting that they were involved in representing the food location while it was invisible. Later research has shown similar delay-active neurons also in the posterior [[parietal cortex]], the [[thalamus]], the [[Caudate nucleus|caudate]], and the [[globus pallidus]].<ref>{{Cite journal|vauthors=Ashby FG, Ell SW, Valentin VV, Casale MB |title=FROST: a distributed neurocomputational model of working memory maintenance |journal=Journal of Cognitive Neuroscience |volume=17 |issue=11 |pages=1728–43 |date=November 2005 |pmid=16269109 |doi=10.1162/089892905774589271|citeseerx=10.1.1.456.7179 }}</ref> The work of [[Patricia Goldman-Rakic|Goldman-Rakic]] and others showed that principal sulcal, dorsolateral PFC interconnects with all of these brain regions, and that neuronal microcircuits within PFC are able to maintain information in working memory through recurrent excitatory glutamate networks of pyramidal cells that continue to fire throughout the delay period.<ref>{{Cite journal|author=Goldman-Rakic PS|title= Cellular basis of working memory |journal=Neuron |volume=14 |issue= 3 |pages=447–485 |year=1995 | pmid = 7695894 | doi = 10.1016/0896-6273(95)90304-6 }}</ref> These circuits are tuned by lateral inhibition from GABAergic interneurons.<ref>{{Cite journal|vauthors=Rao SG, Williams GV, Goldman-Rakic PS |title= Destruction and creation of spatial tuning by disinhibition: GABA(A) blockade of prefrontal cortical neurons engaged by working memory |journal=Journal of Neuroscience |volume=20 |pages=485–494 |year=2000|pmid=10627624 |pmc= 6774140 |issue=1|doi= 10.1523/JNEUROSCI.20-01-00485.2000 }}</ref> The neuromodulatory arousal systems markedly alter PFC working memory function; for example, either too little or too much dopamine or norepinephrine impairs PFC network firing<ref>{{Cite journal|doi=10.1016/j.tics.2010.05.003|author1=Arnsten AFT |author2=Paspalas CD |author3=Gamo NJ |author4=Y. Y |author5=Wang M |title= Dynamic Network Connectivity: A new form of neuroplasticity|journal=Trends in Cognitive Sciences|volume=14 |pages=365–375 |year=2010|issue=8|pmid=20554470|pmc=2914830}}</ref> and working memory performance.<ref>{{Cite journal|doi=10.1146/annurev.neuro.051508.135535|vauthors=Robbins TW, Arnsten AF |title= The neuropsychopharmacology of fronto-executive function: monoaminergic modulation |journal=Annu Rev Neurosci|volume=32 |pages=267–287 |year=2009|pmid=19555290|pmc=2863127}}</ref><br />
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The first insights into the neuronal and neurotransmitter basis of working memory came from animal research. The work of Jacobsen and Fulton in the 1930s first showed that lesions to the PFC impaired spatial working memory performance in monkeys. The later work of Joaquin Fuster recorded the electrical activity of neurons in the PFC of monkeys while they were doing a delayed matching task. In that task, the monkey sees how the experimenter places a bit of food under one of two identical-looking cups. A shutter is then lowered for a variable delay period, screening off the cups from the monkey's view. After the delay, the shutter opens and the monkey is allowed to retrieve the food from under the cups. Successful retrieval in the first attempt – something the animal can achieve after some training on the task – requires holding the location of the food in memory over the delay period. Fuster found neurons in the PFC that fired mostly during the delay period, suggesting that they were involved in representing the food location while it was invisible. Later research has shown similar delay-active neurons also in the posterior parietal cortex, the thalamus, the caudate, and the globus pallidus. The work of Goldman-Rakic and others showed that principal sulcal, dorsolateral PFC interconnects with all of these brain regions, and that neuronal microcircuits within PFC are able to maintain information in working memory through recurrent excitatory glutamate networks of pyramidal cells that continue to fire throughout the delay period. These circuits are tuned by lateral inhibition from GABAergic interneurons. The neuromodulatory arousal systems markedly alter PFC working memory function; for example, either too little or too much dopamine or norepinephrine impairs PFC network firing and working memory performance.<br />
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最初,关于工作记忆神经元和神经递质基础的见解来自于对动物的研究。20世纪30年代,雅各布森 Jacobsen <ref>{{Cite journal|author=Jacobsen CF|title= Studies of cerebral function in primates |journal=Comparative Psychology Monographs |volume=13 |issue=3 |pages=1–68 |year=1938 |oclc=250695441 }}</ref>和富尔顿 Fulton在研究中首次证明了猴子的空间工作记忆能力会因PFC而减损。华金 · 福斯特 Joaquin Fuster <ref>{{Cite journal|author=Fuster JM |title=Unit activity in prefrontal cortex during delayed-response performance: neuronal correlates of transient memory |journal=Journal of Neurophysiology |volume=36 |issue=1 |pages=61–78 |date=January 1973 |pmid=4196203 |doi=10.1152/jn.1973.36.1.61 }}</ref>的后续工作记录了猴子在完成延迟匹配任务时 PFC 中神经元的电活动。在该任务中有两个相同的杯子,猴子看到实验人员把一点食物放在其中一个下面。然后一个挡板降下,暂时挡住猴子看向杯子的视线(延迟变量)。之后挡板打开,允许猴子从杯子下面取出食物。在第一次尝试中它成功地得到了食物——这是动物经过特定训练后应该能够完成的任务——要求动物在延迟期内维持对食物位置的记忆。Fuster发现在延迟期间,PFC中的大部分神经元被激活了,表明它们参与了在隔离期间对食物位置的记忆维持。后来的研究发现后'''<font color="#ff8000">顶叶皮层posterior parietal cortex</font>'''、'''<font color="#ff8000">丘脑thalamus</font>'''、'''<font color="#ff8000">尾状核caudate</font>'''和'''<font color="#ff8000">苍白球globus pallidus</font>'''也有类似的延迟活动神经元。<ref>{{Cite journal|vauthors=Ashby FG, Ell SW, Valentin VV, Casale MB |title=FROST: a distributed neurocomputational model of working memory maintenance |journal=Journal of Cognitive Neuroscience |volume=17 |issue=11 |pages=1728–43 |date=November 2005 |pmid=16269109 |doi=10.1162/089892905774589271|citeseerx=10.1.1.456.7179 }}</ref>高德马・拉齐克 Goldman-Rakic 等人的研究表明,脊髓背外侧的PFC与这些大脑区域相互连接,PFC内的神经元微回路凭借反复兴奋的锥体细胞谷氨酸网络来维持工作记忆中的信息——这些神经元网络在延迟期间是持续激活的<ref>{{Cite journal|author=Goldman-Rakic PS|title= Cellular basis of working memory |journal=Neuron |volume=14 |issue= 3 |pages=447–485 |year=1995 | pmid = 7695894 | doi = 10.1016/0896-6273(95)90304-6 }}</ref>。这些回路由GABA能中间神经元的侧抑制调节<ref>{{Cite journal|vauthors=Rao SG, Williams GV, Goldman-Rakic PS |title= Destruction and creation of spatial tuning by disinhibition: GABA(A) blockade of prefrontal cortical neurons engaged by working memory |journal=Journal of Neuroscience |volume=20 |pages=485–494 |year=2000|pmid=10627624 |pmc= 6774140 |issue=1|doi= 10.1523/JNEUROSCI.20-01-00485.2000 }}</ref>。神经调节性唤起系统对PFC工作记忆功能产生了显著影响; 例如,过多或过少的多巴胺或去甲肾上腺素会减损PFC神经网络放电功能<ref>{{Cite journal|doi=10.1016/j.tics.2010.05.003|author1=Arnsten AFT |author2=Paspalas CD |author3=Gamo NJ |author4=Y. Y |author5=Wang M |title= Dynamic Network Connectivity: A new form of neuroplasticity|journal=Trends in Cognitive Sciences|volume=14 |pages=365–375 |year=2010|issue=8|pmid=20554470|pmc=2914830}}</ref>和工作记忆表现<ref>{{Cite journal|doi=10.1146/annurev.neuro.051508.135535|vauthors=Robbins TW, Arnsten AF |title= The neuropsychopharmacology of fronto-executive function: monoaminergic modulation |journal=Annu Rev Neurosci|volume=32 |pages=267–287 |year=2009|pmid=19555290|pmc=2863127}}</ref>。<br />
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The research described above on persistent firing of certain neurons in the delay period of working memory tasks shows that the brain has a mechanism of keeping representations active without external input. Keeping representations active, however, is not enough if the task demands maintaining more than one chunk of information. In addition, the components and features of each chunk must be bound together to prevent them from being mixed up. For example, if a red triangle and a green square must be remembered at the same time, one must make sure that "red" is bound to "triangle" and "green" is bound to "square". One way of establishing such bindings is by having the neurons that represent features of the same chunk fire in synchrony, and those that represent features belonging to different chunks fire out of sync.<ref>{{Cite journal|date=August 2001|title=A cortical mechanism for binding in visual working memory|journal=Journal of Cognitive Neuroscience|volume=13|issue=6|pages=766–85|doi=10.1162/08989290152541430|pmid=11564321|vauthors=Raffone A, Wolters G}}</ref> In the example, neurons representing redness would fire in synchrony with neurons representing the triangular shape, but out of sync with those representing the square shape. So far, there is no direct evidence that working memory uses this binding mechanism, and other mechanisms have been proposed as well.<ref>{{Cite book|title=The unity of consciousness: Binding, integration, and dissociation|last2=Busby|first2=Richard S.|last3=Soto|first3=Rodolfo|publisher=Oxford University Press|year=2003|isbn=978-0-19-850857-1|location=Oxford|pages=168–90|chapter=Three forms of binding and their neural substrates: Alternatives to temporal synchrony|oclc=50747505|first1=Randall C.|last1=O'Reilly|editor1-first=Axel|editor1-last=Cleeremans|chapterurl=http://psycnet.apa.org/psycinfo/2003-88180-008}}</ref> It has been speculated that synchronous firing of neurons involved in working memory oscillate with frequencies in the [[theta rhythm|theta]] band (4 to 8&nbsp;Hz). Indeed, the power of theta frequency in the EEG increases with working memory load,<ref>{{Cite book|title=Handbook of binding and memory|publisher=Oxford University Press|year=2006|location=Oxford|pages=115–144|chapter=Binding principles in the theta frequency range|last1=Klimesch|first1=W.|editor1-first=H. D.|editor1-last=Zimmer|editor2-first=A.|editor2-last=Mecklinger|editor3-first=U.|editor3-last=Lindenberger}}</ref> and oscillations in the theta band measured over different parts of the skull become more coordinated when the person tries to remember the binding between two components of information.<ref>{{Cite journal|date=May 2007|title=Binding of verbal and spatial information in human working memory involves large-scale neural synchronization at theta frequency|journal=NeuroImage|volume=35|issue=4|pages=1654–62|doi=10.1016/j.neuroimage.2007.02.011|pmid=17379539|vauthors=Wu X, Chen X, Li Z, Han S, Zhang D}}</ref><br />
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The research described above on persistent firing of certain neurons in the delay period of working memory tasks shows that the brain has a mechanism of keeping representations active without external input. Keeping representations active, however, is not enough if the task demands maintaining more than one chunk of information. In addition, the components and features of each chunk must be bound together to prevent them from being mixed up. For example, if a red triangle and a green square must be remembered at the same time, one must make sure that "red" is bound to "triangle" and "green" is bound to "square". One way of establishing such bindings is by having the neurons that represent features of the same chunk fire in synchrony, and those that represent features belonging to different chunks fire out of sync. In the example, neurons representing redness would fire in synchrony with neurons representing the triangular shape, but out of sync with those representing the square shape. So far, there is no direct evidence that working memory uses this binding mechanism, and other mechanisms have been proposed as well. It has been speculated that synchronous firing of neurons involved in working memory oscillate with frequencies in the theta band (4 to 8&nbsp;Hz). Indeed, the power of theta frequency in the EEG increases with working memory load, and oscillations in the theta band measured over different parts of the skull become more coordinated when the person tries to remember the binding between two components of information.<br />
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上述关于工作记忆任务延迟期间某些神经元持续放电的研究表明,大脑有一种机制能使在无外部输入的情况下表征依旧保持活跃。但这不足以应对维护多个信息块的任务。此外,每个组块的组件和特性必须绑定在一起,以防止混淆。例如,如果必须同时记住一个红色三角形和一个绿色正方形,就必须确保“红色”与“三角形”绑定,而“绿色”与“正方形”绑定。实现该目标的一种方法是让表现同一组块特征的神经元同步激活,那些表现不同组块特征的神经元则不同步激活<ref>{{Cite journal|date=August 2001|title=A cortical mechanism for binding in visual working memory|journal=Journal of Cognitive Neuroscience|volume=13|issue=6|pages=766–85|doi=10.1162/08989290152541430|pmid=11564321|vauthors=Raffone A, Wolters G}}</ref>。在这个例子中,代表红色的神经元会与代表三角形的神经元同步激活,与代表正方形的神经元不同步激活。不过目前还没有直接的证据表明工作记忆使用这种结合机制,因此学界也提出了其他一些观点<ref>{{Cite book|title=The unity of consciousness: Binding, integration, and dissociation|last2=Busby|first2=Richard S.|last3=Soto|first3=Rodolfo|publisher=Oxford University Press|year=2003|isbn=978-0-19-850857-1|location=Oxford|pages=168–90|chapter=Three forms of binding and their neural substrates: Alternatives to temporal synchrony|oclc=50747505|first1=Randall C.|last1=O'Reilly|editor1-first=Axel|editor1-last=Cleeremans|chapterurl=http://psycnet.apa.org/psycinfo/2003-88180-008}}</ref>。据推测,工作记忆相关神经元的同步激活是在'''<font color="#ff8000">θ波段 theta band</font>''' (4ー8赫兹)振荡。脑电图θ频率的能量确实随工作记忆负荷的增加而增加<ref>{{Cite book|title=Handbook of binding and memory|publisher=Oxford University Press|year=2006|location=Oxford|pages=115–144|chapter=Binding principles in the theta frequency range|last1=Klimesch|first1=W.|editor1-first=H. D.|editor1-last=Zimmer|editor2-first=A.|editor2-last=Mecklinger|editor3-first=U.|editor3-last=Lindenberger}}</ref>,当受试者试图记住信息的两个组成部分之间的联系时,在头骨不同部位测量到的 θ 波段的振荡变得更加协调<ref>{{Cite journal|date=May 2007|title=Binding of verbal and spatial information in human working memory involves large-scale neural synchronization at theta frequency|journal=NeuroImage|volume=35|issue=4|pages=1654–62|doi=10.1016/j.neuroimage.2007.02.011|pmid=17379539|vauthors=Wu X, Chen X, Li Z, Han S, Zhang D}}</ref>。<br />
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=== 脑内定位 Localization in the brain ===<br />
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Localization of brain functions in humans has become much easier with the advent of [[brain imaging]] methods ([[Positron emission tomography|PET]] and [[fMRI]]). This research has confirmed that areas in the PFC are involved in working memory functions. During the 1990s much debate has centered on the different functions of the ventrolateral (i.e.,&nbsp;lower areas) and the [[Dorsolateral prefrontal cortex|dorsolateral (higher) areas of the PFC]]. A human lesion study provides additional evidence for the role of the [[dorsolateral prefrontal cortex]] in working memory.<ref>{{cite journal|last2=Koenigs|first2=Michael|last3=Grafman|first3=Jordan|year=2013|title=Dorsolateral prefrontal contributions to human working memory|journal=Cortex|volume=49|issue=5|pages=1195–1205|doi=10.1016/j.cortex.2012.05.022|pmid=22789779|last1=Barbey|first1=Aron K.|pmc=3495093}}</ref> One view was that the dorsolateral areas are responsible for spatial working memory and the ventrolateral areas for non-spatial working memory. Another view proposed a functional distinction, arguing that ventrolateral areas are mostly involved in pure maintenance of information, whereas dorsolateral areas are more involved in tasks requiring some processing of the memorized material. The debate is not entirely resolved but most of the evidence supports the functional distinction.<ref>{{Cite journal|author=Owen, A. M.|title=The functional organization of working memory processes within human lateral frontal cortex: the contribution of functional neuroimaging |journal=The European Journal of Neuroscience |volume=9 |issue=7 |pages=1329–39 |date=July 1997 |pmid=9240390 |doi=10.1111/j.1460-9568.1997.tb01487.x}}</ref><br />
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Localization of brain functions in humans has become much easier with the advent of brain imaging methods (PET and fMRI). This research has confirmed that areas in the PFC are involved in working memory functions. During the 1990s much debate has centered on the different functions of the ventrolateral (i.e.,&nbsp;lower areas) and the dorsolateral (higher) areas of the PFC. A human lesion study provides additional evidence for the role of the dorsolateral prefrontal cortex in working memory. One view was that the dorsolateral areas are responsible for spatial working memory and the ventrolateral areas for non-spatial working memory. Another view proposed a functional distinction, arguing that ventrolateral areas are mostly involved in pure maintenance of information, whereas dorsolateral areas are more involved in tasks requiring some processing of the memorized material. The debate is not entirely resolved but most of the evidence supports the functional distinction.<br />
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'''<font color="#ff8000">脑成像brain imaging</font>'''方法(PET和fMRI)的出现让人脑功能定位更加容易。一项研究证实PFC中的一些区域确实影响了工作记忆功能。在20世纪90年代,讨论大多集中在腹外侧区(即较低区域)和背外侧区(较高区域)的不同功能上。一项关于人体损伤的研究为背外侧脑前额叶外皮在工作记忆中发挥作用提供了额外的证据<ref>{{cite journal|last2=Koenigs|first2=Michael|last3=Grafman|first3=Jordan|year=2013|title=Dorsolateral prefrontal contributions to human working memory|journal=Cortex|volume=49|issue=5|pages=1195–1205|doi=10.1016/j.cortex.2012.05.022|pmid=22789779|last1=Barbey|first1=Aron K.|pmc=3495093}}</ref>。一种观点认为,背外侧区负责空间工作记忆,腹外侧区负责非空间工作记忆。另一种观点则是'''<font color="#ff8000">功能区分说functional distinction</font>''',认为腹外侧区域主要负责纯粹的信息维护,而背外侧区域则更倾向于负责记忆材料的处理。虽然分歧并没有彻底解决,但功能区分说还是得到了大多数证据的支持<ref>{{Cite journal|author=Owen, A. M.|title=The functional organization of working memory processes within human lateral frontal cortex: the contribution of functional neuroimaging |journal=The European Journal of Neuroscience |volume=9 |issue=7 |pages=1329–39 |date=July 1997 |pmid=9240390 |doi=10.1111/j.1460-9568.1997.tb01487.x}}</ref>。<br />
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Brain imaging has revealed that working memory functions are not limited to the PFC. A review of numerous studies<ref>{{Cite journal|vauthors=Smith EE, Jonides J |title=Storage and executive processes in the frontal lobes |journal=Science |volume=283 |issue=5408 |pages=1657–61 |date=March 1999 |pmid=10073923 |doi=10.1126/science.283.5408.1657|citeseerx=10.1.1.207.8961 }}</ref> shows areas of activation during working memory tasks scattered over a large part of the cortex. There is a tendency for spatial tasks to recruit more right-hemisphere areas, and for verbal and object working memory to recruit more left-hemisphere areas. The activation during verbal working memory tasks can be broken down into one component reflecting maintenance, in the left posterior parietal cortex, and a component reflecting subvocal rehearsal, in the left frontal cortex (Broca's area, known to be involved in speech production).<ref>{{Cite journal|author=Smith, E. E.|author2=Jonides, J.|author3=Marshuetz, C.|author4=Koeppe, R. A.|title=Components of verbal working memory: evidence from neuroimaging |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=95 |issue=3 |pages=876–82 |date=February 1998 |pmid=9448254 |pmc=33811 |doi=10.1073/pnas.95.3.876|bibcode=1998PNAS...95..876S }}</ref><br />
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Brain imaging has revealed that working memory functions are not limited to the PFC. A review of numerous studies shows areas of activation during working memory tasks scattered over a large part of the cortex. There is a tendency for spatial tasks to recruit more right-hemisphere areas, and for verbal and object working memory to recruit more left-hemisphere areas. The activation during verbal working memory tasks can be broken down into one component reflecting maintenance, in the left posterior parietal cortex, and a component reflecting subvocal rehearsal, in the left frontal cortex (Broca's area, known to be involved in speech production).<br />
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脑成像已经证明工作记忆功能并不局限于PFC。大量研究表明<ref>{{Cite journal|vauthors=Smith EE, Jonides J |title=Storage and executive processes in the frontal lobes |journal=Science |volume=283 |issue=5408 |pages=1657–61 |date=March 1999 |pmid=10073923 |doi=10.1126/science.283.5408.1657|citeseerx=10.1.1.207.8961 }}</ref>,工作记忆任务中的激活区域广泛分布于大脑皮层。其中,空间任务倾向于使用右半球区域,言语和物体工作记忆倾向于使用左半球区域。非文字工作记忆任务中的激活可以分解为在左后顶叶皮层反映维持的组件,以及在左额叶皮层的反映次声练习的组件(已知与语言产生有关的Broca区域)<ref>{{Cite journal|author=Smith, E. E.|author2=Jonides, J.|author3=Marshuetz, C.|author4=Koeppe, R. A.|title=Components of verbal working memory: evidence from neuroimaging |journal=Proceedings of the National Academy of Sciences of the United States of America |volume=95 |issue=3 |pages=876–82 |date=February 1998 |pmid=9448254 |pmc=33811 |doi=10.1073/pnas.95.3.876|bibcode=1998PNAS...95..876S }}</ref><br />
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There is an emerging consensus that most working memory tasks recruit a network of PFC and parietal areas. A study has shown that during a working memory task the connectivity between these areas increases.<ref>{{Cite journal|author=Honey, G. D.|author2=Fu, C. H.|author3=Kim, J.|title=Effects of verbal working memory load on corticocortical connectivity modeled by path analysis of functional magnetic resonance imaging data |journal=NeuroImage |volume=17 |issue=2 |pages=573–82 |date=October 2002 |pmid=12377135 |doi=10.1016/S1053-8119(02)91193-6|display-authors=etal}}</ref> Another study has demonstrated that these areas are necessary for working memory, and not simply activated accidentally during working memory tasks, by temporarily blocking them through [[transcranial magnetic stimulation]] (TMS), thereby producing an impairment in task performance.<ref>{{Cite journal|author=Mottaghy, F. M.|title=Interfering with working memory in humans |journal=Neuroscience |volume=139 |issue=1 |pages=85–90 |date=April 2006 |pmid=16337091 |doi=10.1016/j.neuroscience.2005.05.037}}</ref><br />
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There is an emerging consensus that most working memory tasks recruit a network of PFC and parietal areas. A study has shown that during a working memory task the connectivity between these areas increases. Another study has demonstrated that these areas are necessary for working memory, and not simply activated accidentally during working memory tasks, by temporarily blocking them through transcranial magnetic stimulation (TMS), thereby producing an impairment in task performance.<br />
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人们逐渐达成共识,认为大多数工作记忆任务使用的是PFC顶叶区域组成的网络。一项研究表明,这些区域之间的连通性在工作记忆任务的执行过程中有所增加<ref>{{Cite journal|author=Honey, G. D.|author2=Fu, C. H.|author3=Kim, J.|title=Effects of verbal working memory load on corticocortical connectivity modeled by path analysis of functional magnetic resonance imaging data |journal=NeuroImage |volume=17 |issue=2 |pages=573–82 |date=October 2002 |pmid=12377135 |doi=10.1016/S1053-8119(02)91193-6|display-authors=etal}}</ref>。另一项研究表明,这些区域是工作记忆所必备的,并非是被意外激活的。通过经颅磁刺激(TMS)暂时阻止它们,从而导致任务性能受损<ref>{{Cite journal|author=Mottaghy, F. M.|title=Interfering with working memory in humans |journal=Neuroscience |volume=139 |issue=1 |pages=85–90 |date=April 2006 |pmid=16337091 |doi=10.1016/j.neuroscience.2005.05.037}}</ref>。<br />
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A current debate concerns the function of these brain areas. The PFC has been found to be active in a variety of tasks that require executive functions.<ref name="Kane MJ, Engle RW 2002 637–71" /> This has led some researchers to argue that the role of PFC in working memory is in controlling attention, selecting strategies, and manipulating information in working memory, but not in maintenance of information. The maintenance function is attributed to more posterior areas of the brain, including the parietal cortex.<ref>{{Cite journal|author=Curtis, C. E.|author2=D'Esposito, M.|title=Persistent activity in the prefrontal cortex during working memory |journal=Trends in Cognitive Sciences |volume=7 |issue=9 |pages=415–423 |date=September 2003 |pmid=12963473 |doi=10.1016/S1364-6613(03)00197-9|citeseerx=10.1.1.319.8928}}</ref><ref name="Postle">{{Cite journal|author=Postle BR |title=Working memory as an emergent property of the mind and brain |journal=Neuroscience |volume=139 |issue=1 |pages=23–38 |date=April 2006 |pmid=16324795 |pmc=1428794 |doi=10.1016/j.neuroscience.2005.06.005}}</ref> Other authors interpret the activity in parietal cortex as reflecting [[executive functions]], because the same area is also activated in other tasks requiring attention but not memory.<ref>{{Cite journal|author=Collette, F.|author2= Hogge, M.|author3= Salmon, E.|author4=Van der Linden, M.|title=Exploration of the neural substrates of executive functioning by functional neuroimaging |journal=Neuroscience |volume=139 |issue=1 |pages=209–21 |date=April 2006 |pmid=16324796 |doi=10.1016/j.neuroscience.2005.05.035|hdl= 2268/5937|hdl-access=free }}</ref><br />
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A current debate concerns the function of these brain areas. The PFC has been found to be active in a variety of tasks that require executive functions. Other authors interpret the activity in parietal cortex as reflecting executive functions, because the same area is also activated in other tasks requiring attention but not memory.<br />
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目前的争论集中于大脑各个区域功能的研究。研究发现,在许多需要执行功能的任务中,PFC都具有活性。<ref name="Kane MJ, Engle RW 2002 637–71" />这使得一些研究人员认为,PFC在工作记忆中的作用是控制注意力,选择策略以及操纵信息,而非信息维护。信息维护功能更多的由大脑后部区域负责——包括顶叶皮层<ref>{{Cite journal|author=Curtis, C. E.|author2=D'Esposito, M.|title=Persistent activity in the prefrontal cortex during working memory |journal=Trends in Cognitive Sciences |volume=7 |issue=9 |pages=415–423 |date=September 2003 |pmid=12963473 |doi=10.1016/S1364-6613(03)00197-9|citeseerx=10.1.1.319.8928}}</ref><ref name="Postle">{{Cite journal|author=Postle BR |title=Working memory as an emergent property of the mind and brain |journal=Neuroscience |volume=139 |issue=1 |pages=23–38 |date=April 2006 |pmid=16324795 |pmc=1428794 |doi=10.1016/j.neuroscience.2005.06.005}}</ref>。其他研究者把顶叶皮层的活动理解为对执行功能的反映,因为在其他需要注意力而不是记忆的任务中该区域同样被激活<ref>{{Cite journal|author=Collette, F.|author2= Hogge, M.|author3= Salmon, E.|author4=Van der Linden, M.|title=Exploration of the neural substrates of executive functioning by functional neuroimaging |journal=Neuroscience |volume=139 |issue=1 |pages=209–21 |date=April 2006 |pmid=16324796 |doi=10.1016/j.neuroscience.2005.05.035|hdl= 2268/5937|hdl-access=free }}</ref><br />
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A 2003 meta-analysis of 60 neuroimaging studies found left [[Frontal lobe|frontal]] cortex was involved in low-task demand verbal working memory and right [[Frontal lobe|frontal]] cortex for spatial working memory. Brodmann's areas (BAs) [[Brodmann area 6|6]], [[Brodmann area 8|8]], and [[Brodmann area 9|9]], in the [[Superior frontal gyrus|superior frontal cortex]] was involved when working memory must be continuously updated and when memory for temporal order had to be maintained. Right Brodmann [[Brodmann area 10|10]] and [[Brodmann area 47|47]] in the ventral frontal cortex were involved more frequently with demand for manipulation such as dual-task requirements or mental operations, and Brodmann 7 in the [[posterior parietal cortex]] was also involved in all types of executive function.<ref>{{Cite journal|title = Neuroimaging studies of working memory: a meta-analysis|journal = Cognitive, Affective & Behavioral Neuroscience|date = 2003-12-01|issn = 1530-7026|pmid = 15040547|pages = 255–274|volume = 3|issue = 4|first1 = Tor D.|last1 = Wager|first2 = Edward E.|last2 = Smith|doi=10.3758/cabn.3.4.255|doi-access = free}}</ref><br />
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A 2003 meta-analysis of 60 neuroimaging studies found left frontal cortex was involved in low-task demand verbal working memory and right frontal cortex for spatial working memory. Brodmann's areas (BAs) 6, 8, and 9, in the superior frontal cortex was involved when working memory must be continuously updated and when memory for temporal order had to be maintained. Right Brodmann 10 and 47 in the ventral frontal cortex were involved more frequently with demand for manipulation such as dual-task requirements or mental operations, and Brodmann 7 in the posterior parietal cortex was also involved in all types of executive function.<br />
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在2003年,一份对60项神经成像研究结果的元分析发现,左额叶皮层参与低任务需求的语言工作记忆,而右额叶皮层参与空间工作记忆。罗德曼大脑上额叶皮层区域(BAs)的6、8、9号参与需要不断更新的以及需要维持特定顺序的工作记忆。腹侧额叶皮层的右布罗德曼10和47号区域较频繁地参与需要双重任务或心理操作的工作记忆,其中后顶叶皮层的罗德曼7号区域参与了全部的执行功能<ref>{{Cite journal|title = Neuroimaging studies of working memory: a meta-analysis|journal = Cognitive, Affective & Behavioral Neuroscience|date = 2003-12-01|issn = 1530-7026|pmid = 15040547|pages = 255–274|volume = 3|issue = 4|first1 = Tor D.|last1 = Wager|first2 = Edward E.|last2 = Smith|doi=10.3758/cabn.3.4.255|doi-access = free}}</ref>。<br />
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Working memory has been suggested to involve two processes with different neuroanatomical locations in the frontal and parietal lobes.<ref name="Bledowski">{{Cite journal|author=Bledowski, C.|author2=Rahm, B.|author3=Rowe, J. B. |title=What 'works' in working memory? Separate systems for selection and updating of critical information |journal=The Journal of Neuroscience |volume=29 |issue=43 |pages=13735–41 |date=October 2009 |pmid=19864586 |doi=10.1523/JNEUROSCI.2547-09.2009 |pmc=2785708}}</ref> First, a selection operation that retrieves the most relevant item, and second an updating operation that changes the focus of attention made upon it. Updating the attentional focus has been found to involve the transient activation in the caudal [[superior frontal sulcus]] and [[posterior parietal cortex]], while increasing demands on selection selectively changes activation in the rostral superior frontal sulcus and posterior cingulate/[[precuneus]].<ref name="Bledowski" /><br />
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Working memory has been suggested to involve two processes with different neuroanatomical locations in the frontal and parietal lobes. First, a selection operation that retrieves the most relevant item, and second an updating operation that changes the focus of attention made upon it. Updating the attentional focus has been found to involve the transient activation in the caudal superior frontal sulcus and posterior parietal cortex, while increasing demands on selection selectively changes activation in the rostral superior frontal sulcus and posterior cingulate/precuneus.<br />
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我们一般认为,工作记忆包括两种过程——两类过程发生于额叶和顶叶两个不同位置<ref name="Bledowski">{{Cite journal|author=Bledowski, C.|author2=Rahm, B.|author3=Rowe, J. B. |title=What 'works' in working memory? Separate systems for selection and updating of critical information |journal=The Journal of Neuroscience |volume=29 |issue=43 |pages=13735–41 |date=October 2009 |pmid=19864586 |doi=10.1523/JNEUROSCI.2547-09.2009 |pmc=2785708}}</ref>。首先是检索最相关项的选择操作,其次是更改关注焦点的更新操作。更新操作包括'''<font color="#ff8000">额上沟superior frontal sulcus</font>'''尾部和'''<font color="#ff8000">后顶叶皮质posterior parietal cortex</font>'''的短暂激活,选择操作随选择的需求增加而选择性地发生额上沟和后扣带回/楔前叶激活<ref name="Bledowski" />。<br />
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Articulating the differential function of brain regions involved in working memory is dependent on tasks able to distinguish these functions.<ref name="Coltheart-2006">{{Cite journal | last1 = Coltheart | first1 = M. | title = What has functional neuroimaging told us about the mind (so far)? | journal = Cortex | volume = 42 | issue = 3 | pages = 323–31 |date=Apr 2006 | doi = 10.1016/S0010-9452(08)70358-7 | pmid = 16771037 }}</ref> Most brain imaging studies of working memory have used recognition tasks such as delayed recognition of one or several stimuli, or the n-back task, in which each new stimulus in a long series must be compared to the one presented n steps back in the series. The advantage of recognition tasks is that they require minimal movement (just pressing one of two keys), making fixation of the head in the scanner easier. Experimental research and research on individual differences in working memory, however, has used largely recall tasks (e.g.,&nbsp;the [[reading span task]], see below). It is not clear to what degree recognition and recall tasks reflect the same processes and the same capacity limitations.<br />
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Articulating the differential function of brain regions involved in working memory is dependent on tasks able to distinguish these functions. Most brain imaging studies of working memory have used recognition tasks such as delayed recognition of one or several stimuli, or the n-back task, in which each new stimulus in a long series must be compared to the one presented n steps back in the series. The advantage of recognition tasks is that they require minimal movement (just pressing one of two keys), making fixation of the head in the scanner easier. Experimental research and research on individual differences in working memory, however, has used largely recall tasks (e.g.,&nbsp;the reading span task, see below). It is not clear to what degree recognition and recall tasks reflect the same processes and the same capacity limitations.<br />
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要想阐明与工作记忆相关的大脑区域功能,首先需要区分这些功能的任务<ref name="Coltheart-2006">{{Cite journal | last1 = Coltheart | first1 = M. | title = What has functional neuroimaging told us about the mind (so far)? | journal = Cortex | volume = 42 | issue = 3 | pages = 323–31 |date=Apr 2006 | doi = 10.1016/S0010-9452(08)70358-7 | pmid = 16771037 }}</ref>。大多数关于工作记忆的脑成像研究都使用了识别任务,比如延迟识别一个或多个刺激,或 n-back 任务,即一个长系列中的每个新刺激都需与该系列中的一个n步后的刺激进行比较。识别任务的优势在于只需要最低限度的运动(只需二选一按键),这使头部扫描的定位更加容易。然而,关于工作记忆个体差异的实验研究大量使用的是回忆任务(例如阅读广度任务,见下文)。不过我们目前尚不清楚识别任务和回忆任务能在多大程度上反映相同过程和相同能力极限。<br />
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Brain imaging studies have been conducted with the reading span task or related tasks. Increased activation during these tasks was found in the PFC and, in several studies, also in the [[anterior cingulate cortex]] (ACC). People performing better on the task showed larger increase of activation in these areas, and their activation was correlated more over time, suggesting that their neural activity in these two areas was better coordinated, possibly due to stronger connectivity.<ref>{{Cite journal|author=Kondo, H.|author2=Osaka, N.|author3=Osaka, M.|title=Cooperation of the anterior cingulate cortex and dorsolateral prefrontal cortex for attention shifting |journal=NeuroImage |volume=23 |issue=2 |pages=670–9 |date=October 2004 |pmid=15488417 |doi=10.1016/j.neuroimage.2004.06.014}}</ref><ref>{{Cite journal|vauthors=Osaka N, Osaka M, Kondo H, Morishita M, Fukuyama H, Shibasaki H |title=The neural basis of executive function in working memory: an fMRI study based on individual differences |journal=NeuroImage |volume=21 |issue=2 |pages=623–31 |date=February 2004 |pmid=14980565 |doi=10.1016/j.neuroimage.2003.09.069}}</ref><br />
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Brain imaging studies have been conducted with the reading span task or related tasks. Increased activation during these tasks was found in the PFC and, in several studies, also in the anterior cingulate cortex (ACC). People performing better on the task showed larger increase of activation in these areas, and their activation was correlated more over time, suggesting that their neural activity in these two areas was better coordinated, possibly due to stronger connectivity.<br />
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脑成像研究已用于进行阅读广度任务或相关任务。任务过程中,PFC的活跃性增加,'''<font color="#ff8000">前扣带皮层anterior cingulate cortex </font>''' (ACC)的活性也有所增强。那些在任务中表现更好的人的这些区域活性显著提升,且随着时间的推移变得更强。这表明这两个区域的神经活动协调度更高——可能是因为区域间有更强的关联性<ref>{{Cite journal|author=Kondo, H.|author2=Osaka, N.|author3=Osaka, M.|title=Cooperation of the anterior cingulate cortex and dorsolateral prefrontal cortex for attention shifting |journal=NeuroImage |volume=23 |issue=2 |pages=670–9 |date=October 2004 |pmid=15488417 |doi=10.1016/j.neuroimage.2004.06.014}}</ref><ref>{{Cite journal|vauthors=Osaka N, Osaka M, Kondo H, Morishita M, Fukuyama H, Shibasaki H |title=The neural basis of executive function in working memory: an fMRI study based on individual differences |journal=NeuroImage |volume=21 |issue=2 |pages=623–31 |date=February 2004 |pmid=14980565 |doi=10.1016/j.neuroimage.2003.09.069}}</ref><br />
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=== 神经模型 Neural models ===<br />
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One approach to modeling the neurophysiology and the functioning of working memory is [[PBWM|prefrontal cortex basal ganglia working memory (PBWM)]]. In this model, the prefrontal cortex works hand-in-hand with the basal ganglia to accomplish the tasks of working memory. Many studies have shown this to be the case.<ref>{{Cite journal|last1=Baier|first1=B.|last2=Karnath|first2=H.-O.|last3=Dieterich|first3=M.|last4=Birklein|first4=F.|last5=Heinze|first5=C.|last6=Muller|first6=N. G.|date=2010-07-21|title=Keeping Memory Clear and Stable--The Contribution of Human Basal Ganglia and Prefrontal Cortex to Working Memory|journal=Journal of Neuroscience|volume=30|issue=29|pages=9788–9792|doi=10.1523/jneurosci.1513-10.2010|pmid=20660261|pmc=6632833|issn=0270-6474|doi-access=free}}</ref> One used ablation techniques in patients who had suffered from seizures and had damage to the prefrontal cortex and basal ganglia.<ref name=":2" /> Researchers found that such damage resulted in decreased capacity to carry out the executive function of working memory.<ref name=":2">{{Cite journal|last1=Voytek|first1=B.|last2=Knight|first2=R. T.|date=2010-10-04|title=Prefrontal cortex and basal ganglia contributions to visual working memory|journal=Proceedings of the National Academy of Sciences|volume=107|issue=42|pages=18167–18172|doi=10.1073/pnas.1007277107|pmid=20921401|issn=0027-8424|doi-access=free}}</ref> Additional research conducted on patients with brain alterations due to methamphetamine use found that training working memory increases volume in the basal ganglia.<ref>{{Cite journal|last1=Brooks|first1=S. J.|last2=Burch|first2=K. H.|last3=Maiorana|first3=S. A.|last4=Cocolas|first4=E.|last5=Schioth|first5=H. B.|last6=Nilsson|first6=E. K.|last7=Kamaloodien|first7=K.|last8=Stein|first8=D. J.|date=2016-02-01|title=Psychological intervention with working memory training increases basal ganglia volume: A VBM study of inpatient treatment for methamphetamine use|url=http://www.sciencedirect.com/science/article/pii/S2213158216301541|journal=NeuroImage: Clinical|language=en|volume=12|pages=478–491|doi=10.1016/j.nicl.2016.08.019|pmid=27625988|issn=2213-1582|doi-access=free}}</ref><br />
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One approach to modeling the neurophysiology and the functioning of working memory is prefrontal cortex basal ganglia working memory (PBWM). In this model, the prefrontal cortex works hand-in-hand with the basal ganglia to accomplish the tasks of working memory. Many studies have shown this to be the case. One used ablation techniques in patients who had suffered from seizures and had damage to the prefrontal cortex and basal ganglia. Researchers found that such damage resulted in decreased capacity to carry out the executive function of working memory .Additional research conducted on patients with brain alterations due to methamphetamine use found that training working memory increases volume in the basal ganglia.<br />
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'''<font color="#ff8000">前额叶皮质基底节工作记忆记忆模型 Prefrontal Cortex Basal Ganglia Working Memory (PBWM)</font>'''是模拟神经生理学和工作记忆功能模型的一种。<br />
在该模型中,脑前额叶外皮与基底神经节协力完成工作记忆任务,并得到许多研究证明支持<ref>{{Cite journal|last1=Baier|first1=B.|last2=Karnath|first2=H.-O.|last3=Dieterich|first3=M.|last4=Birklein|first4=F.|last5=Heinze|first5=C.|last6=Muller|first6=N. G.|date=2010-07-21|title=Keeping Memory Clear and Stable--The Contribution of Human Basal Ganglia and Prefrontal Cortex to Working Memory|journal=Journal of Neuroscience|volume=30|issue=29|pages=9788–9792|doi=10.1523/jneurosci.1513-10.2010|pmid=20660261|pmc=6632833|issn=0270-6474|doi-access=free}}</ref>,例如使用'''<font color="#ff8000">消融技术ablation techniques</font>'''治疗脑前额叶外皮和基底神经节受损、癫痫发作患者等。<ref name=":2" />研究人员发现,这种损害使得工作记忆的执行功能受损。<ref name=":2">{{Cite journal|last1=Voytek|first1=B.|last2=Knight|first2=R. T.|date=2010-10-04|title=Prefrontal cortex and basal ganglia contributions to visual working memory|journal=Proceedings of the National Academy of Sciences|volume=107|issue=42|pages=18167–18172|doi=10.1073/pnas.1007277107|pmid=20921401|issn=0027-8424|doi-access=free}}</ref>此外还有对因服用'''<font color="#ff8000">甲基苯丙胺 methamphetamine</font>'''而导致大脑改变的病人进行工作记忆训练后成功增加其基底神经节容量的案例<ref>{{Cite journal|last1=Brooks|first1=S. J.|last2=Burch|first2=K. H.|last3=Maiorana|first3=S. A.|last4=Cocolas|first4=E.|last5=Schioth|first5=H. B.|last6=Nilsson|first6=E. K.|last7=Kamaloodien|first7=K.|last8=Stein|first8=D. J.|date=2016-02-01|title=Psychological intervention with working memory training increases basal ganglia volume: A VBM study of inpatient treatment for methamphetamine use|url=http://www.sciencedirect.com/science/article/pii/S2213158216301541|journal=NeuroImage: Clinical|language=en|volume=12|pages=478–491|doi=10.1016/j.nicl.2016.08.019|pmid=27625988|issn=2213-1582|doi-access=free}}</ref>。<br />
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=== 神经生理学的压力效果 Effects of stress on neurophysiology ===<br />
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Working memory is impaired by acute and chronic psychological stress. This phenomenon was first discovered in animal studies by Arnsten and colleagues,<ref>{{Cite journal|doi=10.1126/science.280.5370.1711|author=Arnsten, A. F.|title=The biology of being frazzled |journal=Science |volume=280 |issue=5370 |pages=1711–2 |date=June 1998 |pmid=9660710}}</ref> who have shown that stress-induced [[catecholamine]] release in PFC rapidly decreases PFC neuronal firing and impairs working memory performance through feedforward, intracellular signaling pathways.<ref>{{Cite journal|author=Arnsten, AF |title=Stress signalling pathways that impair prefrontal cortex structure and function |journal=Nature Reviews Neuroscience |volume=10 |issue=6 |pages=410–22 |date=June 2009 |pmid=19455173|pmc=2907136 |doi=10.1038/nrn2648}}</ref> Exposure to chronic stress leads to more profound working memory deficits and additional architectural changes in PFC, including dendritic atrophy and spine loss,<ref>{{Cite journal|author=Radley, J. J.|author2= Rocher, A. B.|author3=Miller, M.|author4= Janssen, W. G.|author5=Liston, C.|author6=Hof, P. R.|author7=McEwen, B. S.|author8=Morrison, J. H.|title=Repeated stress induces dendritic spine loss in the rat medial prefrontal cortex |journal=Cereb Cortex |volume=16 |issue=3 |pages=313–20 |date=Mar 2006 |pmid=15901656 |doi=10.1093/cercor/bhi104|doi-access=free}}</ref> which can be prevented by inhibition of protein kinase C signaling.<ref>{{Cite journal|author=Hains, A. B.|author2=Vu, M. A.|author3=Maciejewski, P. K.|author4= van Dyck, C. H. |authorlink4=Christopher H. van Dyck |author5=Gottron, M.|author6= Arnsten, A. F. |title=Inhibition of protein kinase C signaling protects prefrontal cortex dendritic spines and cognition from the effects of chronic stress |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=42 |pages=17957–62 |date=Oct 2009 |pmid=19805148|pmc=2742406 |doi=10.1073/pnas.0908563106|bibcode=2009PNAS..10617957H }}</ref> [[fMRI]] research has extended this research to humans, and confirms that reduced working memory caused by acute stress links to reduced activation of the PFC, and stress increased levels of [[catecholamine]]s.<ref>{{Cite journal|vauthors=Qin S, Hermans EJ, van Marle HJ, Luo J, Fernández G |title=Acute psychological stress reduces working memory-related activity in the dorsolateral prefrontal cortex |journal=Biological Psychiatry |volume=66 |issue=1 |pages=25–32 |date=July 2009 |pmid=19403118 |doi=10.1016/j.biopsych.2009.03.006}}</ref> Imaging studies of medical students undergoing stressful exams have also shown weakened PFC functional connectivity, consistent with the animal studies.<ref>{{Cite journal|vauthors=Liston C, McEwen BS, Casey BJ |title=Psychosocial stress reversibly disrupts prefrontal processing and attentional control |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=3 |pages=912–7 |date=Jan 2009 |pmid=19139412|pmc=2621252 |doi=10.1073/pnas.0807041106|bibcode=2009PNAS..106..912L }}</ref> The marked effects of stress on PFC structure and function may help to explain how stress can cause or exacerbate mental illness.<br />
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Working memory is impaired by acute and chronic psychological stress. This phenomenon was first discovered in animal studies by Arnsten and colleagues, who have shown that stress-induced catecholamine release in PFC rapidly decreases PFC neuronal firing and impairs working memory performance through feedforward, intracellular signaling pathways. Exposure to chronic stress leads to more profound working memory deficits and additional architectural changes in PFC, including dendritic atrophy and spine loss, which can be prevented by inhibition of protein kinase C signaling. fMRI research has extended this research to humans, and confirms that reduced working memory caused by acute stress links to reduced activation of the PFC, and stress increased levels of catecholamines. Imaging studies of medical students undergoing stressful exams have also shown weakened PFC functional connectivity, consistent with the animal studies. The marked effects of stress on PFC structure and function may help to explain how stress can cause or exacerbate mental illness.<br />
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急性和慢性心理压力都会损害工作记忆。这最早由安斯登 Arnsten 和他的同事们<ref>{{Cite journal|doi=10.1126/science.280.5370.1711|author=Arnsten, A. F.|title=The biology of being frazzled |journal=Science |volume=280 |issue=5370 |pages=1711–2 |date=June 1998 |pmid=9660710}}</ref>在动物实验中发现。他们发现应激诱导PFC中'''<font color="#ff8000">儿茶酚胺 catecholamine</font>'''的释放可迅速降低PFC神经元的放电频率,并通过前馈和细胞内信号通路损害工作记忆<ref>{{Cite journal|author=Arnsten, AF |title=Stress signalling pathways that impair prefrontal cortex structure and function |journal=Nature Reviews Neuroscience |volume=10 |issue=6 |pages=410–22 |date=June 2009 |pmid=19455173|pmc=2907136 |doi=10.1038/nrn2648}}</ref>。长期暴露在压力下会导致更深层次的工作记忆缺陷和额外的PFC结构变化——包括树突萎缩和脊柱丧失<ref>{{Cite journal|author=Radley, J. J.|author2= Rocher, A. B.|author3=Miller, M.|author4= Janssen, W. G.|author5=Liston, C.|author6=Hof, P. R.|author7=McEwen, B. S.|author8=Morrison, J. H.|title=Repeated stress induces dendritic spine loss in the rat medial prefrontal cortex |journal=Cereb Cortex |volume=16 |issue=3 |pages=313–20 |date=Mar 2006 |pmid=15901656 |doi=10.1093/cercor/bhi104|doi-access=free}}</ref>——这些都可以通过抑制蛋白激酶C信号来预防<ref>{{Cite journal|author=Hains, A. B.|author2=Vu, M. A.|author3=Maciejewski, P. K.|author4= van Dyck, C. H. |authorlink4=Christopher H. van Dyck |author5=Gottron, M.|author6= Arnsten, A. F. |title=Inhibition of protein kinase C signaling protects prefrontal cortex dendritic spines and cognition from the effects of chronic stress |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=42 |pages=17957–62 |date=Oct 2009 |pmid=19805148|pmc=2742406 |doi=10.1073/pnas.0908563106|bibcode=2009PNAS..10617957H }}</ref>。功能磁共振成像研究已经将这项研究进一步扩展到人类,并证实了急性压力导致的工作记忆减少会降低PFC的活性,同时,压力还会导致儿茶酚胺水平提高<ref>{{Cite journal|vauthors=Qin S, Hermans EJ, van Marle HJ, Luo J, Fernández G |title=Acute psychological stress reduces working memory-related activity in the dorsolateral prefrontal cortex |journal=Biological Psychiatry |volume=66 |issue=1 |pages=25–32 |date=July 2009 |pmid=19403118 |doi=10.1016/j.biopsych.2009.03.006}}</ref>。在经历紧张的考试后,医学院学生的成像研究也表明其PFC功能减弱,与动物实验的结果一致<ref>{{Cite journal|vauthors=Liston C, McEwen BS, Casey BJ |title=Psychosocial stress reversibly disrupts prefrontal processing and attentional control |journal=Proceedings of the National Academy of Sciences|volume=106 |issue=3 |pages=912–7 |date=Jan 2009 |pmid=19139412|pmc=2621252 |doi=10.1073/pnas.0807041106|bibcode=2009PNAS..106..912L }}</ref>。压力对PFC结构和功能的显著影响可能有助于解释为何压力会加重甚至导致精神疾病。<br />
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The more stress in one's life, the lower the efficiency of working memory in performing simple cognitive tasks. Students who performed exercises that reduced the intrusion of negative thoughts showed an increase in their working memory capacity. Mood states (positive or negative) can have an influence on the neurotransmitter dopamine, which in turn can affect problem solving.<ref>{{cite book|last=Revlin|first=Russell|title=Human Cognition : Theory and Practice.|year=2007|publisher=Worth Pub|location=New York, NY|isbn=978-0-7167-5667-5|page=147|edition=International}}</ref><br />
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The more stress in one's life, the lower the efficiency of working memory in performing simple cognitive tasks. Students who performed exercises that reduced the intrusion of negative thoughts showed an increase in their working memory capacity. Mood states (positive or negative) can have an influence on the neurotransmitter dopamine, which in turn can affect problem solving.<br />
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人在生活中的压力越大工作记忆在完成简单认知任务时的效率就会越低。接受过限制负面思想入侵练习的学生,其工作记忆容量明显有所增加。因此我们说,情绪状态(积极或消极)会影响神经递质多巴胺,进而影响问题解决效果<ref>{{cite book|last=Revlin|first=Russell|title=Human Cognition : Theory and Practice.|year=2007|publisher=Worth Pub|location=New York, NY|isbn=978-0-7167-5667-5|page=147|edition=International}}</ref>。<br />
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=== 神经生理学的酒精效果 Effects of alcohol on neurophysiology ===<br />
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Alcohol abuse can result in brain damage which impairs working memory.<ref name="pmid21466500">{{cite journal |vauthors=van Holst RJ, Schilt T |title=Drug-related decrease in neuropsychological functions of abstinent drug users |journal=Curr Drug Abuse Rev |volume=4 |issue=1 |pages=42–56 | date=March 2011 |pmid=21466500 |doi= 10.2174/1874473711104010042}}</ref> Alcohol has an effect on the [[Blood-oxygen-level dependent|blood-oxygen-level-dependent]] (BOLD) response. The BOLD response correlates increased blood oxygenation with brain activity, which makes this response a useful tool for measuring neuronal activity.<ref>{{cite journal | author = Jacobus J.|author2=Tapert S. F. | year = 2013 | title = Neurotoxic Effects of Alcohol in Adolescence | journal = [[Annual Review of Clinical Psychology]] | volume = 9 | issue = 1| pages = 703–721 | doi = 10.1146/annurev-clinpsy-050212-185610 | pmc = 3873326 | pmid=23245341}}</ref> The BOLD response affects regions of the brain such as the basal ganglia and thalamus when performing a working memory task. Adolescents who start drinking at a young age show a decreased BOLD response in these brain regions.<ref>{{cite journal | vauthors = Weiland BJ, Nigg JT, Welsh RC, Yau WY, Zubieta JK | displayauthors=etal | year = 2012 | title = Resiliency in adolescents at high risk for substance abuse: flexible adaptation via subthalamic nucleus and linkage to drinking and drug use in early adulthood | journal = Alcohol. Clin. Exp. Res. | volume = 36 | issue = 8| pages = 1355–64 | doi=10.1111/j.1530-0277.2012.01741.x| pmc = 3412943 | pmid=22587751}}</ref> Alcohol dependent young women in particular exhibit less of a BOLD response in parietal and frontal cortices when performing a spatial working memory task.<ref>{{cite journal | vauthors = Tapert SF, Brown GG, Kindermann SS, Cheung EH, Frank LR, Brown SA | year = 2001 | title = fMRI measurement of brain dysfunction in alcohol-dependent young women | journal = Alcohol. Clin. Exp. Res. | volume = 25 | issue = 2| pages = 236–45 | doi=10.1111/j.1530-0277.2001.tb02204.x | pmid=11236838}}</ref> Binge drinking, specifically, can also affect one's performance on working memory tasks, particularly visual working memory.<ref>{{cite journal | vauthors = Ferrett HL, Carey PD, Thomas KG, Tapert SF, Fein G | year = 2010 | title = Neuropsychological performance of South African treatment-naive adolescents with alcohol dependence | journal = Drug Alcohol Depend | volume = 110 | issue = 1–2| pages = 8–14 | doi=10.1016/j.drugalcdep.2010.01.019| pmc = 4456395 | pmid=20227839}}</ref><ref>{{cite journal | vauthors = Crego A, Holguin SR, Parada M, Mota N, Corral M, Cadaveira F | year = 2009 | title = Binge drinking affects attentional and visual working memory processing in young university students | journal = Alcohol. Clin. Exp. Res. | volume = 33 | issue = 11| pages = 1870–79 | doi=10.1111/j.1530-0277.2009.01025.x| pmid = 19673739 | hdl = 10347/16832 | hdl-access = free }}</ref> Additionally, there seems to be a gender difference in regards to how alcohol affects working memory. While women perform better on verbal working memory tasks after consuming alcohol compared to men, they appear to perform worse on spatial working memory tasks as indicated by less brain activity.<ref>{{cite journal | vauthors = Greenstein JE, Kassel JD, Wardle MC, Veilleux JC, Evatt DP, Heinz AJ, Yates MC | year = 2010 | title = The separate and combined effects of nicotine and alcohol on working memory capacity in nonabstinent smokers | journal = [[Experimental and Clinical Psychopharmacology]] | volume = 18 | issue = 2| pages = 120–128 | doi = 10.1037/a0018782 | pmid = 20384423 }}</ref><ref>{{cite journal | vauthors = Squeglia LM, Schweinsburg AD, Pulido C, Tapert SF | year = 2011 | title = Adolescent binge drinking linked to abnormal spatial working memory brain activation: Differential gender effects | journal = Alcoholism: Clinical and Experimental Research | volume = 35 | issue = 10| pages = 1831–1841 | doi = 10.1111/j.1530-0277.2011.01527.x | pmc = 3183294 | pmid=21762178}}</ref> Finally, age seems to be an additional factor. Older adults are more susceptible than others to the effects of alcohol on working memory.<ref>{{cite journal | vauthors = Boissoneault J, Sklar A, Prather R, Nixon SJ | year = 2014 | title = Acute effects of moderate alcohol on psychomotor, set shifting, and working memory function in older and younger social drinkers | journal = Journal of Studies on Alcohol and Drugs | volume = 75 | issue = 5| pages = 870–879 | doi = 10.15288/jsad.2014.75.870 | pmc = 4161706 | pmid=25208205}}</ref><br />
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Alcohol abuse can result in brain damage which impairs working memory. Alcohol has an effect on the blood-oxygen-level-dependent (BOLD) response. The BOLD response correlates increased blood oxygenation with brain activity, which makes this response a useful tool for measuring neuronal activity. The BOLD response affects regions of the brain such as the basal ganglia and thalamus when performing a working memory task. Adolescents who start drinking at a young age show a decreased BOLD response in these brain regions. Alcohol dependent young women in particular exhibit less of a BOLD response in parietal and frontal cortices when performing a spatial working memory task. Binge drinking, specifically, can also affect one's performance on working memory tasks, particularly visual working memory. Additionally, there seems to be a gender difference in regards to how alcohol affects working memory. While women perform better on verbal working memory tasks after consuming alcohol compared to men, they appear to perform worse on spatial working memory tasks as indicated by less brain activity. Finally, age seems to be an additional factor. Older adults are more susceptible than others to the effects of alcohol on working memory.<br />
<br />
酗酒会损伤大脑,进而损害工作记忆<ref name="pmid21466500">{{cite journal |vauthors=van Holst RJ, Schilt T |title=Drug-related decrease in neuropsychological functions of abstinent drug users |journal=Curr Drug Abuse Rev |volume=4 |issue=1 |pages=42–56 | date=March 2011 |pmid=21466500 |doi= 10.2174/1874473711104010042}}</ref>。酒精会影响'''<font color="#ff8000">血氧水平依赖性 Blood-Oxygen-Level-Dependent(BOLD)</font>'''反应。BOLD反应把血氧含量增加与大脑活动联系起来,这使得其成为测量神经元活动的有效指标<ref>{{cite journal | author = Jacobus J.|author2=Tapert S. F. | year = 2013 | title = Neurotoxic Effects of Alcohol in Adolescence | journal = [[Annual Review of Clinical Psychology]] | volume = 9 | issue = 1| pages = 703–721 | doi = 10.1146/annurev-clinpsy-050212-185610 | pmc = 3873326 | pmid=23245341}}</ref>。在执行工作记忆任务时,BOLD反应影响大脑的基底神经节和丘脑等区域。从小就喝酒的青少年BOLD反应相应较低。特别的<ref>{{cite journal | vauthors = Weiland BJ, Nigg JT, Welsh RC, Yau WY, Zubieta JK | displayauthors=etal | year = 2012 | title = Resiliency in adolescents at high risk for substance abuse: flexible adaptation via subthalamic nucleus and linkage to drinking and drug use in early adulthood | journal = Alcohol. Clin. Exp. Res. | volume = 36 | issue = 8| pages = 1355–64 | doi=10.1111/j.1530-0277.2012.01741.x| pmc = 3412943 | pmid=22587751}}</ref>,有酒精依赖的年轻女性在执行空间工作记忆任务时顶叶和额叶皮层的BOLD反应较弱<ref>{{cite journal | vauthors = Tapert SF, Brown GG, Kindermann SS, Cheung EH, Frank LR, Brown SA | year = 2001 | title = fMRI measurement of brain dysfunction in alcohol-dependent young women | journal = Alcohol. Clin. Exp. Res. | volume = 25 | issue = 2| pages = 236–45 | doi=10.1111/j.1530-0277.2001.tb02204.x | pmid=11236838}}</ref>。酗酒工作记忆任务表现有显著影响——特别是视觉工作记忆<ref>{{cite journal | vauthors = Ferrett HL, Carey PD, Thomas KG, Tapert SF, Fein G | year = 2010 | title = Neuropsychological performance of South African treatment-naive adolescents with alcohol dependence | journal = Drug Alcohol Depend | volume = 110 | issue = 1–2| pages = 8–14 | doi=10.1016/j.drugalcdep.2010.01.019| pmc = 4456395 | pmid=20227839}}</ref><ref>{{cite journal | vauthors = Crego A, Holguin SR, Parada M, Mota N, Corral M, Cadaveira F | year = 2009 | title = Binge drinking affects attentional and visual working memory processing in young university students | journal = Alcohol. Clin. Exp. Res. | volume = 33 | issue = 11| pages = 1870–79 | doi=10.1111/j.1530-0277.2009.01025.x| pmid = 19673739 | hdl = 10347/16832 | hdl-access = free }}</ref>。此外,酒精对工作记忆的影响似乎也存在性别差异。与男性相比,女性酒后的非文字工作记忆任务完成得更好,但空间工作记忆任务完成得似乎更差(大脑活动迟缓)<ref>{{cite journal | vauthors = Greenstein JE, Kassel JD, Wardle MC, Veilleux JC, Evatt DP, Heinz AJ, Yates MC | year = 2010 | title = The separate and combined effects of nicotine and alcohol on working memory capacity in nonabstinent smokers | journal = [[Experimental and Clinical Psychopharmacology]] | volume = 18 | issue = 2| pages = 120–128 | doi = 10.1037/a0018782 | pmid = 20384423 }}</ref><ref>{{cite journal | vauthors = Squeglia LM, Schweinsburg AD, Pulido C, Tapert SF | year = 2011 | title = Adolescent binge drinking linked to abnormal spatial working memory brain activation: Differential gender effects | journal = Alcoholism: Clinical and Experimental Research | volume = 35 | issue = 10| pages = 1831–1841 | doi = 10.1111/j.1530-0277.2011.01527.x | pmc = 3183294 | pmid=21762178}}</ref>。最后,年龄似乎也是一个可考虑的因素。老年人更容易受到酒精的影响<ref>{{cite journal | vauthors = Boissoneault J, Sklar A, Prather R, Nixon SJ | year = 2014 | title = Acute effects of moderate alcohol on psychomotor, set shifting, and working memory function in older and younger social drinkers | journal = Journal of Studies on Alcohol and Drugs | volume = 75 | issue = 5| pages = 870–879 | doi = 10.15288/jsad.2014.75.870 | pmc = 4161706 | pmid=25208205}}</ref><br />
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== 基因 Genetics ==<br />
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=== 行为基因 Behavioral genetics ===<br />
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Individual differences in working-memory capacity are to some extent [[heritable]]; that is, about half of the variation between individuals is related to differences in their genes.<ref name=":1">{{Cite journal|last1=Engelhardt|first1=Laura E.|last2=Mann|first2=Frank D.|last3=Briley|first3=Daniel A.|last4=Church|first4=Jessica A.|last5=Harden|first5=K. Paige|last6=Tucker-Drob|first6=Elliot M.|title=Strong genetic overlap between executive functions and intelligence.|journal=Journal of Experimental Psychology: General|volume=145|issue=9|pages=1141–1159|doi=10.1037/xge0000195|pmc=5001920|pmid=27359131|year=2016}}</ref><ref name="Ando 615–624">{{Cite journal|last1=Ando|first1=Juko|last2=Ono|first2=Yutaka|last3=Wright|first3=Margaret J.|title=Genetic Structure of Spatial and Verbal Working Memory|journal=Behavior Genetics|language=en|volume=31|issue=6|pages=615–624|doi=10.1023/A:1013353613591|pmid=11838538|issn=0001-8244|year=2001}}</ref><ref>{{Cite journal|last1=Blokland|first1=Gabriëlla A. M.|last2=McMahon|first2=Katie L.|last3=Thompson|first3=Paul M.|last4=Martin|first4=Nicholas G.|last5=de Zubicaray|first5=Greig I.|last6=Wright|first6=Margaret J.|date=2011-07-27|title=Heritability of Working Memory Brain Activation|journal=Journal of Neuroscience|volume=31|issue=30|pages=10882–10890|doi=10.1523/jneurosci.5334-10.2011|pmid=21795540|pmc=3163233}}</ref> The genetic component of variability of working-memory capacity is largely shared with that of fluid intelligence.<ref name="Ando 615–624"/><ref name=":1" /><br />
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Individual differences in working-memory capacity are to some extent heritable; that is, about half of the variation between individuals is related to differences in their genes. The genetic component of variability of working-memory capacity is largely shared with that of fluid intelligence.<br />
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工作记忆能力的个体差异在某种程度上是遗传的,即个体间约一半的差异与基因差异有关<ref name=":1">{{Cite journal|last1=Engelhardt|first1=Laura E.|last2=Mann|first2=Frank D.|last3=Briley|first3=Daniel A.|last4=Church|first4=Jessica A.|last5=Harden|first5=K. Paige|last6=Tucker-Drob|first6=Elliot M.|title=Strong genetic overlap between executive functions and intelligence.|journal=Journal of Experimental Psychology: General|volume=145|issue=9|pages=1141–1159|doi=10.1037/xge0000195|pmc=5001920|pmid=27359131|year=2016}}</ref><ref name="Ando 615–624">{{Cite journal|last1=Ando|first1=Juko|last2=Ono|first2=Yutaka|last3=Wright|first3=Margaret J.|title=Genetic Structure of Spatial and Verbal Working Memory|journal=Behavior Genetics|language=en|volume=31|issue=6|pages=615–624|doi=10.1023/A:1013353613591|pmid=11838538|issn=0001-8244|year=2001}}</ref><ref>{{Cite journal|last1=Blokland|first1=Gabriëlla A. M.|last2=McMahon|first2=Katie L.|last3=Thompson|first3=Paul M.|last4=Martin|first4=Nicholas G.|last5=de Zubicaray|first5=Greig I.|last6=Wright|first6=Margaret J.|date=2011-07-27|title=Heritability of Working Memory Brain Activation|journal=Journal of Neuroscience|volume=31|issue=30|pages=10882–10890|doi=10.1523/jneurosci.5334-10.2011|pmid=21795540|pmc=3163233}}</ref>。工作记忆能力变异的遗传成分与流体智力的遗传成分大致相同<ref name="Ando 615–624"/><ref name=":1" /><br />
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=== 识别个别基因的尝试 Attempts to identify individual genes ===<br />
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Little is known about which genes are related to the functioning of working memory. Within the theoretical framework of the multi-component model, one candidate gene has been proposed, namely [[ROBO1]] for the hypothetical [[phonological loop]] component of working memory.<ref>{{Cite journal|last=Bates|first=Timothy|date=2011|title=Genetic Variance in a Component of the Language Acquisition Device: ROBO1 Polymorphisms Associated with Phonological Buffer Deficits|journal=Behavior Genetics|volume=41|issue=1|pages=50–7|doi=10.1007/s10519-010-9402-9|pmid=20949370}}</ref><br />
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Little is known about which genes are related to the functioning of working memory. Within the theoretical framework of the multi-component model, one candidate gene has been proposed, namely ROBO1 for the hypothetical phonological loop component of working memory.<br />
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我们对哪些基因与工作记忆的功能有关知之甚少。多成分模型的理论框架提出了一个候选基因——即工作记忆的语音回路ROBO1<ref>{{Cite journal|last=Bates|first=Timothy|date=2011|title=Genetic Variance in a Component of the Language Acquisition Device: ROBO1 Polymorphisms Associated with Phonological Buffer Deficits|journal=Behavior Genetics|volume=41|issue=1|pages=50–7|doi=10.1007/s10519-010-9402-9|pmid=20949370}}</ref>。<br />
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== 在学术成就方面的角色 Role in academic achievement ==<br />
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Working memory capacity is correlated with learning outcomes in literacy and numeracy. Initial evidence for this relation comes from the correlation between working-memory capacity and reading comprehension, as first observed by Daneman and Carpenter (1980)<ref>{{Cite journal|title = Individual differences in working memory and reading|journal = Journal of Verbal Learning and Verbal Behavior|date = 1980-08-01|pages = 450–466|volume = 19|issue = 4|doi = 10.1016/S0022-5371(80)90312-6|first1 = Meredyth|last1 = Daneman|first2 = Patricia A.|last2 = Carpenter}}</ref> and confirmed in a later meta-analytic review of several studies.<ref>{{Cite journal|last1=Daneman|first1=Meredyth|last2=Merikle|first2=Philip M.|title=Working memory and language comprehension: A meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=3|issue=4|pages=422–433|doi=10.3758/BF03214546|pmid=24213976|issn=1069-9384|year=1996|doi-access=free}}</ref> Subsequent work found that working memory performance in primary school children accurately predicted performance in mathematical problem solving.<ref>{{Cite journal|last1=Swanson|first1=H. Lee|last2=Beebe-Frankenberger|first2=Margaret|year=2004|title=The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties|journal=Journal of Educational Psychology|volume=96|issue=3|pages=471–491|doi=10.1037/0022-0663.96.3.471}}</ref> One longitudinal study showed that a child's working memory at 5 years old is a better predictor of academic success than IQ.<ref>{{Cite journal|vauthors=Alloway TP, Alloway RG |title=Investigating the predictive roles of working memory and IQ in academic attainment |journal=Journal of Experimental Child Psychology |volume=106|issue=1|pages= 20–9|year=2010|pmid=20018296 |doi=10.1016/j.jecp.2009.11.003|url=https://www.pure.ed.ac.uk/ws/files/11958608/Investigating_the_predictive_roles_of_working_memory_and_IQ_in_academic_attainment.pdf }}</ref><br />
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Working memory capacity is correlated with learning outcomes in literacy and numeracy. Initial evidence for this relation comes from the correlation between working-memory capacity and reading comprehension, as first observed by Daneman and Carpenter (1980) and confirmed in a later meta-analytic review of several studies. Subsequent work found that working memory performance in primary school children accurately predicted performance in mathematical problem solving. One longitudinal study showed that a child's working memory at 5 years old is a better predictor of academic success than IQ.<br />
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工作记忆容量与识字和算术能力的学习成果相关。1980年Daneman 和卡朋特 Carpenter首次从工作记忆容量和阅读理解的相关性研究中获得证据<ref>{{Cite journal|title = Individual differences in working memory and reading|journal = Journal of Verbal Learning and Verbal Behavior|date = 1980-08-01|pages = 450–466|volume = 19|issue = 4|doi = 10.1016/S0022-5371(80)90312-6|first1 = Meredyth|last1 = Daneman|first2 = Patricia A.|last2 = Carpenter}}</ref>——这在后来几项研究的元分析中也得到了证实<ref>{{Cite journal|last1=Daneman|first1=Meredyth|last2=Merikle|first2=Philip M.|title=Working memory and language comprehension: A meta-analysis|journal=Psychonomic Bulletin & Review|language=en|volume=3|issue=4|pages=422–433|doi=10.3758/BF03214546|pmid=24213976|issn=1069-9384|year=1996|doi-access=free}}</ref>。随后的研究发现,小学生的工作记忆能力能够精确地反映在数学问题解决上<ref>{{Cite journal|last1=Swanson|first1=H. Lee|last2=Beebe-Frankenberger|first2=Margaret|year=2004|title=The Relationship Between Working Memory and Mathematical Problem Solving in Children at Risk and Not at Risk for Serious Math Difficulties|journal=Journal of Educational Psychology|volume=96|issue=3|pages=471–491|doi=10.1037/0022-0663.96.3.471}}</ref>。一项后续研究表明,孩子5岁时的工作记忆能力与智商相比,是我们预测其未来学术成就地更好依据<ref>{{Cite journal|vauthors=Alloway TP, Alloway RG |title=Investigating the predictive roles of working memory and IQ in academic attainment |journal=Journal of Experimental Child Psychology |volume=106|issue=1|pages= 20–9|year=2010|pmid=20018296 |doi=10.1016/j.jecp.2009.11.003|url=https://www.pure.ed.ac.uk/ws/files/11958608/Investigating_the_predictive_roles_of_working_memory_and_IQ_in_academic_attainment.pdf }}</ref>。<br />
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In a large-scale screening study, one in ten children in mainstream classrooms were identified with working memory deficits. The majority of them performed very poorly in academic achievements, independent of their IQ.<ref>{{Cite journal|vauthors=Alloway TP, Gathercole SE, Kirkwood H, Elliott J |title=The cognitive and behavioral characteristics of children with low working memory |journal=Child Development |volume=80 |issue=2 |pages=606–21 |year=2009 |pmid=19467014 |doi=10.1111/j.1467-8624.2009.01282.x|hdl=1893/978 |hdl-access=free }}</ref> Similarly, working memory deficits have been identified in national curriculum low-achievers as young as seven years of age.<ref>{{Cite journal|title = Working memory deficits in children with low achievements in the national curriculum at 7 years of age|journal = British Journal of Educational Psychology|date = 2000-06-01|issn = 2044-8279|pages = 177–194|volume = 70|issue = 2|doi = 10.1348/000709900158047|language = en|first1 = Susan E.|last1 = Gathercole|first2 = Susan J.|last2 = Pickering|pmid=10900777}}</ref> Without appropriate intervention, these children lag behind their peers. A recent study of 37 school-age children with significant learning disabilities has shown that working memory capacity at baseline measurement, but not IQ, predicts learning outcomes two years later.<ref>{{Cite journal|first1=Tracy Packiam |last1=Alloway |year=2009 |journal=European Journal of Psychological Assessment |volume=25 |issue=2 |pages=92–8 |doi=10.1027/1015-5759.25.2.92 |title=Working Memory, but Not IQ, Predicts Subsequent Learning in Children with Learning Difficulties|hdl=1893/1005 |hdl-access=free }}</ref> This suggests that working memory impairments are associated with low learning outcomes and constitute a high risk factor for educational underachievement for children. In children with learning disabilities such as [[dyslexia]], [[ADHD]], and developmental coordination disorder, a similar pattern is evident.<ref>{{cite book | last1 = Pickering | first1 = Susan J. | title = Working memory in dyslexia | editor1 = Tracy Packiam Alloway |editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Wagner | first1 = Richard K. | last2 = Muse | first2 = Andrea | title = Short-term memory deficits in developmental dyslexia | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Roodenrys | first1 = Steve | title = Working memory function in attention deficit hyperactivity disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Alloway | first1 = Tracy Packiam | title = Working memory skills in children with developmental coordination disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><br />
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In a large-scale screening study, one in ten children in mainstream classrooms were identified with working memory deficits. The majority of them performed very poorly in academic achievements, independent of their IQ. Similarly, working memory deficits have been identified in national curriculum low-achievers as young as seven years of age. Without appropriate intervention, these children lag behind their peers. A recent study of 37 school-age children with significant learning disabilities has shown that working memory capacity at baseline measurement, but not IQ, predicts learning outcomes two years later. This suggests that working memory impairments are associated with low learning outcomes and constitute a high risk factor for educational underachievement for children. In children with learning disabilities such as dyslexia, ADHD, and developmental coordination disorder, a similar pattern is evident.<br />
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在一项大规模的筛查研究中,大班教学模式中十分之一的儿童被认为患有工作记忆缺陷。他们中的大多数人在学术成就上乏善可陈——这与智商无关<ref>{{Cite journal|vauthors=Alloway TP, Gathercole SE, Kirkwood H, Elliott J |title=The cognitive and behavioral characteristics of children with low working memory |journal=Child Development |volume=80 |issue=2 |pages=606–21 |year=2009 |pmid=19467014 |doi=10.1111/j.1467-8624.2009.01282.x|hdl=1893/978 |hdl-access=free }}</ref>。同样,国家课程标准把最早在7岁就表现出工作记忆缺陷的儿童定性为低成就学生<ref>{{Cite journal|title = Working memory deficits in children with low achievements in the national curriculum at 7 years of age|journal = British Journal of Educational Psychology|date = 2000-06-01|issn = 2044-8279|pages = 177–194|volume = 70|issue = 2|doi = 10.1348/000709900158047|language = en|first1 = Susan E.|last1 = Gathercole|first2 = Susan J.|last2 = Pickering|pmid=10900777}}</ref>。如果没有适当的干预,这些孩子就会落后于同龄人。最近,一项针对37名具有显著学习障碍的学龄儿童的研究表明,基线测量的工作记忆能力(而非智商)可预测两年后的学习结果<ref>{{Cite journal|first1=Tracy Packiam |last1=Alloway |year=2009 |journal=European Journal of Psychological Assessment |volume=25 |issue=2 |pages=92–8 |doi=10.1027/1015-5759.25.2.92 |title=Working Memory, but Not IQ, Predicts Subsequent Learning in Children with Learning Difficulties|hdl=1893/1005 |hdl-access=free }}</ref>。这表明低分与工作记忆障碍有关,甚至成为导致教育失败的高风险因素。在有学习障碍的儿童中(如'''<font color="#ff8000">诵读困难dyslexia</font>'''、'''<font color="#ff8000">多动症ADHD</font>'''和失用症),类似模式是显而易见的<ref>{{cite book | last1 = Pickering | first1 = Susan J. | title = Working memory in dyslexia | editor1 = Tracy Packiam Alloway |editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Wagner | first1 = Richard K. | last2 = Muse | first2 = Andrea | title = Short-term memory deficits in developmental dyslexia | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = Working memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Roodenrys | first1 = Steve | title = Working memory function in attention deficit hyperactivity disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref><ref>{{cite book | last1 = Alloway | first1 = Tracy Packiam | title = Working memory skills in children with developmental coordination disorder | editor1 = Tracy Packiam Alloway|editor2=Susan E Gathercole | work = orking memory and neurodevelopmental disorders | publisher = Psychology Press | year = 2006 | location = New York, NY | isbn = 978-1-84169-560-0 |oclc = 63692704}}</ref>。<br />
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== 与注意力的关系 Relation to attention ==<br />
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There is some evidence that optimal working memory performance links to the neural ability to focus attention on task-relevant information and to ignore distractions,<ref>{{Cite journal|date=March 2009|title=Neural suppression of irrelevant information underlies optimal working memory performance|journal=The Journal of Neuroscience|volume=29|issue=10|pages=3059–66|doi=10.1523/JNEUROSCI.4621-08.2009|pmc=2704557|pmid=19279242|author=Zanto, T. P.|author2=Gazzaley, A.}}</ref> and that practice-related improvement in working memory is due to increasing these abilities.<ref>{{cite journal|last2=Zanto|first2=T.&nbsp;P.|last3=Rutman|first3=A.&nbsp;M.|last4=Clapp|first4=W.&nbsp;C.|last5=Gazzaley|first5=A.|year=2009|title=Practice-related improvement in working memory is modulated by changes in processing external interference|journal=Journal of Neurophysiology|volume=102|issue=3|pages=1779–89|doi=10.1152/jn.00179.2009|pmc=2746773|pmid=19587320|last1=Berry|first1=A.&nbsp;S.}}</ref> One line of research suggests a link between the working memory capacities of a person and their ability to control the orientation of attention to stimuli in the environment.<ref name="attention09">{{Cite journal|vauthors=Fukuda K, Vogel EK |title=Human variation in overriding attentional capture |journal=The Journal of Neuroscience |volume=29 |issue=27 |pages=8726–33 |date=July 2009 |pmid=19587279 |pmc=6664881 |doi=10.1523/JNEUROSCI.2145-09.2009}}</ref> Such control enables people to attend to information important for their current goals, and to ignore goal-irrelevant stimuli that tend to capture their attention due to their sensory [[salience (neuroscience)|saliency]] (such as an ambulance siren). The direction of attention according to one's goals is assumed to rely on "top-down" signals from the pre-frontal cortex (PFC) that biases processing in [[posterior cortex|posterior cortical areas]].<ref>{{Cite journal|vauthors=Desimone R, Duncan J |title=Neural mechanisms of selective visual attention |journal=Annual Review of Neuroscience |volume=18 |pages=193–222 |year=1995 |pmid=7605061 |doi=10.1146/annurev.ne.18.030195.001205}}</ref> Capture of attention by salient stimuli is assumed to be driven by "bottom-up" signals from subcortical structures and the primary sensory cortices.<ref>{{Cite journal|vauthors=Yantis S, Jonides J |title=Abrupt visual onsets and selective attention: voluntary versus automatic allocation |journal=Journal of Experimental Psychology. Human Perception and Performance |volume=16 |issue=1 |pages=121–34 |date=February 1990 |pmid=2137514 |url=http://content.apa.org/journals/xhp/16/1/121 |doi=10.1037/0096-1523.16.1.121|citeseerx=10.1.1.211.5016 }}</ref> The ability to override "bottom-up" capture of attention differs between individuals, and this difference has been found to correlate with their performance in a working-memory test for visual information.<ref name="attention09" /> Another study, however, found no correlation between the ability to override attentional capture and measures of more general working-memory capacity.<ref>{{Cite journal|last1=Mall|first1=Jonathan T.|last2=Morey|first2=Candice C.|last3=Wolff|first3=Michael J.|last4=Lehnert|first4=Franziska|date=2014-01-09|title=Visual selective attention is equally functional for individuals with low and high working memory capacity: Evidence from accuracy and eye movements|journal=Attention, Perception, & Psychophysics|language=en|volume=76|issue=7|pages=1998–2014|doi=10.3758/s13414-013-0610-2|pmid=24402698|issn=1943-3921|url=http://orca.cf.ac.uk/105362/1/Morey.%20Visual%20selective.pdf}}</ref><br />
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There is some evidence that optimal working memory performance links to the neural ability to focus attention on task-relevant information and to ignore distractions, and that practice-related improvement in working memory is due to increasing these abilities. One line of research suggests a link between the working memory capacities of a person and their ability to control the orientation of attention to stimuli in the environment. Such control enables people to attend to information important for their current goals, and to ignore goal-irrelevant stimuli that tend to capture their attention due to their sensory saliency (such as an ambulance siren). The direction of attention according to one's goals is assumed to rely on "top-down" signals from the pre-frontal cortex (PFC) that biases processing in posterior cortical areas. Capture of attention by salient stimuli is assumed to be driven by "bottom-up" signals from subcortical structures and the primary sensory cortices. The ability to override "bottom-up" capture of attention differs between individuals, and this difference has been found to correlate with their performance in a working-memory test for visual information. Another study, however, found no correlation between the ability to override attentional capture and measures of more general working-memory capacity.<br />
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有证据表明,较佳的工作记忆表现与能否忽略干扰集中注意力于任务相关信息的神经能力有关<ref>{{Cite journal|date=March 2009|title=Neural suppression of irrelevant information underlies optimal working memory performance|journal=The Journal of Neuroscience|volume=29|issue=10|pages=3059–66|doi=10.1523/JNEUROSCI.4621-08.2009|pmc=2704557|pmid=19279242|author=Zanto, T. P.|author2=Gazzaley, A.}}</ref>,也就是说训练之后的工作记忆之所以能够改善,是因为上述能力得到了改善<ref>{{cite journal|last2=Zanto|first2=T.&nbsp;P.|last3=Rutman|first3=A.&nbsp;M.|last4=Clapp|first4=W.&nbsp;C.|last5=Gazzaley|first5=A.|year=2009|title=Practice-related improvement in working memory is modulated by changes in processing external interference|journal=Journal of Neurophysiology|volume=102|issue=3|pages=1779–89|doi=10.1152/jn.00179.2009|pmc=2746773|pmid=19587320|last1=Berry|first1=A.&nbsp;S.}}</ref>。一项研究表明,工作记忆能力和面对环境刺激人能否控制注意力方向之间存在联系<ref name="attention09">{{Cite journal|vauthors=Fukuda K, Vogel EK |title=Human variation in overriding attentional capture |journal=The Journal of Neuroscience |volume=29 |issue=27 |pages=8726–33 |date=July 2009 |pmid=19587279 |pmc=6664881 |doi=10.1523/JNEUROSCI.2145-09.2009}}</ref>。因为这种控制会引导人关注相关的信息而忽略与目标无关的刺激——这些刺激往往因其感官显著性(如救护车警报器)而吸引人的注意力<ref>{{Cite journal|vauthors=Desimone R, Duncan J |title=Neural mechanisms of selective visual attention |journal=Annual Review of Neuroscience |volume=18 |pages=193–222 |year=1995 |pmid=7605061 |doi=10.1146/annurev.ne.18.030195.001205}}</ref>。个体的注意力方向被认为取决于前额叶皮质(PFC)“自上而下”发出的信号,这种信号偏好于在后皮质区处理任务<ref>{{Cite journal|vauthors=Yantis S, Jonides J |title=Abrupt visual onsets and selective attention: voluntary versus automatic allocation |journal=Journal of Experimental Psychology. Human Perception and Performance |volume=16 |issue=1 |pages=121–34 |date=February 1990 |pmid=2137514 |url=http://content.apa.org/journals/xhp/16/1/121 |doi=10.1037/0096-1523.16.1.121|citeseerx=10.1.1.211.5016 }}</ref>。皮层下结构和初级感觉皮层发出的“自下而上”的信号驱动着由显著刺激引发的注意力。<ref name="attention09" />然而,另一项研究发现,注意力过度集中对在工作记忆能力测量过程中没有起到预期作用<ref>{{Cite journal|last1=Mall|first1=Jonathan T.|last2=Morey|first2=Candice C.|last3=Wolff|first3=Michael J.|last4=Lehnert|first4=Franziska|date=2014-01-09|title=Visual selective attention is equally functional for individuals with low and high working memory capacity: Evidence from accuracy and eye movements|journal=Attention, Perception, & Psychophysics|language=en|volume=76|issue=7|pages=1998–2014|doi=10.3758/s13414-013-0610-2|pmid=24402698|issn=1943-3921|url=http://orca.cf.ac.uk/105362/1/Morey.%20Visual%20selective.pdf}}</ref><br />
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== 与神经系统疾病的关系 Relationship with neural disorders ==<br />
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An impairment of working memory functioning is normally seen in several neural disorders:<br />
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An impairment of working memory functioning is normally seen in several neural disorders:<br />
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工作记忆功能障碍通常见于以下神经系统疾病:<br />
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'''ADHD:''' Several authors<ref>Barkley; Castellanos and Tannock; Pennington and Ozonoff; Schachar (according to the source)</ref> have proposed that symptoms of [[ADHD]] arise from a primary deficit in a specific executive function (EF) domain such as working memory, response inhibition or a more general weakness in executive control.<ref name="WillcuttDoyle2005">{{cite journal|date=June 2005|title=Validity of the executive function theory of attention-deficit/hyperactivity disorder: a meta-analytic review|journal=Biol. Psychiatry|volume=57|issue=11|pages=1336–46|doi=10.1016/j.biopsych.2005.02.006|pmid=15950006|vauthors=Willcutt EG, Doyle AE, Nigg JT, Faraone SV, Pennington BF}}</ref> A meta-analytical review cites several studies that found significant lower group results for ADHD in spatial and verbal working memory tasks, and in several other EF tasks. However, the authors concluded that EF weaknesses neither are necessary nor sufficient to cause all cases of ADHD.<ref name="WillcuttDoyle2005" /><br />
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ADHD: Several authors have proposed that symptoms of ADHD arise from a primary deficit in a specific executive function (EF) domain such as working memory, response inhibition or a more general weakness in executive control. A meta-analytical review cites several studies that found significant lower group results for ADHD in spatial and verbal working memory tasks, and in several other EF tasks. However, the authors concluded that EF weaknesses neither are necessary nor sufficient to cause all cases of ADHD.<br />
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注意力缺陷多动障碍(ADHD): 一些研究者<ref>Barkley; Castellanos and Tannock; Pennington and Ozonoff; Schachar (according to the source)</ref>提出,ADHD 源于特定 '''<font color="#ff8000">执行功能(EF) Executive Function (EF)</font>'''领域——如工作记忆、反应抑制或执行控制方面——的原发性缺陷<ref name="WillcuttDoyle2005">{{cite journal|date=June 2005|title=Validity of the executive function theory of attention-deficit/hyperactivity disorder: a meta-analytic review|journal=Biol. Psychiatry|volume=57|issue=11|pages=1336–46|doi=10.1016/j.biopsych.2005.02.006|pmid=15950006|vauthors=Willcutt EG, Doyle AE, Nigg JT, Faraone SV, Pennington BF}}</ref>。引用了几项研究之后,研究人员得出一份元分析报告,发现在空间和语言工作记忆任务及其他几项EF任务中,ADHD群体有较低的成绩。然而,研究者的结论是EF缺陷既不必然也不足以引发所有的ADHD病例<ref name="WillcuttDoyle2005" /><br />
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Several [[neurotransmitters]], such as [[dopamine]] and [[glutamate]] may be both involved in ADHD and working memory. Both are associated with the [[frontal lobe|frontal]] brain, self-direction and self-regulation, but [[Causality|cause–effect]] have not been confirmed, so it is unclear whether working memory dysfunction leads to ADHD, or ADHD distractibility leads to poor functionality of working memory, or if there is some other connection.<ref>[http://guilfordjournals.com/doi/abs/10.1521/adhd.2008.16.6.8 Working Memory as a Core Deficit in ADHD: Preliminary Findings and Implications] – 2008</ref><ref name="Clark Blackwell 2007">{{cite journal|date=June 2007|title=Association between response inhibition and working memory in adult ADHD: a link to right frontal cortex pathology?|journal=Biol. Psychiatry|volume=61|issue=12|pages=1395–401|doi=10.1016/j.biopsych.2006.07.020|pmid=17046725|vauthors=Clark L, Blackwell AD, Aron AR, etal}}</ref><ref name="Roodenrys Koloski 2001">{{cite journal|last2=Koloski|first2=Natasha|last3=Grainger|first3=Jessica|year=2001|title=Working memory function in attention deficit hyperactivity disordered and reading disabled children|journal=British Journal of Developmental Psychology|volume=19|issue=3|pages=325–337|doi=10.1348/026151001166128|issn=0261-510X|last1=Roodenrys|first1=Steven}}</ref><br />
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Several neurotransmitters, such as dopamine and glutamate may be both involved in ADHD and working memory. Both are associated with the frontal brain, self-direction and self-regulation, but cause–effect have not been confirmed, so it is unclear whether working memory dysfunction leads to ADHD, or ADHD distractibility leads to poor functionality of working memory, or if there is some other connection.<br />
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多巴胺和谷氨酸盐等多种神经递质可能都与ADHD和工作记忆有关。两者都与额叶大脑、'''<font color="#ff8000">自我定向self-direction</font>'''和'''<font color="#ff8000">自我调节self-regulation</font>'''有关,但其中的因果关系尚未得到确认。所以目前不清楚是工作记忆功能障碍导致 ADHD,还是注意力分散导致ADHD工作记忆功能低下,亦或存在着其他联系<ref>[http://guilfordjournals.com/doi/abs/10.1521/adhd.2008.16.6.8 Working Memory as a Core Deficit in ADHD: Preliminary Findings and Implications] – 2008</ref><ref name="Clark Blackwell 2007">{{cite journal|date=June 2007|title=Association between response inhibition and working memory in adult ADHD: a link to right frontal cortex pathology?|journal=Biol. Psychiatry|volume=61|issue=12|pages=1395–401|doi=10.1016/j.biopsych.2006.07.020|pmid=17046725|vauthors=Clark L, Blackwell AD, Aron AR, etal}}</ref><ref name="Roodenrys Koloski 2001">{{cite journal|last2=Koloski|first2=Natasha|last3=Grainger|first3=Jessica|year=2001|title=Working memory function in attention deficit hyperactivity disordered and reading disabled children|journal=British Journal of Developmental Psychology|volume=19|issue=3|pages=325–337|doi=10.1348/026151001166128|issn=0261-510X|last1=Roodenrys|first1=Steven}}</ref>。<br />
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'''Parkinson's disease''':&nbsp;Patients with [[Parkinson's]] show signs of a reduced verbal function of working memory. They wanted to find if the reduction is due to a lack of ability to focus on relevant tasks, or a low amount of memory capacity. Twenty-one patients with Parkinson's were tested in comparison to the control group of 28 participants of the same age. The researchers found that both hypotheses were the reason working memory function is reduced which did not fully agree with their hypothesis that it is either one or the other.<ref>{{Cite journal|pmc=2929336|title=Visual working memory deficits in patients with Parkinson's disease are due to both reduced storage capacity and impaired ability to filter out irrelevant information|last=Lee|first=Eun-Young|date=5 August 2010|journal=Brain|volume=133|issue=9|pages=2677–2689|doi=10.1093/brain/awq197|pmid=20688815}}</ref><br />
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Parkinson's disease:&nbsp;Patients with Parkinson's show signs of a reduced verbal function of working memory. They wanted to find if the reduction is due to a lack of ability to focus on relevant tasks, or a low amount of memory capacity. Twenty-one patients with Parkinson's were tested in comparison to the control group of 28 participants of the same age. The researchers found that both hypotheses were the reason working memory function is reduced which did not fully agree with their hypothesis that it is either one or the other.<br />
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'''<font color="#ff8000">帕金森病 Parkinson's Disease</font>''': 帕金森病患者表现出工作记忆语言功能的减退。研究者想知道这种减少是因为缺乏专注于相关任务的能力,还是因为记忆容量太小。他们对21名帕金森病患者与28名同龄对照组进行了测试。研究人员发现二者都是工作记忆功能减退的原因,而非他们先前假设的原因在二者之一<ref>{{Cite journal|pmc=2929336|title=Visual working memory deficits in patients with Parkinson's disease are due to both reduced storage capacity and impaired ability to filter out irrelevant information|last=Lee|first=Eun-Young|date=5 August 2010|journal=Brain|volume=133|issue=9|pages=2677–2689|doi=10.1093/brain/awq197|pmid=20688815}}</ref>。<br />
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'''Alzheimer's disease''': As [[Alzheimer's disease]] becomes more serious, less working memory functions. There is one study that focuses on the neural connections and fluidity of working memory in mice brains. Half of the mice were given an injection that is similar to Alzheimer's effects, and the other half were not. Then they were expected to go through a maze that is a task to test working memory. The study help answer questions about how Alzheimer's can deteriorate the working memory and ultimately obliterate memory functions.<ref>{{Cite journal|last=Tiaotiao|first=Liu|date=December 2014|title=Functional connectivity in a rat model of Alzheimer's disease during a working memory task|journal=Current Alzheimer Research|volume=11|issue=10|pages=981–991|doi=10.2174/1567205011666141107125912 |pmid=25387338}}</ref><br />
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Alzheimer's disease: As Alzheimer's disease becomes more serious, less working memory functions. There is one study that focuses on the neural connections and fluidity of working memory in mice brains. Half of the mice were given an injection that is similar to Alzheimer's effects, and the other half were not. Then they were expected to go through a maze that is a task to test working memory. The study help answer questions about how Alzheimer's can deteriorate the working memory and ultimately obliterate memory functions.<br />
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'''<font color="#ff8000">阿尔茨海默病 Alzheimer's Disease</font>''': 工作记忆功能随着阿尔茨海默症病情的加重而降低。在一项针对老鼠大脑中的神经连接和工作记忆流动性的研究中,一半的老鼠注射了可以引发类阿尔茨海默症的药物,另一半则不注射药物。然后让它们穿越一个迷宫,即完成一个工作记忆测试任务。这项研究有助于回答阿尔兹海默症是如何损害工作记忆并最终消除记忆功能的<ref>{{Cite journal|last=Tiaotiao|first=Liu|date=December 2014|title=Functional connectivity in a rat model of Alzheimer's disease during a working memory task|journal=Current Alzheimer Research|volume=11|issue=10|pages=981–991|doi=10.2174/1567205011666141107125912 |pmid=25387338}}</ref>。<br />
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'''Huntington's disease''':&nbsp;A group of researchers hosted a study that researched the function and connectivity of working memory over a 30-month longitudinal experiment. It found that there were certain places in the brain where most connectivity was decreased in pre-[[Huntington disease]]d patients, in comparison to the control group that remained consistently functional.<ref>{{Cite journal|last=Poudel|first=Govinda R.|date=January 2015|title=Functional changes during working memory in Huntington's disease: 30-month longitudinal data from the IMAGE-HD study|journal=Brain Structure and Function|volume=220|issue=1|pages=501–512|pmid=24240602|doi=10.1007/s00429-013-0670-z}}</ref><br />
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Huntington's disease:&nbsp;A group of researchers hosted a study that researched the function and connectivity of working memory over a 30-month longitudinal experiment. It found that there were certain places in the brain where most connectivity was decreased in pre-Huntington diseased patients, in comparison to the control group that remained consistently functional.<br />
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'''<font color="#ff8000">亨廷顿氏病 Huntington's Disease</font>''': 一组研究人员进行了为期30个月的纵向实验,研究工作记忆的功能和关联性。研究发现,亨廷顿症患者大脑中特定部位的关联性降低,而对照组功能正常<ref>{{Cite journal|last=Poudel|first=Govinda R.|date=January 2015|title=Functional changes during working memory in Huntington's disease: 30-month longitudinal data from the IMAGE-HD study|journal=Brain Structure and Function|volume=220|issue=1|pages=501–512|pmid=24240602|doi=10.1007/s00429-013-0670-z}}</ref><br />
。<br />
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== 参见 See also ==<br />
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* [[多重记忆模型 Atkinson–Shiffrin memory model]]<br />
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* {{Section link|Prefrontal cortex|注意力和记忆 Attention and memory}}<br />
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* [[孤独症与工作记忆 Autism and working memory]]<br />
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* [[模糊痕迹理论 Fuzzy-trace theory]]<br />
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* [[中期记忆 Intermediate-term memory]]<br />
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* [[记忆与老化 Memory and aging]]<br />
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* [[PBWM|前额叶基底节工作记忆 Prefrontal cortex basal ganglia working memory (PBWM)]]<br />
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* [[意识结构 Cognitive architecture]]<br />
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* [[提姆・沙丽斯 Tim Shallice]]<br />
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== 参考文献 References ==<br />
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{{Reflist|33em}}<br />
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== 外部链接 External links ==<br />
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* [http://psych.colorado.edu/~miyake/MWM%20Chapter%201.pdf Models of Working Memory (Mechanisms of Active Maintenance and Executive Control)]<br />
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{{Memory}}<br />
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{{Dyslexia}}<br />
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[[Category:Memory processes]]<br />
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Category:Memory processes<br />
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分类: 记忆过程<br />
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[[Category:Problem solving]]<br />
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Category:Problem solving<br />
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分类: 解决问题<br />
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[[Category:Human behavior]]<br />
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Category:Human behavior<br />
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分类: 人类行为<br />
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<small>This page was moved from [[wikipedia:en:Working memory]]. Its edit history can be viewed at [[工作记忆/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21544网络中心性2021-02-03T16:32:09Z<p>Vicky:/* 卡兹中心性 Katz centrality */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
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In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
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They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
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They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
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在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
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==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
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'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
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“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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< math > sum _ { k = 0} ^ infty a _ { r } ^ { k } beta ^ k </math > <br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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for matrix exponentials, where<br />
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for matrix exponentials, where<br />
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矩阵指数,其中<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,权限分配的解决方案()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心度得分差异对节点的重要性提供一些见解。此外,弗里曼中心度使人们能够通过比较几个网络的最高中心度得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心度。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心度如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
<br />
For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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<br />
<br />
where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
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In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
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一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
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==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
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'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到削减。在数学上,它被定义为<br />
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:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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[数学][数学]<br />
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<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
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:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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(x _ j + 1) <br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
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It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
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== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
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{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
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PageRank satisfies the following equation<br />
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网页排名满足下面的等式<br />
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:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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1-alpha { n } ,</math > <br />
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<br />
where<br />
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where<br />
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其中<br />
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:<math>L(j) = \sum_{i} a_{ji}</math><br />
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<math>L(j) = \sum_{i} a_{ji}</math><br />
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[ math > l (j) = sum { i } a { ji } </math > <br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
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是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
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在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
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<br />
'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
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:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
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where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
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The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
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The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
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渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
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==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
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Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
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复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
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==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''==<br />
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The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
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The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
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任何网络的中心度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>中心度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的中心度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
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:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
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是具有相同节点数的任何图的点中心性的最大差值之和,然后网络中心度是:<br />
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:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
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== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
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[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
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In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
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在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
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In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
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In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
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为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
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:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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数学,数学<br />
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where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
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where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
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这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
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:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
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值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
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:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
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where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
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where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
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其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
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==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
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经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<br />
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对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
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中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
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* [[Distance (graph theory)|Distance in graphs]]<br />
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*阿尔法中心性<br />
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*核心—外围结构<br />
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*距离(图理论)图中的距离<br />
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==Notes and references==<br />
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{{Reflist}}<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21543网络中心性2021-02-03T16:29:55Z<p>Vicky:/* 博弈论中心性Game-theoretic centrality */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
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In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
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They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
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They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
<br />
在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
<br />
==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
<br />
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
<br />
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
<br />
'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
<br />
The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
<br />
"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
<br />
“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
<br />
When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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< math > sum _ { k = 0} ^ infty a _ { r } ^ { k } beta ^ k </math > <br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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for matrix exponentials, where<br />
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for matrix exponentials, where<br />
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矩阵指数,其中<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,权限分配的解决方案()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心度得分差异对节点的重要性提供一些见解。此外,弗里曼中心度使人们能够通过比较几个网络的最高中心度得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心度。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心度如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
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In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
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一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
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==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
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'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到'''<font color="#32CD32"> '削弱 Penalized</font>''。在数学上,它被定义为<br />
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:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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[数学][数学]<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
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:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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(x _ j + 1) <br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
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It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
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== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
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{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
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PageRank satisfies the following equation<br />
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网页排名满足下面的等式<br />
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:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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1-alpha { n } ,</math > <br />
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where<br />
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where<br />
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其中<br />
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:<math>L(j) = \sum_{i} a_{ji}</math><br />
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<math>L(j) = \sum_{i} a_{ji}</math><br />
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[ math > l (j) = sum { i } a { ji } </math > <br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
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是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
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A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
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在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
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'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
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:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
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where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
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The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
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渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
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==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
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Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
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==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''==<br />
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The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
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任何网络的中心度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>中心度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的中心度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
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:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
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是具有相同节点数的任何图的点中心性的最大差值之和,然后网络中心度是:<br />
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:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
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== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
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[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
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In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
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在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
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In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
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In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
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为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
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:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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数学,数学<br />
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<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
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这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
<br />
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:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
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值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
<br />
<br />
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:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
<br />
<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
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其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
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==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
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经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<br />
<br />
对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
<br />
The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
<br />
中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
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* [[Distance (graph theory)|Distance in graphs]]<br />
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*阿尔法中心性<br />
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*核心—外围结构<br />
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*距离(图理论)图中的距离<br />
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==Notes and references==<br />
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{{Reflist}}<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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[[Category:Graph theory]]<br />
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Category:Graph theory<br />
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分类: 图论<br />
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[[Category:Graph algorithms]]<br />
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Category:Graph algorithms<br />
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分类: 图形算法<br />
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[[Category:Algebraic graph theory]]<br />
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Category:Algebraic graph theory<br />
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分类: 代数图论<br />
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[[Category:Networks]]<br />
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Category:Networks<br />
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分类: 网络<br />
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[[Category:Network analysis]]<br />
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Category:Network analysis<br />
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分类: 网络分析<br />
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[[Category:Network theory]]<br />
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Category:Network theory<br />
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分类: 网络理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%9B%B8%E5%8F%98&diff=21533相变2021-02-03T14:37:42Z<p>Vicky:/* Modern classifications 现代分类法 */</p>
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<div>此词条由Jie翻译,由和光同尘审校。<br />
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[[文件:Nomenclature for the different phase transitions.png|300px|thumb|right|此图显示了不同相变的命名法]]<br />
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The term '''phase transition''' (or '''phase change''') is most commonly used to describe transitions between [[solid]], [[liquid]], and [[gas]]eous [[states of matter]], as well as [[plasma (physics)|plasma]] in rare cases. A phase of a thermodynamic system and the states of matter have uniform [[physical property|physical properties]]. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as [[temperature]], [[pressure]], or others. For example, a liquid may become gas upon heating to the [[boiling point]], resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies.<br />
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The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid, and gaseous states of matter, as well as plasma in rare cases. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change, often discontinuously, as a result of the change of external conditions, such as temperature, pressure, or others. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions commonly occur in nature and are used today in many technologies.<br />
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'''<font color="#ff8000"> 相变Phase transition (or phase change)</font>'''一词常用于描述物质在'''<font color="#ff8000">固态solid </font>''','''<font color="#ff8000">液态liquid </font>'''和'''<font color="#ff8000">气态gaseous </font>'''之间的转变,在极少数情况下还涉及'''<font color="#ff8000">等离子体plasma </font>'''。热力学系统的相和物质的状态具有统一的物理属性。由于外部条件(例如温度,压强等)的变化,在给定介质的相变过程中介质的某些属性通常会间断的发生变化。例如,液体在被加热到沸点时可能会变成气体,其体积因此发生突变。综合考量变化发生的外部条件,这种变化被称为相变。相变通常发生在自然界,如今被越来越多地用于科技行业。<br />
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== Types of phase transition 相变的种类==<br />
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[[文件:典型的相图.png|300px|thumb|right|该图为典型的相图。其中虚线部分表示了水的反常行为]]<br />
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Examples of phase transitions include:<br />
Examples of phase transitions include:<br />
相变的例子包括:<br />
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*The transitions between the solid, liquid, and gaseous phases of a single component, due to the effects of temperature and/or [[pressure]]:<br />
由于温度和/或压强的影响,单组分在固相,液相和气相之间转换:<br />
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[[文件:物质的相变big.png|500px|thumb|centre|参见蒸汽压和相图]]<br />
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[[文件:固体氩快速溶解.jpg|200px|thumb|right|一小块固体氩在快速溶解,同时显示出从固体到液体以及从液体到气体的转变。]]<br />
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[[文件:二氧化碳(红色)和水(蓝色)的相图比较.png|thumb|upright=2|二氧化碳(红色)和水(蓝色)的相图比较,解释了它们在1个大气压下的不同相变]]<br />
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{{Condensed matter physics}}<br />
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* A [[eutectic]] transformation, in which a two-component single-phase liquid is cooled and transforms into two solid phases. The same process, but beginning with a solid instead of a liquid is called a [[eutectoid]] transformation.<br />
'''<font color="#ff8000"> 共晶转变Eutectic transformation</font>''',即互溶液体(由两种不同成分组成的单相液体)经过冷却后转变成为两个不同的固相。如果把互溶液体改成固体,那这一过程就被称为'''<font color="#ff8000"> 共析转变 eutectoid transformation</font>'''。<br />
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* A [[metastable]] to equilibrium phase transformation. A metastable polymorph which forms rapidly due to lower surface energy will transform to an equilibrium phase given sufficient thermal input to overcome an energetic barrier.<br />
亚稳态到平衡态的相变。由于较低的表面能而迅速形成的'''<font color="#ff8000"> 亚稳多晶体metastable polymorph</font>''',在有足以克服能量位垒的热输入时会逐渐转换为一种平衡相。<br />
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* A [[peritectic]] transformation, in which a two-component single-phase solid is heated and transforms into a solid phase and a liquid phase.<br />
'''<font color="#ff8000"> 包晶转变Peritectic transformation</font>'''。包含两种不同成分的单相固体经过加热后转变为一种固相和一种液相。<br />
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* A [[spinodal decomposition]], in which a single phase is cooled and separates into two different compositions of that same phase.<br />
'''<font color="#ff8000"> 亚稳相分解Spinodal decomposition</font>'''。一个单相经过冷却后分离为两种不同的相。<br />
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* Transition to a [[mesophase]] between solid and liquid, such as one of the "[[liquid crystal]]" phases.<br />
处于固体和液体过渡状态的'''<font color="#ff8000"> 中间相mesophase</font>''',例如一种“'''<font color="#ff8000"> 液晶liquid crystal</font>'''”相。<br />
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* The transition between the [[ferromagnetism|ferromagnetic]] and [[paramagnetism|paramagnetic]] phases of [[magnet]]ic materials at the [[Curie point]].<br />
磁性材料处于'''<font color="#ff8000"> 居里点Curie point</font>'''(居里温度)时,在'''<font color="#ff8000"> 铁磁ferromagnetism</font>'''和'''<font color="#ff8000"> 顺磁paramagnetism</font>'''相之间转变。<br />
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* The transition between differently ordered, [[ANNNI model|commensurate]] or [[commensurability (mathematics)|incommensurate]], magnetic structures, such as in cerium [[antimonide]].<br />
在以不同方式组织的'''<font color="#ff8000"> 相称commensurate</font>'''或'''<font color="#ff8000"> 不相称incommensurate</font>'''的磁性结构(如在'''<font color="#ff8000"> 锑化铈Antimonide</font>'''中)之间的转变。<br />
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* The [[martensitic transformation]] which occurs as one of the many phase transformations in carbon steel and stands as a model for [[displacive phase transformations]].<br />
'''<font color="#ff8000"> 马氏体转变Martensitic transformation</font>''',作为碳钢的众多相变之一,也是典型的'''<font color="#ff8000"> 位移相变displacive phase transformations</font>'''<br />
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* Changes in the [[crystallographic]] structure such as between [[Allotropes of iron|ferrite]] and [[austenite]] of iron.<br />
'''<font color="#ff8000">晶体结构crystallographic structure </font>'''的变化,例如铁在'''<font color="#ff8000"> 铁素体Ferrite</font>'''和'''<font color="#ff8000"> 奥氏体Austenite</font>'''之间的转变。<br />
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* Order-disorder transitions such as in alpha-[[titanium aluminide]]s.<br />
以'''<font color="#ff8000">α-钛铝化物</font>'''为例——从有序到无序的转变。<br />
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* The dependence of the [[adsorption]] geometry on coverage and temperature, such as for [[hydrogen]] on iron (110).<br />
以'''<font color="#ff8000">氢</font>'''对铁(110)的依赖为例¬——吸附几何结构对覆盖率和温度存在依赖性。<br />
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* The emergence of [[superconductivity]] in certain metals and ceramics when cooled below a critical temperature.<br />
当冷却到临界温度以下时,某些金属和陶瓷中出现'''<font color="#ff8000"> 超导Superconductivity</font>'''现象。<br />
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* The transition between different molecular structures ([[Polymorphism (materials science)|polymorphs]], [[allotropy|allotropes]] or [[polyamorphism|polyamorphs]]), especially of solids, such as between an [[amorphous solid|amorphous]] structure and a [[crystal]] structure, between two different crystal structures, or between two amorphous structures.<br />
不同分子结构('''<font color="#ff8000"> 同质多形体polymorphs</font>''','''<font color="#ff8000"> 同素异形体allotropes</font>'''或'''<font color="#ff8000"> 非晶多形体polyamorphs</font>''')之间的转变——特别是固体之间的,例如非晶结构和晶体结构、两种不同晶体结构之间或两种非晶结构之间。<br />
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* Quantum condensation of [[boson]]ic fluids ([[Bose–Einstein condensate|Bose–Einstein condensation]]). The [[superfluidity|superfluid]] transition in liquid [[helium]] is an example of this.<br />
'''<font color="#ff8000"> 玻色子Bosonic</font>'''流体的量子凝聚('''<font color="#ff8000"> 玻色–爱因斯坦凝聚Bose–Einstein condensation</font>''')。液态氦中的超流体转变就是一个例子。<br />
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* The [[Symmetry breaking|breaking of symmetries]] in the laws of physics during the early history of the universe as its temperature cooled.<br />
物理学中的'''<font color="#ff8000"> 对称性破裂breaking of symmetries</font>'''——发生在宇宙温度降低的早期阶段<br />
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* [[Isotope fractionation]] occurs during a phase transition, the ratio of light to heavy isotopes in the involved molecules changes. When [[water vapor]] condenses (an [[equilibrium fractionation]]), the heavier water isotopes (18O and 2H) become enriched in the liquid phase while the lighter isotopes (16O and 1H) tend toward the vapor phase.<br />
'''<font color="#ff8000"> 同位素分馏Isotope fractionation</font>'''发生在相变过程中,所涉及分子的轻同位素与重同位素的比率发生变化。当水蒸气冷凝('''<font color="#ff8000">平衡分馏equilibrium fractionation </font>)时,较重的同位素(18O和2H)在液相中富集,而较轻的同位素(16O和1H)则趋向于气相。<br />
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Phase transitions occur when the [[thermodynamic free energy]] of a system is [[analytic function|non-analytic]] for some choice of thermodynamic variables (cf. [[phase (matter)|phases]]). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks.<br />
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Phase transitions occur when the thermodynamic free energy of a system is non-analytic for some choice of thermodynamic variables (cf. phases). This condition generally stems from the interactions of a large number of particles in a system, and does not appear in systems that are too small. It is important to note that phase transitions can occur and are defined for non-thermodynamic systems, where temperature is not a parameter. Examples include: quantum phase transitions, dynamic phase transitions, and topological (structural) phase transitions. In these types of systems other parameters take the place of temperature. For instance, connection probability replaces temperature for percolating networks.<br />
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当系统的热力学自由能无法对某些热力学变量进行解析时,相变就会发生。这通常是因为系统中存在大量相互作用的粒子。如果系统太小,则不会出现。值得注意的是,相变同样可以存在于参数不包括温度的非热力学系统中。例如:量子相变,动态相变和拓扑(结构)相变。在这些系统中,其他参数代替了温度(在'''<font color="#ff8000"> 渗滤网络percolating networks</font>'''中,连接概率代替温度)。<br />
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At the phase transition point (for instance, [[boiling point]]) the two phases of a substance, liquid and [[vapor]], have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred.<br />
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At the phase transition point (for instance, boiling point) the two phases of a substance, liquid and vapor, have identical free energies and therefore are equally likely to exist. Below the boiling point, the liquid is the more stable state of the two, whereas above the gaseous form is preferred.<br />
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物质的两个相(液相和气相)在相变点(如沸点)具有相同的自由能,因此它们存在的可能性相同。而当温度低于沸点时,液态在两者中更稳定;当温度高于沸点时,气态更具优势。<br />
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It is sometimes possible to change the state of a system [[diabatic]]ally (as opposed to [[adiabatic invariant|adiabatic]]ally) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is [[metastable]], i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in [[superheating]], [[supercooling]], and [[supersaturation]], for example.<br />
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It is sometimes possible to change the state of a system diabatically (as opposed to adiabatically) in such a way that it can be brought past a phase transition point without undergoing a phase transition. The resulting state is metastable, i.e., less stable than the phase to which the transition would have occurred, but not unstable either. This occurs in superheating, supercooling, and supersaturation, for example.<br />
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有时系统状态可以通过传热方式(与绝热方式相对)改变,这使系统状态得以通过相变点而又不经历相变。此时该系统会处于亚稳态(与发生了相变的相相比,其状态没有那么稳定,但也并非不稳定)。过热、过冷以及过饱和时都会发生这种现象。<br />
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== Classifications 分类==<br />
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=== Ehrenfest classification 埃伦费斯特分类法 ===<br />
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[[Paul Ehrenfest]] classified phase transitions based on the behavior of the [[thermodynamic free energy]] as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. ''First-order phase transitions'' exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. ''Second-order phase transitions'' are continuous in the first derivative (the [[Phase transition#order parameters|order parameter]], which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the [[magnetization]], which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the [[Curie temperature]]. The [[magnetic susceptibility]], the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.<br />
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Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free energy as a function of other thermodynamic variables. Under this scheme, phase transitions were labeled by the lowest derivative of the free energy that is discontinuous at the transition. First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. The various solid/liquid/gas transitions are classified as first-order transitions because they involve a discontinuous change in density, which is the (inverse of the) first derivative of the free energy with respect to pressure. Second-order phase transitions are continuous in the first derivative (the order parameter, which is the first derivative of the free energy with respect to the external field, is continuous across the transition) but exhibit discontinuity in a second derivative of the free energy. These include the ferromagnetic phase transition in materials such as iron, where the magnetization, which is the first derivative of the free energy with respect to the applied magnetic field strength, increases continuously from zero as the temperature is lowered below the Curie temperature. The magnetic susceptibility, the second derivative of the free energy with the field, changes discontinuously. Under the Ehrenfest classification scheme, there could in principle be third, fourth, and higher-order phase transitions.<br />
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保罗·埃伦费斯特Paul Ehrenfest根据热力学自由能和其他热力学变量的函数关系对相变进行了分类。根据他的方法,可以按照转变时的不连续自由能最低导数标记相变。'''<font color="#ff8000">一阶相变first-order phase transitions</font>'''相对于某些热力学变量,具有自由能的一阶导数不连续性。我们将各种固/液/气的转变都归为一阶相变,因为它们都涉及到密度的不连续变化——这是自由能相对于压力的一阶导数(一阶导数的逆函数)。而'''<font color="#ff8000"> 二阶相变second-order phase transitions</font>'''在一阶导数中是连续的(有序参数,即自由能相对于外部场的一阶导数,在整个转变过程中是连续的),但在自由能的二阶导数中表现出不连续性。比如'''<font color="#ff8000">铁磁相变ferromagnetic transition </font>'''(发生在铁等材料中),其中磁化强度是自由能相对于施加磁场强度的一阶导数。随着温度降低到居里温度以下,磁化强度将从零开始持续增加。而磁化率,是自由能相对于磁场的二阶导数,它的变化是不连续的。以此类推,按照Ehrenfest的分类方法,原则上可以存在第三,第四甚至更高阶的相变。<br />
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The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the [[supercritical liquid–gas boundaries]].<br />
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The Ehrenfest classification implicitly allows for continuous phase transformations, where the bonding character of a material changes, but there is no discontinuity in any free energy derivative. An example of this occurs at the supercritical liquid–gas boundaries.<br />
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'''<font color="#ff8000"> 埃伦费斯特分类法Ehrenfest classification</font>'''隐含连续相变,其中材料的成键特征发生了变化,但任何自由能导数都没有间断。比如说超临界液气的边界。<br />
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=== Modern classifications 现代分类法 ===<br />
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In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:<br />
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In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes:<br />
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在现代分类方案中,相变被分为两大类,命名方式类似于埃伦费斯特分类法:<br />
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'''First-order phase transitions''' are those that involve a [[latent heat]]. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into [[water vapor|vapor]], but forms a [[turbulence|turbulent]] mixture of liquid water and vapor bubbles). [[Yoseph Imry|Imry]] and Wortis showed that [[quenched disorder]] can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.<br />
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First-order phase transitions are those that involve a latent heat. During such a transition, a system either absorbs or releases a fixed (and typically large) amount of energy per volume. During this process, the temperature of the system will stay constant as heat is added: the system is in a "mixed-phase regime" in which some parts of the system have completed the transition and others have not. Familiar examples are the melting of ice or the boiling of water (the water does not instantly turn into vapor, but forms a turbulent mixture of liquid water and vapor bubbles). Imry and Wortis showed that quenched disorder can broaden a first-order transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.<br />
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一阶相变是那些涉及潜伏热的相变。在这种相变过程中,系统会吸收或释放固定(通常是大量)的能量。在此过程中,即使热量增加,系统的温度也保持恒定:系统处于“混合相状态”,也就是说某些部分已完成转变,而其他部分尚未完成。常见的例子是冰的融化或水的沸腾(水不会立即变成蒸气,而是成为液态水和蒸气气泡的湍流混合物)。物理学家伊姆利 Imry和沃迪斯 Wortis研究发现,可以将'''<font color="#ff8000"> 淬火无序quenched disorder</font>'''视为一阶转变。即在有限的温度范围内完成相变,但是过冷或过热现象仍然存在,并且滞后仍然存在于热循环中。<br />
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'''Second-order phase transitions''' are also called ''"continuous phase transitions"''. They are characterized by a divergent susceptibility, an infinite [[Correlation function (statistical mechanics)|correlation length]], and a [[power law]] decay of correlations near [[Critical point (thermodynamics)|criticality]]. Examples of second-order phase transitions are the [[Ferromagnetism|ferromagnetic]] transition, superconducting transition (for a [[Type-I superconductor]] the phase transition is second-order at zero external field and for a [[Type-II superconductor]] the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the [[superfluid]] transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using [[differential scanning calorimetry]] measurements. [[Lev Landau]] gave a [[Phenomenology (particle physics)|phenomenological]] [[Landau theory|theory]] of second-order phase transitions.<br />
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Second-order phase transitions are also called "continuous phase transitions". They are characterized by a divergent susceptibility, an infinite correlation length, and a power law decay of correlations near criticality. Examples of second-order phase transitions are the ferromagnetic transition, superconducting transition (for a Type-I superconductor the phase transition is second-order at zero external field and for a Type-II superconductor the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions) and the superfluid transition. In contrast to viscosity, thermal expansion and heat capacity of amorphous materials show a relatively sudden change at the glass transition temperature which enables accurate detection using differential scanning calorimetry measurements. Lev Landau gave a phenomenological theory of second-order phase transitions.<br />
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'''<font color="#ff8000">二阶相变Second-order phase transitions </font>''',或称为“连续相变”,它们的特征是敏感度发散,相关长度无限以及接近临界的相关性幂律衰减。二阶相变的例子是铁磁相变,'''<font color="#ff8000">超导相变superconducting transition </font>'''(对于I型超导体,在零外场下的相变是二阶的;对于II型超导体,从常态到混合态以及混合态到超导状态的转变都是二阶的)和'''<font color="#ff8000">超流体转换superfluid transition </font>'''。另外,对'''<font color="#ff8000">非晶体材料amorphous materials</font>'''而言,'''<font color="#ff8000">热膨胀thermal expansion</font>'''和'''<font color="#ff8000">热容属性heat capacity</font>'''在玻璃相变温度下会发生突变——这与粘度属性相反。我们可以使用差示扫描量热法来精确检测变化数值。列夫·兰道Lev Landau后来得出了二阶相变的现象学理论。<br />
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Apart from isolated, simple phase transitions, there exist transition lines as well as [[multicritical point]]s, when varying external parameters like the magnetic field or composition.<br />
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Apart from isolated, simple phase transitions, there exist transition lines as well as multicritical points, when varying external parameters like the magnetic field or composition.<br />
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当改变诸如磁场、成分之类的外部参数时,除了独立、简单的相变,还存在'''<font color="#ff8000">跃迁谱线transition lines</font>'''以及多个'''<font color="#ff8000">临界点multicritical points</font>'''。<br />
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Several transitions are known as ''infinite-order phase transitions''.They are continuous but break no [[#Symmetry|symmetries]]. The most famous example is the [[Kosterlitz–Thouless transition]] in the two-dimensional [[XY model]]. Many [[quantum phase transition]]s, e.g., in [[two-dimensional electron gas]]es, belong to this class.<br />
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Several transitions are known as infinite-order phase transitions.They are continuous but break no symmetries. The most famous example is the Kosterlitz–Thouless transition in the two-dimensional XY model. Many quantum phase transitions, e.g., in two-dimensional electron gases, belong to this class.<br />
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另外还存在其他相变类型,例如'''<font color="#ff8000">无限阶相变 infinite-order phase transitions</font>'''。无限阶相变是连续的,但并不破坏对称性。最著名的例子是二维XY模型中的'''<font color="#ff8000">KS相变 Kosterlitz-Thouless transition</font>'''。除此之外, '''<font color="#ff8000">二维电子气two-dimensional electron gases </font>'''中的量子相变也属于无限阶相变。<br />
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The [[glass transition|liquid–glass transition]] is observed in many [[polymers]] and other liquids that can be [[supercooling|supercooled]] far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a ''[[quenched disorder]]'' state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions.<br />
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The liquid–glass transition is observed in many polymers and other liquids that can be supercooled far below the melting point of the crystalline phase. This is atypical in several respects. It is not a transition between thermodynamic ground states: it is widely believed that the true ground state is always crystalline. Glass is a quenched disorder state, and its entropy, density, and so on, depend on the thermal history. Therefore, the glass transition is primarily a dynamic phenomenon: on cooling a liquid, internal degrees of freedom successively fall out of equilibrium. Some theoretical methods predict an underlying phase transition in the hypothetical limit of infinitely long relaxation times. No direct experimental evidence supports the existence of these transitions.<br />
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在被冷却至远低于结晶相熔点的聚合物和其他液体中出现了'''<font color="#ff8000">液体-玻璃相变liquid–glass transition</font>'''。综合考虑多个方面,我们认为这是一种非典型相变。它不是热力学基态之间的转变:因为人们普遍认为,真正的基态始终是晶体。玻璃是淬火无序状态,其'''<font color="#ff8000">熵entropy</font>'''、'''<font color="#ff8000">密度density</font>'''等取决于热历史。因此,可以把玻璃相变看作一种动态现象:液体冷却时,其内部自由度会逐渐失去平衡。一些理论预测其潜在相变会发生在无限长'''<font color="#ff8000">弛豫时间relaxation times</font>'''的假设极限内。但是目前并不存在直接的实验证据来支持其存在。<br />
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The gelation transition of colloidal particles has been shown to be a second-order phase transition under nonequilibrium conditions.<br />
在非平衡条件下,'''<font color="#ff8000">胶体粒子colloidal particles</font>'''的凝胶化转变被认为是二级相变。<br />
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== Characteristic properties 特征属性 ==<br />
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=== Phase coexistence 相共存 ===<br />
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A disorder-broadened first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions. If the first-order freezing transition occurs over a range of temperatures, and Tg falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition, such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials,magnetocaloric materials,magnetic shape memory materials,The interesting feature of these observations of Tg falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between Tg and Tc in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses.<br />
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A disorder-broadened first-order transition occurs over a finite range of temperatures where the fraction of the low-temperature equilibrium phase grows from zero to one (100%) as the temperature is lowered. This continuous variation of the coexisting fractions with temperature raised interesting possibilities. On cooling, some liquids vitrify into a glass rather than transform to the equilibrium crystal phase. This happens if the cooling rate is faster than a critical cooling rate, and is attributed to the molecular motions becoming so slow that the molecules cannot rearrange into the crystal positions. This slowing down happens below a glass-formation temperature Tg, which may depend on the applied pressure. If the first-order freezing transition occurs over a range of temperatures, and Tg falls within this range, then there is an interesting possibility that the transition is arrested when it is partial and incomplete. Extending these ideas to first-order magnetic transitions being arrested at low temperatures, resulted in the observation of incomplete magnetic transitions, with two magnetic phases coexisting, down to the lowest temperature. First reported in the case of a ferromagnetic to anti-ferromagnetic transition, such persistent phase coexistence has now been reported across a variety of first-order magnetic transitions. These include colossal-magnetoresistance manganite materials, magnetocaloric materials, magnetic shape memory materials, and other materials.The interesting feature of these observations of Tg falling within the temperature range over which the transition occurs is that the first-order magnetic transition is influenced by magnetic field, just like the structural transition is influenced by pressure. The relative ease with which magnetic fields can be controlled, in contrast to pressure, raises the possibility that one can study the interplay between Tg and Tc in an exhaustive way. Phase coexistence across first-order magnetic transitions will then enable the resolution of outstanding issues in understanding glasses.<br />
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在有限的温度范围内,胶体粒子的凝胶化转变显示为bA紊乱-扩展的一阶转变。随着温度降低,'''<font color="#ff8000">低温平衡相low-temperature equilibrium phase</font>'''的分数从零增加到一(100%)。随温度变化而变化的馏分共存创造了许多有趣的可能性。比如在冷却时,一些液体会逐渐玻璃化,而不是转变为'''<font color="#ff8000">平衡晶相equilibrium crystal phase</font>'''。这种情况往往发生在冷却速率比临界冷却速率快的时候——分子运动变得十分缓慢,以至于分子无法重新排列到晶体位置。分子运动的减速通常发生在气温降至玻璃的形成温度Tg以下时——这可能需要外部施加压力来实现。如果Tg落在该一阶冻结相变发生的特定温度范围内,一种有趣的现象就会发生,即当转变不完整时该转变会停止。同理可以考虑在低温下被阻止的一阶磁相变,我们可以观察到不完全的磁相变,即两个磁相同时存在直至到达最低温度。自关于铁磁到反铁磁相变的报道首次公开以来,人们逐渐发现了各种一阶磁相变的持久相共存现象。包括'''<font color="#ff8000">庞磁电阻锰矿材料colossal-magnetoresistance manganite materials</font>'''、'''<font color="#ff8000">磁制冷材料magnetocaloric materials</font>'''、'''<font color="#ff8000">磁性形状记忆材料magnetic shape memory materials</font>'''等。当Tg落在相变发生的温度范围内时,观测结果非常有趣,其一阶磁相变受到了磁场的影响——就像结构相变会受到压力影响一样。不过与压力相比,控制磁场相对容易,这大大提高了研究者们运用穷举法研究Tg和Tc之间相互作用的成功率。一阶磁相变的相位共存将有助于解决和玻璃有关的一系列突出问题。<br />
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=== Critical points 临界点===<br />
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In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the [[Critical point (thermodynamics)|critical point]], at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of [[critical opalescence]], a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).<br />
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In any system containing liquid and gaseous phases, there exists a special combination of pressure and temperature, known as the critical point, at which the transition between liquid and gas becomes a second-order transition. Near the critical point, the fluid is sufficiently hot and compressed that the distinction between the liquid and gaseous phases is almost non-existent. This is associated with the phenomenon of critical opalescence, a milky appearance of the liquid due to density fluctuations at all possible wavelengths (including those of visible light).<br />
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在任何包含液相和气相的系统中都存在压力和温度的特殊组合,我们称之为临界点。在该临界点处,液相和气相之间的转变即为二级相变。在临界点附近,如果流体足够热并且被压缩,那么液相和气相之间的区别几乎就消失了。这与临界乳光现象有关——液体在所有可能的波长(包括可见光)处产生密度波动,变成乳白色。<br />
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=== Symmetry 对称性===<br />
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Phase transitions often involve a [[symmetry breaking]] process. For instance, the cooling of a fluid into a [[crystalline solid]] breaks continuous [[translation symmetry]]: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to [[spontaneous symmetry breaking]], with the exception of certain [[accidental symmetry|accidental symmetries]] (e.g. the formation of heavy [[virtual particles]], which only occurs at low temperatures).<br />
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Phase transitions often involve a symmetry breaking process. For instance, the cooling of a fluid into a crystalline solid breaks continuous translation symmetry: each point in the fluid has the same properties, but each point in a crystal does not have the same properties (unless the points are chosen from the lattice points of the crystal lattice). Typically, the high-temperature phase contains more symmetries than the low-temperature phase due to spontaneous symmetry breaking, with the exception of certain accidental symmetries (e.g. the formation of heavy virtual particles, which only occurs at low temperatures).<br />
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相变通常涉及到对称破坏。例如,将流体冷却至成结晶固体会破坏其连续的平移对称性:流体中的每个点都具有相同的属性,但是晶体中的点并非如此(除非这些点来自晶格点阵中的晶格点)。通常,由于'''<font color="#ff8000"> 自发对称性破缺spontaneous symmetry breaking</font>''',除了某些特殊的对称性(例如,'''<font color="#ff8000"> 重虚粒子Virtual particles</font>'''的形成,其仅在低温下发生)外,高温相比低温相具有更多的对称性。<br />
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=== Order parameters 序参数 ===<br />
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An '''order parameter''' is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter [[susceptibility (disambiguation)|susceptibility]] will usually diverge.<br />
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An order parameter is a measure of the degree of order across the boundaries in a phase transition system; it normally ranges between zero in one phase (usually above the critical point) and nonzero in the other. At the critical point, the order parameter susceptibility will usually diverge.<br />
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'''<font color="#ff8000"> 序参数Order parameter</font>'''是相变系统中跨边界的有序/无序度量;它通常在一个为零的阶段(通常在临界点以上)和一个非零阶段之间。在临界点,序参数的敏感性通常会有分离趋向。<br />
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An example of an order parameter is the net [[magnetization]] in a [[ferromagnetic]] system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities.<br />
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An example of an order parameter is the net magnetization in a ferromagnetic system undergoing a phase transition. For liquid/gas transitions, the order parameter is the difference of the densities.<br />
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序参数的一个示例是发生相变的铁磁系统中的净磁化强度。对于液/气相而言,序参数就是它们的密度之差。<br />
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From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the [[ferromagnetic]] phase, one must provide the net [[magnetization]], whose direction was spontaneously chosen when the system cooled below the [[Curie point]]. However, note that order parameters can also be defined for non-symmetry-breaking transitions.<br />
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From a theoretical perspective, order parameters arise from symmetry breaking. When this happens, one needs to introduce one or more extra variables to describe the state of the system. For example, in the ferromagnetic phase, one must provide the net magnetization, whose direction was spontaneously chosen when the system cooled below the Curie point. However, note that order parameters can also be defined for non-symmetry-breaking transitions.<br />
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从理论的角度来看,序参数来自对称性破坏。当发生这种情况时,需要引入一个或多个他变量来描述该系统状态。例如,在铁磁相中必须提供净磁化强度,因为当系统降温至居里点以下时,磁化方向会自动确定。但是值得注意的是,非对称性破坏相变也可以定义有序参数。<br />
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Some phase transitions, such as [[superconductivity|superconducting]] and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.<br />
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Some phase transitions, such as superconducting and ferromagnetic, can have order parameters for more than one degree of freedom. In such phases, the order parameter may take the form of a complex number, a vector, or even a tensor, the magnitude of which goes to zero at the phase transition.<br />
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某些相变,例如'''<font color="#ff8000"> 超导superconducting</font>'''和铁磁,可以具有超过一个自由度的多个序参数。在这样的相中,序参数可以采用复数、'''<font color="#ff8000">向量vector</font>'''甚至'''<font color="#ff8000">张量tensor</font>'''的形式,其大小在相变发生时会变为零。<br />
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There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as [[Quantum vortex|vortex]]- or [[Topological defect|defect]] lines.<br />
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There also exist dual descriptions of phase transitions in terms of disorder parameters. These indicate the presence of line-like excitations such as vortex- or defect lines.<br />
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'''<font color="#ff8000">无序参数disorder parameters</font>'''中存在着相变的双重表述。 这就证明了'''<font color="#ff8000"> 线状激励line-like excitations</font>'''确实存在,例如'''<font color="#ff8000"> 涡旋线vortex lines</font>''','''<font color="#ff8000"> 缺陷线defect lines</font>'''等。<br />
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=== Relevance in cosmology 宇宙学的相关性 ===<br />
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Symmetry-breaking phase transitions play an important role in [[physical cosmology|cosmology]]. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the [[electroweak force|electroweak field]] into the U(1) symmetry of the present-day [[electromagnetic field]]. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see [[electroweak baryogenesis]]).<br />
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Symmetry-breaking phase transitions play an important role in cosmology. As the universe expanded and cooled, the vacuum underwent a series of symmetry-breaking phase transitions. For example, the electroweak transition broke the SU(2)×U(1) symmetry of the electroweak field into the U(1) symmetry of the present-day electromagnetic field. This transition is important to understanding the asymmetry between the amount of matter and antimatter in the present-day universe (see electroweak baryogenesis).<br />
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对称性破坏相变在宇宙学中起着重要作用。随着宇宙的膨胀和冷却,太空经历了一系列对称性破坏的相变。例如,电弱过渡破坏了当时电弱场的''SU(2)×U(1)''对称性,生成了当今电磁场的''U(1)''对称性。一旦明白宇宙发生过这种转变,对当今宇宙中物质与反物质之间不对称性的研究对我们来说也就更好理解了(请参阅'''<font color="#ff8000"> 弱电重子生成electroweak baryogenesis</font>''')。<br />
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Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of [[Eric Chaisson]] and [[David Layzer]].<br />
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Progressive phase transitions in an expanding universe are implicated in the development of order in the universe, as is illustrated by the work of Eric Chaisson and David Layzer.<br />
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埃里克·蔡森Eric Chaisson和戴维·莱泽David Layzer的研究表明,相变正在不断膨胀的宇宙中进行,这与宇宙秩序的发展变化有关。<br />
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See also [[relational order theories]] and [[order and disorder]].<br />
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See also relational order theories and order and disorder.<br />
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详情另参见'''<font color="#ff8000">关系秩序理论relational order theories</font>'''和秩序与无序。<br />
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=== Critical exponents and universality classes 临界指数和普适性 ===<br />
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Continuous phase transitions are easier to study than first-order transitions due to the absence of [[latent heat]], and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.<br />
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Continuous phase transitions are easier to study than first-order transitions due to the absence of latent heat, and they have been discovered to have many interesting properties. The phenomena associated with continuous phase transitions are called critical phenomena, due to their association with critical points.<br />
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由于不存在'''<font color="#ff8000"> 潜伏热latent heat</font>''',连续相变比一阶相变更容易研究。目前人们已经发现了许多有趣的性质。与连续相变有关的现象由于与临界点有关而被称为临界现象。<br />
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It turns out that continuous phase transitions can be characterized by parameters known as [[critical exponent]]s. The most important one is perhaps the exponent describing the divergence of the thermal [[correlation length]] by approaching the transition. For instance, let us examine the behavior of the [[heat capacity]] near such a transition. We vary the temperature {{mvar|T}} of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature ''T<sub>c</sub>'' . When {{mvar|T}} is near ''T<sub>c</sub>'' , the heat capacity {{mvar|C}} typically has a [[power law]] behavior,<br />
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It turns out that continuous phase transitions can be characterized by parameters known as critical exponents. The most important one is perhaps the exponent describing the divergence of the thermal correlation length by approaching the transition. For instance, let us examine the behavior of the heat capacity near such a transition. We vary the temperature of the system while keeping all the other thermodynamic variables fixed, and find that the transition occurs at some critical temperature T<sub>c</sub> . When is near T<sub>c</sub> , the heat capacity typically has a power law behavior,<br />
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事实证明,连续相变可以由'''<font color="#ff8000">临界指数critical exponents</font>'''这一参数表征。其中最重要的一个参数也许是描述逼近相变时热相关长度差异的指数。例如,让我们检测相变即将发生时的热容行为。在保持其他所有热力学变量不变的条件下,改变系统温度T,发现相变发生在某个临界温度Tc处。当T接近Tc时,热容C通常具有'''<font color="#ff8000">幂律行为power law behavior</font>''':<br />
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<math> C \propto |T_c - T|^{-\alpha}.</math><br />
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The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent {{mvar|ν}} instead of {{mvar|α}}, applies for the correlation length.<br />
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The heat capacity of amorphous materials has such a behaviour near the glass transition temperature where the universal critical exponent α = 0.59 A similar behavior, but with the exponent instead of , applies for the correlation length.<br />
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当接近玻璃相变温度时,非晶体材料的热容会具有幂律行为,其中通用临界指数α= 0.59。这也适用于相关长度,但要将指数改为ν。<br />
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The exponent {{mvar|ν}} is positive. This is different with {{mvar|α}}. Its actual value depends on the type of phase transition we are considering.<br />
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The exponent is positive. This is different with . Its actual value depends on the type of phase transition we are considering.<br />
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指数ν为正数,这与α不同。临界指数的实际值取决于我们选择的相变类型。<br />
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It is widely believed that the critical exponents are the same above and below the critical temperature. It has now been shown that this is not necessarily true: When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <math>\gamma </math>, the exponent of the susceptibility) are not identical.<br />
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It is widely believed that the critical exponents are the same above and below the critical temperature. It has now been shown that this is not necessarily true: When a continuous symmetry is explicitly broken down to a discrete symmetry by irrelevant (in the renormalization group sense) anisotropies, then some exponents (such as <math>\gamma </math>, the exponent of the susceptibility) are not identical.<br />
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人们曾普遍认为,不管温度在临界温度之上还是临界温度之下,临界指数保持不变。但是现实证明这不一定正确:当连续对称属性因不相关的'''<font color="#ff8000">各向异性anisotropies</font>'''(在'''<font color="#ff8000">重整化群理论renormalization group</font>'''意义上)而分解为离散对称属性时,某些指数(例如γ,'''<font color="#ff8000"> 磁化率指数Exponent of the susceptibility</font>''')会有所不同。<br />
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For −1 &lt; α &lt; 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the [[lambda transition]] from a normal state to the [[superfluid]] state, for which experiments have found {{mvar|α}} = -0.013±0.003.At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample.This experimental value of α agrees with theoretical predictions based on variational perturbation theory.<br />
<br />
For −1 &lt; α &lt; 0, the heat capacity has a "kink" at the transition temperature. This is the behavior of liquid helium at the lambda transition from a normal state to the superfluid state, for which experiments have found = -0.013±0.003.At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample. This experimental value of α agrees with theoretical predictions based on variational perturbation theory.<br />
<br />
当-1 <α<0时,热容在相变温度下具有“扭结”性质。这是'''<font color="#ff8000">液氦liquid helium</font>'''从正常状态到超流体状态的λ相变行为,在此实验中发现α= -0.013±0.003。为最小化样品中的压力差,至少有一次实验在轨道卫星的零重力条件下进行。α的这个实验值与基于'''<font color="#ff8000">变分微扰理论variational perturbation theory</font>'''的预测值相符。<br />
<br />
<br />
<br />
For 0 &lt; {{mvar|α}} &lt; 1, the heat capacity diverges at the transition temperature (though, since {{mvar|α}} &lt; 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional [[Ising model]] for uniaxial magnets, detailed theoretical studies have yielded the exponent {{mvar|α}} ∼ +0.110.<br />
<br />
For 0 &lt; &lt; 1, the heat capacity diverges at the transition temperature (though, since &lt; 1, the enthalpy stays finite). An example of such behavior is the 3D ferromagnetic phase transition. In the three-dimensional Ising model for uniaxial magnets, detailed theoretical studies have yielded the exponent ∼ +0.110.<br />
<br />
当0 <α<1时,热容在相变温度处发散(也因为α<1,所以焓保持有限)。例如'''<font color="#ff8000">3D铁磁相变 3D ferromagnetic phase transition</font>'''。运用'''<font color="#ff8000">单轴磁体uniaxial magnets</font>'''的'''<font color="#ff8000">三维伊辛模型three-dimensional Ising model</font>''',研究人员通过详细的理论研究得出指数α≈+0.110。<br />
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Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a [[logarithm]]ic divergence. However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior.<br />
<br />
Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a logarithmic divergence. However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior.<br />
<br />
当然,存在一些不遵循幂律行为的模型系统。例如,平均场理论预测了相变温度下热容量的有限不连续性,而'''<font color="#ff8000">二维伊辛模型two-dimensional lsing model</font>'''则具有对数散度。但是,这样的系统数量有限,是例外。实际上大多相变仍然表现出幂律行为。<br />
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<br />
Several other critical exponents, {{math| ''β, γ, δ, ν''}}, and {{mvar|η}}, are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as<br />
<br />
Several other critical exponents, , and , are defined, examining the power law behavior of a measurable physical quantity near the phase transition. Exponents are related by scaling relations, such as<br />
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另外还存在其他几个临界指数''β,γ,δ,ν''和''η'',主要用于检查相变附近可测物理量的幂律行为。它们通过比例关系相互联系,例如:<br />
<br />
<math>\beta=\gamma/(\delta-1) , \qquad \nu=\gamma/(2-\eta)</math>.<br />
<br />
It can be shown that there are only two independent exponents, e.g. {{mvar|ν}} and {{mvar|η}}.<br />
It can be shown that there are only two independent exponents, e.g. and .<br />
上式可以证明只有两个独立的指数,例如 ''ν''和''η''。<br />
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<br />
<br />
It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as ''universality''. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid.<br />
<br />
It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid–gas critical point have been found to be independent of the chemical composition of the fluid.<br />
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值得注意的是,在不同系统中发生的相变通常具有相同的临界指数。我们称这种现象为'''<font color="#ff8000">普适性universality</font>'''。例如,液气临界点的临界指数与流体的化学组成无关。<br />
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More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the [[renormalization group]] theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point.<br />
<br />
More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets. Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point.<br />
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以上现象很特别,但并非无法理解,它们与单轴磁体中铁磁相变的临界指数完全匹配。人们认为这类系统具有同一普适性。这里的普适性是相变的重整化群理论的一种预测,指出系统在即将相变时的热力学性质仅取决于少数几个特征,例如'''<font color="#ff8000">维数dimensionality</font>'''和'''<font color="#ff8000">对称性symmetry</font>''',对系统的基本微观特性并不敏感。同样,相关长度的差异性也是非常重要的因素。<br />
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=== Critical slowing down and other phenomena 临界慢化和其他现象 ===<br />
<br />
There are also other critical phenomena; e.g., besides ''static functions'' there is also ''critical dynamics''. As a consequence, at a phase transition one may observe critical slowing down or ''speeding up''. The large ''static universality classes'' of a continuous phase transition split into smaller ''dynamic universality'' classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.<br />
<br />
There are also other critical phenomena; e.g., besides static functions there is also critical dynamics. As a consequence, at a phase transition one may observe critical slowing down or speeding up. The large static universality classes of a continuous phase transition split into smaller dynamic universality classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.<br />
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在相变过程中,还存在其他临界现象。例如,除了'''<font color="#ff8000">静态函数static functions</font>'''外,还存在临界动态。因此在相变发生时,人们可能会观察到明显的减速或加速现象。连续相变的静态普适性可以被分成更小的动态普适性。除了临界指,磁场的某些静态或动态函数以及与临界值的温差也存在普适性关系。<br />
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=== Percolation theory 渗流理论===<br />
<br />
Another phenomenon which shows phase transitions and critical exponents is [[percolation theory|percolation]]. The simplest example is perhaps percolation in a two dimensional square lattice. Sites are randomly occupied with probability p. For small values of p the occupied sites form only small clusters. At a certain threshold p<sub>c</sub> a giant cluster is formed and we have a second-order phase transition. The behavior of P<sub>∞</sub> near p<sub>c</sub> is, P<sub>∞</sub>~(p-p<sub>c</sub>)<sup>β</sup>, where β is a critical exponent.<br />
<br />
Another phenomenon which shows phase transitions and critical exponents is percolation. The simplest example is perhaps percolation in a two dimensional square lattice. Sites are randomly occupied with probability p. For small values of p the occupied sites form only small clusters. At a certain threshold p<sub>c</sub> a giant cluster is formed and we have a second-order phase transition. The behavior of P<sub>∞</sub> near p<sub>c</sub> is, P<sub>∞</sub>~(p-p<sub>c</sub>)<sup>β</sup>, where β is a critical exponent.<br />
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'''<font color="#ff8000">渗流percolation</font>'''具有临界指数,能够发生相变。最简单的例子是发生在二维方格中的渗流。其中每一个格子以概率''p''标记。对于较小的''p''值,格子就形成较小的'''<font color="#ff8000">团簇clusters</font>'''。但是当p达到某个阈值''Pc''时就会出现一个巨大的团簇,此时发生二阶相变。''Pc''附近的P∞行为是''P∞〜(p − pc)β''——其中β是一个临界指数。<br />
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=== Phase transitions in biological systems 生物系统中的相变 ===<br />
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Phase transitions play many important roles in biological systems. Examples include the [[lipid bilayer]] formation, the [[Coil–globule transition|coil-globule transition]] in the process of [[protein folding]] and [[DNA melting]], liquid crystal-like transitions in the process of [[DNA condensation]], and cooperative ligand binding to DNA and proteins with the character of phase transition.<br />
<br />
Phase transitions play many important roles in biological systems. Examples include the lipid bilayer formation, the coil-globule transition in the process of protein folding and DNA melting, liquid crystal-like transitions in the process of DNA condensation, and cooperative ligand binding to DNA and proteins with the character of phase transition.<br />
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相变在生物系统中也具有重要的作用。比如'''<font color="#ff8000"> 脂质双层lipid bilayer</font>'''的形成,'''<font color="#ff8000"> 蛋白质折叠protein folding</font>'''和'''<font color="#ff8000"> DNA解链DNA melting</font>'''过程中的'''<font color="#ff8000"> 坍塌转变coil–globule transition</font>''','''<font color="#ff8000"> DNA缩合DNA condensation</font>'''过程中的液晶转变,以及具有相变特征的配体与DNA和蛋白质的结合。<br />
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In ''biological membranes'', gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by chloroplast thylakoid membranes which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of linolenic acid, 18-carbon chain with 3-double bonds. Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence, [[spin label]] [[electron paramagnetic resonance]] and [[NMR]] by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.<br />
<br />
In biological membranes, gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes. In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by chloroplast thylakoid membranes which are exposed cold environmental temperatures. Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of linolenic acid, 18-carbon chain with 3-double bonds. Gel-to-liquid crystalline phase transition temperature of biological membranes can be determined by many techniques including calorimetry, fluorescence, spin label electron paramagnetic resonance and NMR by recording measurements of the concerned parameter by at series of sample temperatures. A simple method for its determination from 13-C NMR line intensities has also been proposed.<br />
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在'''<font color="#ff8000"> 生物膜biological membranes</font>'''中,从'''<font color="#ff8000">凝胶gel</font>'''到液晶的相变是其维持生理机能的关键。在凝胶相中,由于'''<font color="#ff8000">膜脂质脂肪酰基链membrane lipid fatty-acyl chains</font>'''的流动性低,'''<font color="#ff8000">膜蛋白membrane proteins</font>'''的运动受到限制,因此其生理机能的发挥受到限制。植物非常依赖暴露于低温环境下'''<font color="#ff8000">叶绿体类囊体膜chloroplast thylakoid membranes</font>'''的'''<font color="#ff8000">光合作用photosynthesis</font>'''。由于其高含量的'''<font color="#ff8000">亚麻酸linolenic acid</font>'''——带有3个双键的18碳链允许高度的脂肪酰基紊乱,类囊体膜即使在相对较低的温度下也能保持固有的流动性。运用众多技术,包括'''<font color="#ff8000">量热法calorimetry</font>''','''<font color="#ff8000">荧光法fluorescence</font>''','''<font color="#ff8000">自旋标记电子顺磁共振spin label electron paramagnetic resonance</font>'''和NMR,通过记录各种实验温度下有关参数的测量值来确定生物膜凝胶到液晶相变的温度。人们还提出了一种用13-C NMR谱线强度来测定的简单方法。<br />
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It has been proposed that some biological systems might lie near critical points. Examples include [[neural network]]s in the salamander retina, bird flocks gene expression networks in Drosophila, and protein folding. However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality. It has also been suggested that biological organisms share two key properties of phase transitions: the change of macroscopic behavior and the coherence of a system at a critical point.<br />
<br />
It has been proposed that some biological systems might lie near critical points. Examples include neural networks in the salamander retina, bird flocks gene expression networks in Drosophila, and protein folding. However, it is not clear whether or not alternative reasons could explain some of the phenomena supporting arguments for criticality. It has also been suggested that biological organisms share two key properties of phase transitions: the change of macroscopic behavior and the coherence of a system at a critical point.<br />
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曾经有观点认为生物系统可能位于临界点附近。例如蝾螈视网膜中的神经网络,果蝇中的鸟群基因表达网络和'''<font color="#ff8000">蛋白质折叠protein folding</font>'''。但是,尚不清楚替代原因是否可以解释某些现象来支持关键性论证。另一个观点认为,生物有机体具有两个重要的相变特性:宏观行为的变化和系统在临界点的一致性。<br />
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The characteristic feature of second order phase transitions is the appearance of fractals in some scale-free properties. It has long been known that protein globules are shaped by interactions with water. There are 20 amino acids that form side groups on protein peptide chains range from hydrophilic to hydrophobic, causing the former to lie near the globular surface, while the latter lie closer to the globular center. Twenty fractals were discovered in solvent associated surface areas of > 5000 protein segments [39]. The existence of these fractals proves that proteins function near critical points of second-order phase transitions.<br />
<br />
The characteristic feature of second order phase transitions is the appearance of fractals in some scale-free properties. It has long been known that protein globules are shaped by interactions with water. There are 20 amino acids that form side groups on protein peptide chains range from hydrophilic to hydrophilic, causing the former to lie near the globular surface, while the latter lie closer to the globular center. Twenty fractals were discovered in solvent associated surface areas of > 5000 protein segments [39]. The existence of these fractals proves that proteins function near critical points of second-order phase transitions.<br />
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二阶相变的特征是在某些'''<font color="#ff8000">无标度特性scale-free properties</font>'''中出现了'''<font color="#ff8000">分形fractals</font>'''。众所周知,蛋白质球是通过与水的相互作用形成的。'''<font color="#ff8000">蛋白质肽链protein peptide chains</font>'''上形成侧基的'''<font color="#ff8000">氨基酸amino acids</font>'''有20种(从'''<font color="#ff8000">亲水性hydrophilic</font>'''到'''<font color="#ff8000">疏水性hydrophilic</font>'''都有)使亲水性的氨基酸位于球状表面附近,疏水性的氨基酸更靠近球状中心。实验人员在一个在与溶剂相关的且表面积大于5000个蛋白质片段的区域中发现了二十个分形。这些分形的存在证明了蛋白质在二阶相变的临界点附近起作用。<br />
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In groups of organisms in stress (when approaching critical transitions), correlations tend to increase, while at the same time, fluctuations also increase. This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants.<br />
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In groups of organisms in stress (when approaching critical transitions), correlations tend to increase, while at the same time, fluctuations also increase. This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants.<br />
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在处于压力下的生物群中(接近临界转变时),相关性会增强,波动也会增加。许多以人、小鼠、树木和草类植物为研究对象的实验都得出了支持性的结果。<br />
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== Experimental 实验性 ==<br />
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A variety of methods are applied for studying the various effects. Selected examples are:<br />
A variety of methods are applied for studying the various effects. Selected examples are:<br />
研究各种效果的方法多种多样。部分示例如下:<br />
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* [[Thermogravimetry]] (very common)<br />
* [[X-ray diffraction]] <br />
* [[Neutron diffraction]]<br />
* [[Raman Spectroscopy]]<br />
* [[SQUID]] (measurement of magnetic transitions)<br />
* [[Hall effect]] (measurement of magnetic transitions)<br />
* [[Mössbauer spectroscopy]] (simultaneous measurement of magnetic and non-magnetic transitions. Limited up to about 800-1000&nbsp;°C)<br />
* [[Perturbed angular correlation]] (simultaneous measurement of magnetic and non-magnetic transitions. No temperature limits. Over 2000&nbsp;°C already performed, theoretical possible up to the highest crystal material, such as [[tantalum hafnium carbide]] 4215&nbsp;°C.)<br />
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* '''<font color="#ff8000"> 热重量分析法(非常常见)Thermogravimetry</font>'''<br />
* '''<font color="#ff8000"> X射线衍射法X-ray diffraction</font>'''<br />
* '''<font color="#ff8000"> 中子衍射Neutron diffraction</font>'''<br />
* '''<font color="#ff8000"> 拉曼光谱法Raman Spectroscopy</font>'''<br />
* '''<font color="#ff8000"> SQUID</font>'''(磁跃迁测量)<br />
* '''<font color="#ff8000"> 霍尔效应Hall effect</font>'''(磁跃迁测量)<br />
* '''<font color="#ff8000"> 穆斯堡尔光谱法Mössbauer spectroscopy</font>'''(同时测量磁性和非磁性跃迁。限制在大约800–1000°C的温度下)<br />
* '''<font color="#ff8000"> 扰动角关联Perturbed angular correlation</font>'''(同时测量磁性和非磁性跃迁。没有温度限制。已经执行了超过2000°C的操作,理论上可能达到最高晶体材料,例如钽碳化carbide 4215°C。)<br />
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== See also 其他参考资料 ==<br />
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* '''<font color="#ff8000"> 同素异形体Allotropy </font>'''<br />
* '''<font color="#ff8000"> 自动催化反应和序生成Autocatalytic reactions and order creation </font>'''<br />
* '''<font color="#ff8000"> 晶体生长Crystal growth </font>'''<br />
** '''<font color="#ff8000"> 谷物异常生长Abnormal grain growth </font>'''<br />
* '''<font color="#ff8000"> 差示扫描量热法Differential scanning calorimetry </font>'''<br />
* '''<font color="#ff8000"> 无扩散相变Diffusionless transformations </font>'''<br />
* '''<font color="#ff8000"> 埃伦费斯特方程Ehrenfest equations </font>'''<br />
* '''<font color="#ff8000"> 阻塞(物理)Jamming (physics) </font>'''<br />
* '''<font color="#ff8000"> 开尔文探针力显微镜Kelvin probe force microscope </font>'''<br />
* '''<font color="#ff8000"> 朗道二阶相变理论Landau theory of second order phase transition</font>'''<br />
* '''<font color="#ff8000"> 激光加热基座法Laser-heated pedestal growth </font>'''<br />
* '''<font color="#ff8000"> 物质状态列表List of states of matter </font>'''<br />
* '''<font color="#ff8000"> 微下拉法Micro-pulling-down </font>'''<br />
* '''<font color="#ff8000"> 渗流理论Percolation theory </font>'''<br />
** '''<font color="#ff8000"> 连续介质渗流理论Continuum percolation theory </font>'''<br />
* '''<font color="#ff8000"> 超流体膜Superfluid film </font>'''<br />
* '''<font color="#ff8000"> 超辐射相变Superradiant phase transition </font>'''<br />
* '''<font color="#ff8000"> 拓扑量子场论Topological quantum field theory </font>'''<br />
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{{Div col end}}<br />
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== References 参考文献 ==<br />
<br />
{{reflist|30em}}<br />
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== Further reading 扩展阅读 ==<br />
<br />
* [[Philip Warren Anderson|Anderson, P.W.]], ''Basic Notions of Condensed Matter Physics'', [[Perseus Publishing]] (1997).<br />
<br />
* [[Amir Faghri|Faghri, A.]], and [[Yuwen Zhang|Zhang, Y.]], [https://www.springer.com/gp/book/9783030221362 Fundamentals of Multiphase Heat Transfer and Flow], [[Springer Nature]] Switzerland AG, 2020.<br />
<br />
* {{cite journal | last1 = Fisher | first1 = M.E. | authorlink = Michael E. Fisher | year = 1974 | title = The renormalization group in the theory of critical behavior | url = | journal = Rev. Mod. Phys. | volume = 46 | issue = 4| pages = 597–616 | doi=10.1103/revmodphys.46.597|bibcode = 1974RvMP...46..597F }}<br />
<br />
* Goldenfeld, N., ''Lectures on Phase Transitions and the Renormalization Group'', Perseus Publishing (1992).<br />
<br />
*{{citation |year=2008 |author=Ivancevic, Vladimir G |author2=Ivancevic, Tijana T |title=Chaos, Phase Transitions, Topology Change and Path Integrals |url=https://books.google.com/books?id=wpsPgHgtxEYC&printsec=frontcover&dq=complex+nonlinearity |place=Berlin |publisher=Springer |isbn=978-3-540-79356-4 |accessdate=14 March 2013 }}<br />
<br />
* M.R.Khoshbin-e-Khoshnazar, ''Ice Phase Transition as a sample of finite system phase transition'', (Physics Education(India)Volume 32. No. 2, Apr - Jun 2016)[http://www.physedu.in/uploads/publication/23/371/4.-Ice-Phase-transition-as-a-sample-of-finite-system-phase--transition.pdf]<br />
<br />
* [[Hagen Kleinert|Kleinert, H.]], ''Gauge Fields in Condensed Matter'', Vol. I, "[[:de:Supraflüssigkeit|Superfluid]] and [[vortex|Vortex lines]]; Disorder Fields, [[Phase Transition]]s,", pp.&nbsp;1–742, [https://archive.is/20060514143926/http://www.worldscibooks.com/physics/0356.htm World Scientific (Singapore, 1989)]; Paperback {{ISBN|9971-5-0210-0}} (readable online [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1/contents1.html physik.fu-berlin.de])<br />
<br />
* [[Hagen Kleinert|Kleinert, H.]] and Verena Schulte-Frohlinde, ''Critical Properties of φ<sup>4</sup>-Theories'', [https://web.archive.org/web/20080226151023/http://www.worldscibooks.com/physics/4733.html World Scientific (Singapore, 2001)]; Paperback {{ISBN|981-02-4659-5}}'' (readable online [http://www.physik.fu-berlin.de/~kleinert/b8 here]).''<br />
<br />
* {{cite journal | last1 = Kogut | first1 = J. | authorlink2 = Kenneth G. Wilson | last2 = Wilson | first2 = K | year = 1974 | title = The Renormalization Group and the epsilon-Expansion | url = | journal = Phys. Rep. | volume = 12 | issue = 2| pages = 75–199 |bibcode = 1974PhR....12...75W |doi = 10.1016/0370-1573(74)90023-4 }}<br />
<br />
* Krieger, Martin H., ''Constitutions of matter : mathematically modelling the most everyday of physical phenomena'', [[University of Chicago Press]], 1996. Contains a detailed pedagogical discussion of [[Lars Onsager|Onsager]]'s solution of the 2-D Ising Model.<br />
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* [[Lev Davidovich Landau|Landau, L.D.]] and [[Evgeny Mikhailovich Lifshitz|Lifshitz, E.M.]], ''Statistical Physics Part 1'', vol. 5 of ''[[Course of Theoretical Physics]]'', Pergamon Press, 3rd Ed. (1994).<br />
<br />
* Mussardo G., "Statistical Field Theory. An Introduction to Exactly Solved Models of Statistical Physics", Oxford University Press, 2010.<br />
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*[[Manfred R. Schroeder|Schroeder, Manfred R.]], ''Fractals, chaos, power laws : minutes from an infinite paradise'', New York: [[W. H. Freeman]], 1991. Very well-written book in "semi-popular" style—not a textbook—aimed at an audience with some training in mathematics and the physical sciences. Explains what scaling in phase transitions is all about, among other things.<br />
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* H. E. Stanley, ''Introduction to Phase Transitions and Critical Phenomena'' (Oxford University Press, Oxford and New York 1971).<br />
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* Yeomans J. M., ''Statistical Mechanics of Phase Transitions'', Oxford University Press, 1992.<br />
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<br />
* Anderson, P.W., 《凝聚态物理的基本概念》, Perseus Publishing (1997).<br />
* Faghri, A., and Zhang, Y., 《多相传热与流动基础》, Springer Nature Switzerland AG, 2020.<br />
* Fisher, M.E. (1974). “临界行为理论中的再规范化”. Rev. Mod. Phys. 46 (4): 597–616. Bibcode:1974RvMP...46..597F. doi:10.1103/revmodphys.46.597.<br />
* Goldenfeld, N., 《关于相变和重整化群的讲座》, Perseus Publishing (1992).<br />
* Ivancevic, Vladimir G; Ivancevic, Tijana T (2008), 《混沌,相变,拓扑变化和路径积分》, Berlin: Springer, ISBN 978-3-540-79356-4, retrieved 14 March 2013<br />
* M.R.Khoshbin-e-Khoshnazar, 《冰的相变作为有限系统相变的一个样本》, (Physics Education(India)Volume 32. No. 2, Apr - Jun 2016)[1]<br />
* Kleinert, H., 《凝聚物质的规范场》, Vol. I, “超流体和涡旋线;无序场,相变”, pp. 1–742, World Scientific (Singapore, 1989); Paperback ISBN 9971-5-0210-0 (readable online physik.fu-berlin.de)<br />
* Kleinert, H. and Verena Schulte-Frohlinde, 《φ4-理论的临界性质》, World Scientific (Singapore, 2001); Paperback ISBN 981-02-4659-5 (readable online here).<br />
* Kogut, J.; Wilson, K (1974). “重整化群和epsilon扩展”. Phys. Rep. 12 (2): 75–199. Bibcode:1974PhR....12...75W. doi:10.1016/0370-1573(74)90023-4.<br />
* Krieger, Martin H., 《物质的构成:对物理现象进行最日常的数学建模》, University of Chicago Press, 1996. 其中包含对Onsager的二维伊辛模型解决方案的详细教学讨论。<br />
* Landau, L.D. and Lifshitz, E.M., 《统计物理学》 Part 1, vol. 5 of Course of Theoretical Physics, Pergamon Press, 3rd Ed. (1994).<br />
* Mussardo G., “统计场论。统计物理学的精确求解模型导论”,Oxford University Press, 2010.<br />
* Schroeder, Manfred R., 《分形,混沌,幂定律:距离无限天堂的分钟路程》, New York: W. H. Freeman, 1991. 写得很好的“半大众”风格的书,而不是教科书,旨在介绍数学和物理科学方面的知识。解释相变的标定是什么。<br />
* H. E. Stanley, 《相变和临界现象导论》(Oxford University Press, Oxford and New York 1971).<br />
* Yeomans J. M., 《相变的统计力学》, Oxford University Press, 1992.<br />
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== External links 相关链接 ==<br />
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{{Commons category|Phase changes}}<br />
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*[http://www.ibiblio.org/e-notes/Perc/contents.htm Interactive Phase Transitions on lattices] with Java applets 使用Java小程序在晶格上进行交互式相变<br />
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*[http://www.sklogwiki.org/SklogWiki/index.php/Universality_classes Universality classes 普适性分类] from Sklogwiki<br />
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{{States of matter}}<br />
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{{DEFAULTSORT:Phase Transition}}<br />
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[[Category:Phase transitions| ]]<br />
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[[Category:Concepts in physics]]<br />
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Category:Concepts in physics<br />
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分类: 物理概念<br />
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[[Category:Critical phenomena]]<br />
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Category:Critical phenomena<br />
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范畴: 临界现象<br />
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<small>This page was moved from [[wikipedia:en:Phase transition]]. Its edit history can be viewed at [[相变/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21436网络中心性2021-01-29T08:40:16Z<p>Vicky:/* 重要限制Important limitations */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
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In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
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They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
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They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
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在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
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==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
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'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
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“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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< math > sum _ { k = 0} ^ infty a _ { r } ^ { k } beta ^ k </math > <br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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for matrix exponentials, where<br />
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for matrix exponentials, where<br />
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矩阵指数,其中<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,'''<font color="#32CD32">加权分布概念的解()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心度得分差异对节点的重要性提供一些见解。此外,弗里曼中心度使人们能够通过比较几个网络的最高中心度得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心度。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心度如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
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In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
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一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
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==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
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'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到'''<font color="#32CD32"> '削弱 Penalized</font>''。在数学上,它被定义为<br />
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:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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[数学][数学]<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
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:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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(x _ j + 1) <br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
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It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
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== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
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{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
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PageRank satisfies the following equation<br />
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网页排名满足下面的等式<br />
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:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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1-alpha { n } ,</math > <br />
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where<br />
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where<br />
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其中<br />
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:<math>L(j) = \sum_{i} a_{ji}</math><br />
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<math>L(j) = \sum_{i} a_{ji}</math><br />
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[ math > l (j) = sum { i } a { ji } </math > <br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
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是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
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A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
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在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
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'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
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:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
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where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
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The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
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渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
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==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
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Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
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==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''==<br />
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The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
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任何网络的中心度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>中心度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的中心度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
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:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
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是具有相同节点数的任何图的点中心性的最大差值之和,然后网络中心度是:<br />
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:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
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== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
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[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
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In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
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在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
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In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
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In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
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为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
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:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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数学,数学<br />
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<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
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这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
<br />
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:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
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值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
<br />
<br />
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:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
<br />
<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
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其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
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==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
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经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<br />
<br />
对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
<br />
The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
<br />
中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
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* [[Distance (graph theory)|Distance in graphs]]<br />
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*阿尔法中心性<br />
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*核心—外围结构<br />
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*距离(图理论)图中的距离<br />
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==Notes and references==<br />
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{{Reflist}}<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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[[Category:Graph theory]]<br />
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Category:Graph theory<br />
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分类: 图论<br />
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[[Category:Graph algorithms]]<br />
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Category:Graph algorithms<br />
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分类: 图形算法<br />
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[[Category:Algebraic graph theory]]<br />
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Category:Algebraic graph theory<br />
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分类: 代数图论<br />
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[[Category:Networks]]<br />
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Category:Networks<br />
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分类: 网络<br />
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[[Category:Network analysis]]<br />
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Category:Network analysis<br />
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分类: 网络分析<br />
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[[Category:Network theory]]<br />
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Category:Network theory<br />
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分类: 网络理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21435网络中心性2021-01-29T08:39:14Z<p>Vicky:/* 弗里曼集中度Freeman centralization */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
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In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
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They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
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They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
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在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
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==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
<br />
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
<br />
Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
<br />
'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
<br />
The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
<br />
The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
<br />
“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
<br />
"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
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“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
<br />
When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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for matrix exponentials, where<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,'''<font color="#32CD32">加权分布概念的解()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心度得分差异对节点的重要性提供一些见解。此外,弗里曼集中度使人们能够通过比较几个网络的最高中心度得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心度。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心度如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
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In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
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一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
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==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
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'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
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卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到'''<font color="#32CD32"> '削弱 Penalized</font>''。在数学上,它被定义为<br />
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:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
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[数学][数学]<br />
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<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
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其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
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卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
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:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
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(x _ j + 1) <br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
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与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
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It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
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结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
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== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
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{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
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PageRank satisfies the following equation<br />
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网页排名满足下面的等式<br />
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:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
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1-alpha { n } ,</math > <br />
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where<br />
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where<br />
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其中<br />
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:<math>L(j) = \sum_{i} a_{ji}</math><br />
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<math>L(j) = \sum_{i} a_{ji}</math><br />
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[ math > l (j) = sum { i } a { ji } </math > <br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
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是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
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==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
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在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
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'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
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渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
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:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
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< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
<br />
<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
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其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
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The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
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The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
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渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
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==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
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==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''==<br />
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The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
任何网络的中心度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>中心度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的中心度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
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:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
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是具有相同节点数的任何图的点中心性的最大差值之和,然后网络中心度是:<br />
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:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
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== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
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[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
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In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
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在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
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In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
<br />
In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
<br />
为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
<br />
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:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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数学,数学<br />
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<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
<br />
这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
<br />
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:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
<br />
<br />
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:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
<br />
<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
<br />
其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
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==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
<br />
经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<br />
<br />
对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
<br />
The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
<br />
中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
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* [[Distance (graph theory)|Distance in graphs]]<br />
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*阿尔法中心性<br />
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*核心—外围结构<br />
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*距离(图理论)图中的距离<br />
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==Notes and references==<br />
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{{Reflist}}<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21434网络中心性2021-01-29T08:37:48Z<p>Vicky:/* 度中心性Degree centrality */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
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In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
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They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
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They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
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在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
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==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
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'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
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“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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< math > sum _ { k = 0} ^ infty a _ { r } ^ { k } beta ^ k </math > <br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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for matrix exponentials, where<br />
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for matrix exponentials, where<br />
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矩阵指数,其中<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,'''<font color="#32CD32">加权分布概念的解()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心度得分差异对节点的重要性提供一些见解。此外,弗里曼集中度使人们能够通过比较几个网络的最高中心度得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心度。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心度如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
<br />
In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
<br />
一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
<br />
==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
<br />
'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
<br />
Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
<br />
卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到'''<font color="#32CD32"> '削弱 Penalized</font>''。在数学上,它被定义为<br />
<br />
<br />
:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
<br />
<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
<br />
[数学][数学]<br />
<br />
<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
<br />
其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
<br />
<br />
<br />
Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
<br />
Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
<br />
卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
<br />
<br />
<br />
:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
<br />
<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
<br />
(x _ j + 1) <br />
<br />
<br />
<br />
Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
<br />
Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
<br />
与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
<br />
<br />
<br />
It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
<br />
It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
<br />
结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
<br />
== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
<br />
{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
<br />
PageRank satisfies the following equation<br />
<br />
网页排名满足下面的等式<br />
<br />
<br />
<br />
:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
<br />
<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
<br />
1-alpha { n } ,</math > <br />
<br />
<br />
<br />
where<br />
<br />
where<br />
<br />
其中<br />
<br />
<br />
<br />
:<math>L(j) = \sum_{i} a_{ji}</math><br />
<br />
<math>L(j) = \sum_{i} a_{ji}</math><br />
<br />
[ math > l (j) = sum { i } a { ji } </math > <br />
<br />
<br />
<br />
is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
<br />
is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
<br />
是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
<br />
<br />
==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
<br />
在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
<br />
<br />
<br />
'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
<br />
<br />
<br />
:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
<br />
<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
<br />
< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
<br />
<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
<br />
<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
<br />
渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
<br />
==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
<br />
==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼集中度Freeman centralization</font>'''==<br />
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The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
任何网络的集中度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>集中度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的集中度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
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:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
<br />
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<br />
is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
<br />
is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
<br />
是具有相同节点数的任何图的点中心性的最大差值之和,然后网络集中度是:<br />
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:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
<br />
<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
<br />
< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
<br />
== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
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[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
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In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
<br />
在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
<br />
In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
<br />
In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
<br />
为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
<br />
<br />
<br />
:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
<br />
<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
<br />
数学,数学<br />
<br />
<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
<br />
这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
<br />
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<br />
:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
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<br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
<br />
Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
<br />
这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
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<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
<br />
<br />
<br />
:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
<br />
<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
<br />
1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
<br />
<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
<br />
其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
<br />
==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
<br />
经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
<br />
For generalizations to weighted networks, see Opsahl et al. (2010).<br />
<br />
对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
<br />
The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
<br />
中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
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* [[Distance (graph theory)|Distance in graphs]]<br />
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*阿尔法中心性<br />
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*核心—外围结构<br />
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*距离(图理论)图中的距离<br />
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==Notes and references==<br />
<br />
{{Reflist}}<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21433网络中心性2021-01-29T08:34:42Z<p>Vicky:/* 重要限制Important limitations */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
<br />
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
<br />
They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
<br />
They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
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在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
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==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
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'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
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“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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<br />
:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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< math > sum _ { k = 0} ^ infty a _ { r } ^ { k } beta ^ k </math > <br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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<br />
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for matrix exponentials, where<br />
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for matrix exponentials, where<br />
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矩阵指数,其中<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,'''<font color="#32CD32">加权分布概念的解()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼中心度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心度得分差异对节点的重要性提供一些见解。此外,弗里曼集中度使人们能够通过比较几个网络的最高中心度得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心性。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心性如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
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In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
<br />
一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
<br />
==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
<br />
'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
<br />
Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
<br />
卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到'''<font color="#32CD32"> '削弱 Penalized</font>''。在数学上,它被定义为<br />
<br />
<br />
:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
<br />
<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
<br />
[数学][数学]<br />
<br />
<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
<br />
其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
<br />
<br />
<br />
Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
<br />
Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
<br />
卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
<br />
<br />
<br />
:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
<br />
<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
<br />
(x _ j + 1) <br />
<br />
<br />
<br />
Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
<br />
Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
<br />
与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
<br />
<br />
<br />
It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
<br />
It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
<br />
结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
<br />
== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
<br />
{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
<br />
PageRank satisfies the following equation<br />
<br />
网页排名满足下面的等式<br />
<br />
<br />
<br />
:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
<br />
<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
<br />
1-alpha { n } ,</math > <br />
<br />
<br />
<br />
where<br />
<br />
where<br />
<br />
其中<br />
<br />
<br />
<br />
:<math>L(j) = \sum_{i} a_{ji}</math><br />
<br />
<math>L(j) = \sum_{i} a_{ji}</math><br />
<br />
[ math > l (j) = sum { i } a { ji } </math > <br />
<br />
<br />
<br />
is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
<br />
is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
<br />
是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
<br />
<br />
==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
<br />
在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
<br />
<br />
<br />
'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
<br />
<br />
<br />
:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
<br />
<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
<br />
< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
<br />
<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
<br />
<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
<br />
渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
<br />
==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
<br />
==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼集中度Freeman centralization</font>'''==<br />
<br />
The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
<br />
任何网络的集中度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>集中度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的集中度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
<br />
<br />
<br />
:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
<br />
<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
<br />
< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
<br />
<br />
<br />
is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
<br />
is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
<br />
是具有相同节点数的任何图的点中心性的最大差值之和,然后网络集中度是:<br />
<br />
<br />
:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
<br />
<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
<br />
< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
<br />
== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
<br />
[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
<br />
In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
<br />
在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
<br />
In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
<br />
In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
<br />
为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
<br />
<br />
<br />
:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
<br />
<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
<br />
数学,数学<br />
<br />
<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
<br />
where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
<br />
这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
<br />
<br />
<br />
:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
<br />
<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
<br />
1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
<br />
<br />
<br />
Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
<br />
Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
<br />
这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
<br />
<br />
<br />
Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
<br />
值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
<br />
<br />
<br />
:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
<br />
<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
<br />
1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
<br />
<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
<br />
where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
<br />
其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
<br />
==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
<br />
经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
<br />
<br />
<br />
<br />
For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
<br />
For generalizations to weighted networks, see Opsahl et al. (2010).<br />
<br />
对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
<br />
<br />
<br />
<br />
The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
<br />
The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
<br />
中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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<br />
==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
<br />
* [[Distance (graph theory)|Distance in graphs]]<br />
<br />
*阿尔法中心性<br />
<br />
*核心—外围结构<br />
<br />
*距离(图理论)图中的距离<br />
<br />
==Notes and references==<br />
<br />
{{Reflist}}<br />
<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E7%BD%91%E7%BB%9C%E4%B8%AD%E5%BF%83%E6%80%A7&diff=21432网络中心性2021-01-29T08:20:40Z<p>Vicky:/* 行走结构特征Characterization by walk structure */</p>
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<div>此词条暂由水流心不竞初译,未经审校,带来阅读不便,请见谅。已由Bai审校。<br />
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{{for|the statistical concept|Central tendency}}<br />
{{Network Science}}<br />
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In [[graph theory]] and [[network theory|network analysis]], indicators of '''centrality''' identify the most important [[vertex (graph theory)|vertices]] within a graph. Applications include identifying the most influential person(s) in a [[social network]], key infrastructure nodes in the [[Internet]] or [[urban network]]s, and [[super-spreader]]s of disease. Centrality concepts were first developed in [[social network analysis]], and many of the terms used to measure centrality reflect their [[sociology|sociological]] origin.<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref><br />
<br />
In graph theory and network analysis, indicators of centrality identify the most important vertices within a graph. Applications include identifying the most influential person(s) in a social network, key infrastructure nodes in the Internet or urban networks, and super-spreaders of disease. Centrality concepts were first developed in , and many of the terms used to measure centrality reflect their sociological origin.<br />
<br />
They should not be confused with [[node influence metric]]s, which seek to quantify the influence of every node in the network.<br />
<br />
They should not be confused with node influence metrics, which seek to quantify the influence of every node in the network.<br />
<br />
在'''<font color="#ff8000">图论 graph theory </font>'''和'''<font color="#ff8000">网络分析 network analysis </font>'''中,'''<font color="#ff8000">中心性 centrality </font>'''指标用于识别图中最重要的顶点。其应用包括在社交网络中识别出最有影响力的个人,在因特网或城市网络中识别出最为关键的基础设施节点,以及识别疾病的超级传播者。中心性的概念最初是在'''<font color="#ff8000">社交网络分析 social network analysis</font>'''中发展起来的,许多用于衡量中心性的术语都反映出了它们的社会学起源。<ref name="NewmanNetworks">Newman, M.E.J. 2010. ''Networks: An Introduction.'' Oxford, UK: Oxford University Press.</ref>中心性不应与节点影响度相混淆,后者意在量化网络中每个节点的影响。<br />
<br />
==中心性指数的定义与特性Definition and characterization of centrality indices==<br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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Centrality indices are answers to the question "What characterizes an important vertex?" The answer is given in terms of a real-valued function on the vertices of a graph, where the values produced are expected to provide a ranking which identifies the most important nodes.<br />
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'''<font color="#ff8000">中心性指数 centrality indices</font>'''是对“重要顶点的特征是什么?”这一问题的回答。这个回答是以图中顶点的实值函数的形式给出的,可根据产生的函数值排序以确定最为重要的节点。<ref name="Bonacich1987">{{cite journal |last1= Bonacich |first1= Phillip|year= 1987 |title= Power and Centrality: A Family of Measures | journal=American Journal of Sociology |volume= 92|issue= 5|pages= 1170–1182|doi=10.1086/228631 |url= }}<!--|accessdate=July 11, 2014--></ref><ref name="Borgatti2005">{{cite journal |last1= Borgatti |first1= Stephen P.|year= 2005 |title= Centrality and Network Flow |journal=Social Networks |volume= 27|issue= |pages= 55–71|doi=10.1016/j.socnet.2004.11.008 |url= |citeseerx= 10.1.1.387.419}}<!--|accessdate= July 11, 2014--></ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208">{{cite journal |author = Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista.|title = Eigenvector centrality for characterization of protein allosteric pathways|journal = Proceedings of the National Academy of Sciences|volume = 115|number = 52|pages = E12201–E12208|year = 2018|doi = 10.1073/pnas.1810452115|pmid = 30530700|pmc = 6310864}}</ref><br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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The word "importance" has a wide number of meanings, leading to many different definitions of centrality. Two categorization schemes have been proposed.<br />
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“重要性”的含义十分广泛,因此导致了许多不同的中心性定义方式,我们可以将各种不同的定义方式划分为如下两类。<br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important.<ref name=Borgatti2005/> "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref> Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<ref name=Borgatti2005/><br />
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"Importance" can be conceived in relation to a type of flow or transfer across the network. This allows centralities to be classified by the type of flow they consider important. "Importance" can alternatively be conceived as involvement in the cohesiveness of the network. This allows centralities to be classified based on how they measure cohesiveness.Both of these approaches divide centralities in distinct categories. A further conclusion is that a centrality which is appropriate for one category will often "get it wrong" when applied to a different category.<br />
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“重要性”可以被设想为与网络中的某种流动或传输有关。这允许根据重要的流动的类型对中心性进行分类。<ref name=Borgatti2005/> “重要性”也可以被设想为与网络的'''<font color="#ff8000">内聚力 cohesiveness</font>'''有关。这允许根据内聚力的度量方式对中心性进行分类。<ref name="Borgatti2006">{{cite journal |last1= Borgatti |first1= Stephen P.|last2= Everett |first2= Martin G.|year= 2006 |title= A Graph-Theoretic Perspective on Centrality |journal=Social Networks |volume= 28|issue= 4|pages= 466–484|doi=10.1016/j.socnet.2005.11.005 |url= }}<!--|accessdate= July 11, 2014--></ref>这两种方法在不同类别中划分了中心性。进一步的结论是,适用于某一类别的中心性在应用于另一类别时往往会“出错”。<ref name=Borgatti2005/><br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one ([[Centrality#Degree centrality|degree centrality]]) to infinite walks ([[Centrality#Eigenvector centrality|eigenvalue centrality]]).<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref> The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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When centralities are categorized by their approach to cohesiveness, it becomes apparent that the majority of centralities inhabit one category. The count of the number of walks starting from a given vertex differs only in how walks are defined and counted. Restricting consideration to this group allows for a soft characterization which places centralities on a spectrum from walks of length one (degree centrality) to infinite walks (eigenvalue centrality). The observation that many centralities share this familial relationships perhaps explains the high rank correlations between these indices.<br />
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当根据内聚力方法对中心性进行分类时,很明显大多数中心性都将被划分于同一类别。起始于给定顶点的步数总和仅取决于步数的定义以及计数方式。这种分类方式的不足表现为它仅能较弱的描绘中心性特征,即按照一步步长('''<font color="#ff8000">度中心性 degree centrality</font>''')到无穷步步长('''<font color="#ff8000">特征向量中心性 eigenvalue centrality</font>''')的方式将中心性置于一种光谱状的分类中。<ref name=Bonacich1987/><ref name="Benzi2013">{{cite journal | last1=Benzi | first1=Michele | last2=Klymko| first2=Christine | year=2013 |title= A matrix analysis of different centrality measures |arxiv=1312.6722 | doi=10.1137/130950550 | volume=36 | issue=2 | journal=SIAM Journal on Matrix Analysis and Applications | pages=686–706}}</ref>观察到许多中心性共享这种家庭关系,这或许能解释这些指数之间的高阶相关性。<br />
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===网络流特征Characterization by network flows===<br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at once.<ref name=Borgatti2005/><br />
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A network can be considered a description of the paths along which something flows. This allows a characterization based on the type of flow and the type of path encoded by the centrality. A flow can be based on transfers, where each indivisible item goes from one node to another, like a package delivery going from the delivery site to the client's house. A second case is serial duplication, in which an item is replicated so that both the source and the target have it. An example is the propagation of information through gossip, with the information being propagated in a private way and with both the source and the target nodes being informed at the end of the process. The last case is parallel duplication, with the item being duplicated to several links at the same time, like a radio broadcast which provides the same information to many listeners at oe.<br />
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一个网络可以被看成是对某种物体流动的路径描述。这允许基于流动的类型和由中心性编码的路径类型进行表征。流可以基于传输,即每个不可分割的项目从一个节点到另一个节点,就像一个包裹从配送站传递到客户的房子。第二种情况是串行复制,在这种情况下,一个项目被复制以便源头和目标节点都拥有它。例如通过流言传播信息,信息以私有方式传播,并在流程结束时通知源节点和目标节点。最后一种情况是并行复制,即项目同时被复制到几个链接,就像无线电广播一次性向多个听众提供相同的信息。<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to [[Distance (graph theory)|geodesics]] (shortest paths), [[Glossary of graph theory terms#path|paths]] (no vertex is visited more than once), [[Glossary of graph theory terms#trail|trails]] (vertices can be visited multiple times, no edge is traversed more than once), or [[Glossary of graph theory terms#walk|walks]] (vertices and edges can be visited/traversed multiple times).<ref name=Borgatti2005/><br />
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Likewise, the type of path can be constrained to geodesics (shortest paths), paths (no vertex is visited more than once), trails (vertices can be visited multiple times, no edge is traversed more than once), or walks (vertices and edges can be visited/traversed multiple times).<br />
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同样,路径类型可以被限定为'''<font color="#ff8000"> 测地线geodesics </font>'''(最短路径)、路径(对顶点的访问不超过一次)、小径(可以访问多次顶点,没有边被访问超过一次)或者步子(可以多次访问/穿过多次顶点和边)。<br />
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===行走结构特征Characterization by walk structure===<br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either ''radial'' or ''medial.'' Radial centralities count walks which start/end from the given vertex. The [[Centrality#Degree centrality|degree]] and [[Centrality#Eigenvector centrality|eigenvalue]] centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's [[Centrality#Betweenness centrality|betweenness]] centrality, the number of shortest paths which pass through the given vertex.<ref name=Borgatti2006/><br />
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An alternative classification can be derived from how the centrality is constructed. This again splits into two classes. Centralities are either radial or medial. Radial centralities count walks which start/end from the given vertex. The degree and eigenvalue centralities are examples of radial centralities, counting the number of walks of length one or length infinity. Medial centralities count walks which pass through the given vertex. The canonical example is Freeman's betweenness centrality, the number of shortest paths which pass through the given vertex.<br />
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可以从中心性的构造方式推导出另一种分类方法。这又分成了两个类。中心性可以是径向的,也可以是中间的。径向中心性计算从给定顶点开始/结束的步数。度中心性和特征向量中心性是'''<font color="#ff8000"> 径向中心性Radial centralities</font>'''的例子,计算长度为一或无穷大的步数。'''<font color="#ff8000"> 中间中心性Medial centralities</font>'''计算通过给定顶点的步数。典型的例子是弗里曼 Freeman的'''<font color="#ff8000"> 中介中心性Betweenness centrality,</font>''',即通过给定顶点的最短路径的数量。<ref name=Borgatti2006/><br />
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Likewise, the counting can capture either the ''volume'' or the ''length'' of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's [[Centrality#Closeness centrality|closeness]] centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example.<ref name=Borgatti2006/> Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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Likewise, the counting can capture either the volume or the length of walks. Volume is the total number of walks of the given type. The three examples from the previous paragraph fall into this category. Length captures the distance from the given vertex to the remaining vertices in the graph. Freeman's closeness centrality, the total geodesic distance from a given vertex to all other vertices, is the best known example. Note that this classification is independent of the type of walk counted (i.e. walk, trail, path, geodesic).<br />
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同样地,计数可以记录行走的数量或长度。量是给定类型的总步数。上一段的三个例子就属于这一类。长度则给出从给定顶点到图中其余顶点的距离。Freeman的'''<font color="#ff8000"> 接近中心性Closeness centrality</font>''',即从一个给定顶点到所有其他顶点的总测地线距离,是最著名的例子。<ref name=Borgatti2006/>请注意,这种分类独立于步行计数的类型(即:步行,小道,路径,测地线)。<br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<ref name=Borgatti2006/><br />
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Borgatti and Everett propose that this typology provides insight into how best to compare centrality measures. Centralities placed in the same box in this 2×2 classification are similar enough to make plausible alternatives; one can reasonably compare which is better for a given application. Measures from different boxes, however, are categorically distinct. Any evaluation of relative fitness can only occur within the context of predetermining which category is more applicable, rendering the comparison moot.<br />
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博尔加蒂 Borgatti和埃弗雷特 Everett提出,这种类型为如何最好地比较中心性度量提供了见解。在这个2×2分类中,放在同一盒子中的中心性足够相似,可以做出合理的选择; 人们可以合理地比较哪个对于给定的应用更好。然而,不同盒子中的度量方法是截然不同的。只有在预先确定哪个类别更适用的情况下,对相对适应性的评估才会发生,这使得比较变得毫无意义。<ref name=Borgatti2006/><br />
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===光谱上存在的径向量中心Radial-volume centralities exist on a spectrum===<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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The characterization by walk structure shows that almost all centralities in wide use are radial-volume measures. These encode the belief that a vertex's centrality is a function of the centrality of the vertices it is associated with. Centralities distinguish themselves on how association is defined.<br />
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步行结构的特征表明,几乎所有广泛使用的中心性都是径向量的衡量。这得出结论顶点的中心性是与之相关联的顶点中心性的函数。中心性根据如何定义关联而不同。<br />
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Bonacich showed that if association is defined in terms of [[Glossary of graph theory terms#walk|walks]], then a family of centralities can be defined based on the length of walk considered.<ref name="Bonacich1987"/> [[Centrality#Degree centrality|Degree centrality]] counts walks of length one, while [[Centrality#Eigenvector centrality|eigenvalue centrality]] counts walks of length infinity. Alternative definitions of association are also reasonable. [[Alpha centrality]] allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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Bonacich showed that if association is defined in terms of walks, then a family of centralities can be defined based on the length of walk considered. Degree centrality counts walks of length one, while eigenvalue centrality counts walks of length infinity. Alternative definitions of association are also reasonable. Alpha centrality allows vertices to have an external source of influence. Estrada's subgraph centrality proposes only counting closed paths (triangles, squares, etc.).<br />
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博纳奇 Bonacich指出,如果联想是根据行走来定义的,那么可以根据考虑的行走长度来定义一个中心性家族。<ref name="Bonacich1987"/>度中心性计算长度为1的行走,特征向量中心性计算长度为无穷大的行走。关联的其他定义也是合理的。'''<font color="#ff8000"> 阿尔法中心性Alpha centrality</font>'''允许顶点有一个外部影响源。埃斯特拉达 Estrada的'''<font color="#ff8000"> 子图中心性Subgraph centrality </font>'''提出只计算封闭路径(三角形、正方形等)。).<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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The heart of such measures is the observation that powers of the graph's adjacency matrix gives the number of walks of length given by that power. Similarly, the matrix exponential is also closely related to the number of walks of a given length. An initial transformation of the adjacency matrix allows a different definition of the type of walk counted. Under either approach, the centrality of a vertex can be expressed as an infinite sum, either<br />
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这些度量方法的核心是这种现象:图中'''<font color="#ff8000"> 邻接矩阵 adjacency matrix </font>'''的幂给出了由该幂给出的步长的数目。同样,'''<font color="#ff8000"> 矩阵指数Matrix exponential</font>'''也与给定步长的数目密切相关。邻接矩阵的初始转换允许对步行计数的类型进行不同的定义。无论采用哪种方法,顶点的中心性都可以表示为无穷和<br />
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:<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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<math>\sum_{k=0}^\infty A_{R}^{k} \beta^k </math><br />
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< math > sum _ { k = 0} ^ infty a _ { r } ^ { k } beta ^ k </math > <br />
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for matrix powers or<br />
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for matrix powers or<br />
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矩阵幂或者<br />
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:<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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<math>\sum_{k=0}^\infty \frac{(A_R \beta)^k}{k!}</math><br />
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< math > sum { k = 0} ^ infty frac {(a _ r beta) ^ k }{ k!{/math > <br />
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for matrix exponentials, where<br />
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for matrix exponentials, where<br />
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矩阵指数,其中<br />
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* <math>k</math> is walk length,<br />
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* <math>A_R</math> is the transformed adjacency matrix, and<br />
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* <math>\beta</math> is a discount parameter which ensures convergence of the sum.<br />
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K为步长,A_R是邻接矩阵的转秩,\beta是保证收敛的折扣参数。<br />
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Bonacich's family of measures does not transform the adjacency matrix. [[Alpha centrality]] replaces the adjacency matrix with its [[resolvent formalism|resolvent]]. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to [[Centrality#Degree centrality|degree centrality]]. As <math>\beta</math> approaches its maximal value, the indices converge to [[Centrality#Eigenvector centrality|eigenvalue centrality]].<ref name=Benzi2013/><br />
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Bonacich's family of measures does not transform the adjacency matrix. Alpha centrality replaces the adjacency matrix with its resolvent. Subgraph centrality replaces the adjacency matrix with its trace. A startling conclusion is that regardless of the initial transformation of the adjacency matrix, all such approaches have common limiting behavior. As <math>\beta</math> approaches zero, the indices converge to degree centrality. As <math>\beta</math> approaches its maximal value, the indices converge to eigenvalue centrality.<br />
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Bonacich的一系列度量并没有改变邻接矩阵。阿尔法中心性用它的解决方案替代了邻接矩阵。子图中心性用它的踪迹取代了邻接矩阵。一个令人吃惊的结论是,不管邻接矩阵最初的转变是什么,所有这些方法都有共同的限制行为。随着贝塔系数趋近于零,指数收敛到度中心性。随着贝塔系数接近其最大值,指数收敛到特征向量中心性。<ref name=Benzi2013/><br />
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===博弈论中心性Game-theoretic centrality===<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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The common feature of most of the aforementioned standard measures is that they assess the importance of a node by focusing only on the role that a node plays by itself. However, in many applications such an approach is inadequate because of synergies that may occur<br />
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上述大多数标准度量的共同特点是,它们通过只关注一个节点本身所扮演的角色来评估确定节点的重要性。然而, 在许多应用中,这种方法是不充分的,因为可能会发生协同作用<br />
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if the functioning of nodes is considered in groups.<br />
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if the functioning of nodes is considered in groups.<br />
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如果将节点的功能分组考虑。<br />
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[[File:Game-theoretic centrality.png|Example of game-theoretic centrality]]<br />
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Example of game-theoretic centrality<br />
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'''<font color="#ff8000"> 博弈论中心性 Game-theoretic centrality</font>'''的例子<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in <ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref> uses the [[Shapley value]]. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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For example, consider the problem of stopping an epidemic. Looking at above image of network, which nodes should we vaccinate? Based on previously described measures, we want to recognize nodes that are the most important in disease spreading. Approaches based only on centralities, that focus on individual features of nodes, may not be good idea. Nodes in the red square, individually cannot stop disease spreading, but considering them as a group, we clearly see that they can stop disease if it has started in nodes <math>v_1</math>, <math>v_4</math>, and <math>v_5</math>. Game-theoretic centralities try to consult described problems and opportunities, using tools from game-theory. The approach proposed in uses the Shapley value. Because of the time-complexity hardness of the Shapley value calculation, most efforts in this domain are driven into implementing new algorithms and methods which rely on a peculiar topology of the network or a special character of the problem. Such an approach may lead to reducing time-complexity from exponential to polynomial.<br />
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例如,考虑阻止流行病的问题。看看上面的网络图像,我们应该给哪些节点接种疫苗?基于前面描述的度量,我们希望识别在疾病传播中最重要的节点。仅仅基于中心性的方法,即关注节点的个别特性,可能不是一个好主意。红色方块中的节点,单独不能阻止疾病的传播,但把它们作为一个群体来考虑,我们清楚地看到,如果疾病在节点 < math > v _ 1 </math > 、 < math > v _ 4 </math > 和 < math > v _ 5 </math > 中开始,它们就能阻止疾病的传播。博弈论中心性试图利用博弈论中的工具来研究所描述的问题和机会。本文提出的方法<ref>Michalak, Aadithya, Szczepański, Ravindran, & Jennings {{ArXiv|1402.0567}}</ref>使用了 Shapley 值。由于 Shapley 值计算的时间复杂性,这一领域的大部分工作都集中在实现新的算法和方法,这些算法和方法依赖于网络的特殊拓扑结构或问题的特殊性质。这种方法可以将时间复杂度从指数级降低到多项式级。<br />
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Similarly, the solution concept [[authority distribution]] (<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref>) applies the [[Shapley-Shubik power index]], rather than the [[Shapley value]], to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020)<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>, such as ranking U.S. colleges.<br />
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Similarly, the solution concept authority distribution () applies the Shapley-Shubik power index, rather than the Shapley value, to measure the bilateral direct influence between the players. The distribution is indeed a type of engenvector centrality. It is used to sort big data objects in Hu (2020), such as ranking U.S. colleges.<br />
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同样,'''<font color="#32CD32">加权分布概念的解()<ref>{{cite journal |last=Hu |first=Xingwei |first2=Lloyd |last2=Shapley |title=On Authority Distributions in Organizations |journal=Games and Economic Behavior |volume=45 |pages=132–170 |year=2003 | doi = 10.1016/s0899-8256(03)00130-1 }}</ref></font>'''采用 Shapley-Shubik 幂指数,而不是 Shapley 值来衡量参与者之间的双边直接影响。这种分布确实是一种产生特征向量中心性的类型。它用于对 Hu (2020)中的大数据对象进行排序<ref>{{cite journal|last=Hu|first=Xingwei|year=2020|volume=7|title=Sorting big data by revealed preference with application to college ranking |journal=Journal of Big Data|doi=10.1186/s40537-020-00300-1|doi-access=free}}</ref>,比如美国大学排名。<br />
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== 重要限制Important limitations ==<br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the [[Krackhardt kite graph]], for which three different notions of centrality give three different choices of the most central vertex.<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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Centrality indices have two important limitations, one obvious and the other subtle. The obvious limitation is that a centrality which is optimal for one application is often sub-optimal for a different application. Indeed, if this were not so, we would not need so many different centralities. An illustration of this phenomenon is provided by the Krackhardt kite graph, for which three different notions of centrality give three different choices of the most central vertex.<br />
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中心性指标有两个重要的局限性,一个显而易见,另一个则不易察觉。显而易见的局限性是,对于一个应用最优的中心性对于另一个应用常常是次优的。事实上,如果不是这样,我们就不需要这么多不同的中心性。克拉克哈特风筝图为这一现象提供了一个例证,对于这个图,三个不同的中心性概念给出了最中心顶点的三种不同选择。<ref>{{cite journal|title=Assessing the Political Landscape: Structure, Cognition, and Power in Organizations|first=David|last=Krackhardt|authorlink=David Krackhardt|journal=Administrative Science Quarterly|volume=35|issue=2|date=June 1990|pages=342–369|doi=10.2307/2393394|jstor=2393394}}</ref><br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices.<ref name=Bonacich1987/><ref name=Borgatti2005/> This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing [[node influence metric]]s to address this problem.<br />
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The more subtle limitation is the commonly held fallacy that vertex centrality indicates the relative importance of vertices. Centrality indices are explicitly designed to produce a ranking which allows indication of the most important vertices. This they do well, under the limitation just noted. They are not designed to measure the influence of nodes in general. Recently, network physicists have begun developing node influence metrics to address this problem.<br />
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更不易察觉的限制是通常会错误地认为顶点中心性表示顶点的相对重要性。中心性指数被明确地设计来产生一个指出最重要顶点的排名。<ref name=Bonacich1987/><ref name=Borgatti2005/>在刚才提到的限制下,他们做得很好。它们通常不用来度量节点的影响力。最近,网络物理学家已经开始开发'''<font color="#ff8000">节点影响力度量Node influence metrics </font>'''来解决这个问题。<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying [[Centrality#Freeman centralization|Freeman centralization]] to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores.<ref name="Freeman1979"/> This approach, however, is seldom seen in practice.{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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The error is two-fold. Firstly, a ranking only orders vertices by importance, it does not quantify the difference in importance between different levels of the ranking. This may be mitigated by applying Freeman centralization to the centrality measure in question, which provide some insight to the importance of nodes depending on the differences of their centralization scores. Furthermore, Freeman centralization enables one to compare several networks by comparing their highest centralization scores. This approach, however, is seldom seen in practice.<br />
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错误有两方面。首先,一个排名只根据顶点的重要性排序,它并不对节点重要性的不同水平进行量化区分。这可以通过将 '''<font color="#ff8000"> 弗里曼集中度Freeman centralization</font>'''应用到中心性度量来缓解,这可以根据节点的中心性得分差异对节点的重要性提供一些见解。此外,弗里曼集中度使人们能够通过比较几个网络的最高中心性得分来比较它们。<ref name="Freeman1979"/>然而,这种方法在实践中很少见到。{{citation needed|reason=I've come across quite some theoretical studies that indicate otherwise. My suggestion is to remove this sentence, if reasonable citation is not provided.|date=September 2015}}<br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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Secondly, the features which (correctly) identify the most important vertices in a given network/application do not necessarily generalize to the remaining vertices. <br />
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其次,用以(正确地)识别给定网络/应用中最重要顶点的特征并不一定适用于其余顶点。<br />
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For the majority of other network nodes the rankings may be meaningless.<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref> This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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For the majority of other network nodes the rankings may be meaningless. This explains why, for example, only the first few results of a Google image search appear in a reasonable order. The pagerank is a highly unstable measure, showing frequent rank reversals after small adjustments of the jump parameter.<br />
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对于大多数其他网络节点,排名可能是没有意义的。<ref name="Lawyer2015" /><ref name="daSilva2012">{{cite journal | last1=da Silva|first1=Renato |last2=Viana|first2=Matheus|last3=da F. Costa |first3=Luciano| title=Predicting epidemic outbreak from individual features of the spreaders| journal=J. Stat. Mech.: Theory Exp. | year=2012|volume=2012|pages=P07005|number=7 | doi=10.1088/1742-5468/2012/07/p07005|arxiv=1202.0024|bibcode=2012JSMTE..07..005A}}</ref><ref name="Bauer2012">{{cite journal | last1=Bauer|first1=Frank | last2=Lizier|first2=Joseph|title=Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: A walk counting approach| journal=Europhys Lett | year=2012| volume=99| pages=68007|number=6 | doi=10.1209/0295-5075/99/68007|arxiv=1203.0502|bibcode=2012EL.....9968007B}}</ref><ref name="Sikic2013">{{ cite journal| last1= Sikic| first1=Mile|last2=Lancic|first2=Alen|last3=Antulov-Fantulin|first3=Nino|last4=Stefanic|first4=Hrvoje| title = Epidemic centrality -- is there an underestimated epidemic impact of network peripheral nodes? |journal = The European Physical Journal B |volume=86 |number=10 |pages=1–13 |year=2013 | doi=10.1140/epjb/e2013-31025-5|arxiv=1110.2558 | bibcode=2013EPJB...86..440S}}</ref>这就解释了为什么,例如,谷歌图片搜索只有前几个结果以合理的顺序出现。网页排名是一个非常不稳定的度量,在对跳转参数进行小的调整之后显示了频繁的秩逆转。<ref name="Ghoshal2011">{{cite journal | last1=Ghoshal | first1= G. | last2= Barabsi |first2= A L | title = Ranking stability and super-stable nodes in complex networks. | journal = Nat Commun | volume =2 | page = 394| year= 2011 | doi=10.1038/ncomms1396 | pmid= 21772265 | bibcode=2011NatCo...2..394G | doi-access= free }}</ref><br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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While the failure of centrality indices to generalize to the rest of the network may at first seem counter-intuitive, it follows directly from the above definitions.<br />
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虽然中心性指数未能推广到网络的其他部分,乍看起来似乎是违反直觉的,但它直接遵循上述定义。<br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<ref name="Lawyer2015">{{cite journal |last1= Lawyer |first1= Glenn |year= 2015 |title= Understanding the spreading power of all nodes in a network: a continuous-time perspective |journal=Sci Rep |volume=5|pages=8665|doi=10.1038/srep08665 |pmid=25727453 |pmc=4345333|arxiv=1405.6707|bibcode=2015NatSR...5E8665L}}</ref><br />
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Complex networks have heterogeneous topology. To the extent that the optimal measure depends on the network structure of the most important vertices, a measure which is optimal for such vertices is sub-optimal for the remainder of the network.<br />
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复杂网络具有异构的拓扑结构。如果最佳度量取决于最重要顶点的网络结构,对于这些顶点最优的度量对于网络的其余部分是次优的。<br />
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==Degree centrality==<br />
=='''<font color="#ff8000"> 度中心性Degree centrality</font>'''==<br />
{{Main|Degree (graph theory)}} <br />
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[[File:6 centrality measures.png|thumb|right|300px|Examples of A) [[Betweenness centrality]], B) [[Closeness centrality]], C) [[Eigenvector centrality]], D) [[Degree centrality]], E) [[Centrality#Harmonic centrality|Harmonic centrality]] and F) [[Katz centrality]] of the same graph.]]<br />
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Examples of A) [[Betweenness centrality, B) Closeness centrality, C) Eigenvector centrality, D) Degree centrality, E) Harmonic centrality and F) Katz centrality of the same graph.]]<br />
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同一幅图中的实例A中介中心性,B紧密中心性,C特征向量中心性,D度中心性,E调和中心性,F'''<font color="#ff8000">卡兹中心性 Katz centrality </font>'''<br />
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Historically first and conceptually simplest is '''degree centrality''', which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely [[indegree]] and [[outdegree]]. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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Historically first and conceptually simplest is degree centrality, which is defined as the number of links incident upon a node (i.e., the number of ties that a node has). The degree can be interpreted in terms of the immediate risk of a node for catching whatever is flowing through the network (such as a virus, or some information). In the case of a directed network (where ties have direction), we usually define two separate measures of degree centrality, namely indegree and outdegree. Accordingly, indegree is a count of the number of ties directed to the node and outdegree is the number of ties that the node directs to others. When ties are associated to some positive aspects such as friendship or collaboration, indegree is often interpreted as a form of popularity, and outdegree as gregariousness.<br />
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历史上第一个并且概念上最简单是度中心性,它定义为一个节点上事件的链接数量(即一个节点拥有的关系数量)。度可以解释为节点捕获的任何流经网络的东西(例如病毒或某些信息)的直接风险。在有向网络的情况下(关系有方向) ,我们通常定义两个独立的度中心性的度量,即 '''<font color="#ff8000"> 入度Indegree</font>'''和'''<font color="#ff8000"> 出度 Outdegree</font>'''。因此,入度是指向该节点的关系数,出度是该节点指向其他节点的关系数。当关系与一些积极的方面如友谊或合作有关时,入度通常被解释为一种受欢迎的形式,而出度则被解释为一种合群的形式。<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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The degree centrality of a vertex <math>v</math>, for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as<br />
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对于给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边,顶点的度中心性定义为<br />
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:<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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<math>C_D(v)= \deg(v)</math><br />
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Calculating degree centrality for all the nodes in a graph takes [[big theta|<math>\Theta(V^2)</math>]] in a [[dense matrix|dense]] [[adjacency matrix]] representation of the graph, and for edges takes <math>\Theta(E)</math> in a [[sparse matrix]] representation.<br />
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Calculating degree centrality for all the nodes in a graph takes <math>\Theta(V^2)</math> in a dense adjacency matrix representation of the graph, and for edges takes <math>\Theta(E)</math> in a sparse matrix representation.<br />
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计算一个图中所有节点的度中心性,在图的密集邻接矩阵表示中采用 Theta (v ^ 2) </math > ,在边的稀疏矩阵表示中采用Theta (e) </math > 。<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of ''graph centralization''.<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref> Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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The definition of centrality on the node level can be extended to the whole graph, in which case we are speaking of graph centralization. Let <math>v*</math> be the node with highest degree centrality in <math>G</math>. Let <math>X:=(Y,Z)</math> be the <math>|Y|</math>-node connected graph that maximizes the following quantity (with <math>y*</math> being the node with highest degree centrality in <math>X</math>):<br />
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节点级中心性的定义可以扩展到整个图,在这种情况下,我们指的是图的中心性。<ref>Freeman, Linton C. "Centrality in social networks conceptual clarification." Social networks 1.3 (1979): 215–239.</ref>设 < math > v </math > 为 < math > g </math > 中度中心性最高的节点。让 < math > x: = (y,z) </math > 是 < math > | y | </math > 节点连接图,最大化下列数量(< math > y * </math > 是 < math > 中度最高的节点) :<br />
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:<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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<math>H= \sum^{|Y|}_{j=1} [C_D(y*)-C_D(y_j)]</math><br />
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< math > h = sum ^ { | y | }{ j = 1}[ c _ d (y *)-c _ d (y _ j)] </math > <br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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Correspondingly, the degree centralization of the graph <math>G</math> is as follows:<br />
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相应地,图形 < math > g </math > 的度中心性如下:<br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)]}{H}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ h } </math > <br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a [[star graph]]), and in this case<br />
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The value of <math>H</math> is maximized when the graph <math>X</math> contains one central node to which all other nodes are connected (a star graph), and in this case<br />
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当图形 < math > x </math > 包含与一个所有其他节点都连接的中心节点(一个星形图)时,< math > h </math > 的值最大化,在这种情况下<br />
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:<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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<math>H=(n-1)\cdot((n-1)-1)=n^2-3n+2.</math><br />
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(n-1)-1) = n ^ 2-3n + 2<br />
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So, for any graph <math>G:=(V,E),</math><br />
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So, for any graph <math>G:=(V,E),</math><br />
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所以,对于任意的图 < math > g: = (v,e) ,</math > <br />
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:<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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<math>C_D(G)= \frac{\sum^{|V|}_{i=1} [C_D(v*)-C_D(v_i)] }{|V|^2-3|V|+2}</math><br />
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< math > c _ d (g) = frac { sum ^ { | v | } _ { i = 1}[ c _ d (v *)-c _ d (v _ i)]}{ | v | ^ 2-3 | v | + 2} </math ><br />
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==Closeness centrality==<br />
=='''<font color="#ff8000"> 紧密中心性Closeness centrality</font>'''==<br />
{{Main|Closeness centrality}}In a [[Connected component (graph theory)|connected]] [[Graph (discrete mathematics)|graph]], the [[Normalization (statistics)|normalized]] '''closeness centrality''' (or '''closeness''') of a node is the average length of the [[Shortest path problem|shortest path]] between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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In a connected graph, the normalized closeness centrality (or closeness) of a node is the average length of the shortest path between the node and all other nodes in the graph. Thus the more central a node is, the closer it is to all other nodes.<br />
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在连通图中,节点的标准紧密中心性(或贴近性)是节点与图中所有其他节点之间最短路径的平均长度。因此,一个节点越是中心,它就越接近所有其他节点。<br />
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Closeness was defined by [[Alex Bavelas]] (1950) as the [[Multiplicative inverse|reciprocal]] of the '''farness''',<ref>Alex Bavelas. Communication patterns in task-oriented groups. ''J. Acoust. Soc. Am'', '''22'''(6):725–730, 1950.</ref><ref>{{cite journal|year=1966|title=The centrality index of a graph|url=|journal=Psychometrika|volume=31|issue=4|pages=581–603|doi=10.1007/bf02289527|pmid=5232444|hdl=10338.dmlcz/101401|last1=Sabidussi|first1=G|hdl-access=free}}</ref> that is:<br />
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Closeness was defined by Alex Bavelas (1950) as the reciprocal of the farness, that is:<br />
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亚历克斯 · 巴维拉斯 Alex Bavelas (1950)将贴近性定义为相对于距离的倒数,即:<br />
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: <math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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<math>C(x)= \frac{1}{\sum_y d(y,x)}</math><br />
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C (x) = frac {1}{ sum _ y d (y,x)} </math > <br />
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where <math>d(y,x)</math> is the [[Distance (graph theory)|distance]] between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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where <math>d(y,x)</math> is the distance between vertices <math>x</math> and <math>y</math>. However, when speaking of closeness centrality, people usually refer to its normalized form, generally given by the previous formula multiplied by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph. This adjustment allows comparisons between nodes of graphs of different sizes.<br />
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其中 < math > d (y,x) </math > 是顶点 < math > x </math > 和 < math > y </math > 之间的距离。然而,当谈到紧密中心性时,人们通常会提到它的标准化形式,一般是以前的公式乘以 < math > N-1 </math > ,其中 < math > n </math > 是图中的节点数。这种调整允许比较不同大小图形的节点。<br />
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Taking distances ''from'' or ''to'' all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in [[directed graph]]s (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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Taking distances from or to all other nodes is irrelevant in undirected graphs, whereas it can produce totally different results in directed graphs (e.g. a website can have a high closeness centrality from outgoing link, but low closeness centrality from incoming links).<br />
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从所有其他节点或到所有其他节点的距离在'''<font color="#ff8000"> 无向图Undirected graphs</font>'''中是不相关的,但是在'''<font color="#ff8000"> 有向图Directed graphs</font>'''中可能产生完全不同的结果(例如:一个网站可以从传出链接获得高的紧密中心性,而从传入链接获得低的紧密中心性)。<br />
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===Harmonic centrality===<br />
=='''<font color="#ff8000"> 调和中心性Harmonic centrality</font>'''==<br />
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In a (not necessarily connected) graph, the '''harmonic centrality''' reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:<br />
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在一个(不一定是连通的)图中,调和中心性反转了紧密中心性定义中的和互反运算:<br />
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: <math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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<math>H(x)= \sum_{y \neq x} \frac{1}{d(y,x)}</math><br />
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< math > h (x) = sum { y neq x } frac {1}{ d (y,x)} </math > <br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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where <math>1 / d(y,x) = 0</math> if there is no path from <math>y</math> to <math>x</math>. Harmonic centrality can be normalized by dividing by <math>N-1</math>, where <math>N</math> is the number of nodes in the graph.<br />
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其中 < math > 1/d (y,x) = 0 </math > 如果没有来自< math > y </math > to < math > x </math >的路径 。调和中心性可以通过除以 < math > N-1 </math > 来标准化,其中 < math > n </math > 是图中的节点数。<br />
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Harmonic centrality was proposed by [[Massimo Marchiori|Marchiori]] and [[Vito Latora|Latora]] (2000)<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref> and then independently by Dekker (2005), using the name "valued centrality,"<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref> and by Rochat (2009).<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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Harmonic centrality was proposed by Marchiori and Latora (2000) and then independently by Dekker (2005), using the name "valued centrality," and by Rochat (2009).<br />
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调和中心性是由马奇奥里 Marchiori 和拉托拉 Latora (2000)提出的<ref name="marchiorilatora2000">{{citation| journal = Physica A: Statistical Mechanics and Its Applications | last1 = Marchiori | first1 = Massimo | last2 = Latora | first2 = Vito | year = 2000 | volume = 285 | issue = 3–4 | pages = 539–546 | title = Harmony in the small-world | doi=10.1016/s0378-4371(00)00311-3| arxiv = cond-mat/0008357 | bibcode = 2000PhyA..285..539M }}</ref>,然后由德克 Dekker (2005)以“有价值的中心性”之名独立提出的,<ref>{{cite journal|first1=Anthony|last1=Dekker|title=Conceptual Distance in Social Network Analysis|journal=Journal of Social Structure|volume=6|issue=3|year=2005|url=http://www.cmu.edu/joss/content/articles/volume6/dekker/index.html}}</ref>再由罗切特 Rochat提出(2009)。<ref>{{cite conference | author = Yannick Rochat | title = Closeness centrality extended to unconnected graphs: The harmonic centrality index | conference = Applications of Social Network Analysis, ASNA 2009 | url = http://infoscience.epfl.ch/record/200525/files/%5bEN%5dASNA09.pdf }}</ref><br />
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==Betweenness centrality==<br />
=='''<font color="#ff8000"> 中介中心性Betweenness centrality</font>'''==<br />
{{Main|Betweenness centrality}}<br />
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[[File:Graph betweenness.svg|240px|right|thumb|Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.]]<br />
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Hue (from red&nbsp;=&nbsp;0 to blue&nbsp;=&nbsp;max) shows the node betweenness.<br />
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色调(从红色 = 0到蓝色 = max)表示'''<font color="#ff8000"> 节点中介性node betweenness </font>'''。<br />
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'''Betweenness''' is a centrality measure of a [[vertex (graph theory)|vertex]] within a [[Graph (discrete mathematics)|graph]] (there is also [[edge (graph theory)|edge]] betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by [[Linton Freeman]]<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref> In his conception, vertices that have a high probability to occur on a randomly chosen [[shortest path problem|shortest path]] between two randomly chosen vertices have a high betweenness.<br />
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Betweenness is a centrality measure of a vertex within a graph (there is also edge betweenness, which is not discussed here). Betweenness centrality quantifies the number of times a node acts as a bridge along the shortest path between two other nodes. It was introduced as a measure for quantifying the control of a human on the communication between other humans in a social network by Linton Freeman In his conception, vertices that have a high probability to occur on a randomly chosen shortest path between two randomly chosen vertices have a high betweenness.<br />
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中介性是图中顶点的中心性度量(也有边中介性,这里没有讨论)。中介中心性量化了一个节点沿着其他两个节点之间的最短路径充当桥梁的次数。在林顿 · 弗里曼 Linton Freeman<ref name="freeman1977">{{cite journal |last1 = Freeman |first1 = Linton | year=1977| title = A set of measures of centrality based upon betweenness | journal = Sociometry| volume=40|issue = 1 | pages=35–41 | doi=10.2307/3033543|jstor = 3033543 }}</ref>的概念中,它是作为一种量化一个人对社交网络中其他人之间交流控制的度量被引入的,在两个随机选择的顶点之间随机选择的最短路径上出现概率高的顶点具有很高的中介性。<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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The betweenness of a vertex <math>v</math> in a graph <math>G:=(V,E)</math> with <math>V</math> vertices is computed as follows:<br />
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在一个图 < math > g: = (v,e) </math > 与 < math > v </math > 的顶点中介性计算如下:<br />
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# For each pair of vertices (''s'',''t''), compute the [[Shortest path problem|shortest paths]] between them.<br />
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For each pair of vertices (s,t), compute the shortest paths between them.<br />
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对于每一对顶点(s,t) ,计算它们之间的最短路径。<br />
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# For each pair of vertices (''s'',''t''), determine the fraction of shortest paths that pass through the vertex in question (here, vertex ''v'').<br />
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For each pair of vertices (s,t), determine the fraction of shortest paths that pass through the vertex in question (here, vertex v).<br />
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对于每对顶点(s,t) ,确定通过该顶点(这里是顶点 v)的最短路径的分数。<br />
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# Sum this fraction over all pairs of vertices (''s'',''t'').<br />
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Sum this fraction over all pairs of vertices (s,t).<br />
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对所有顶点对(s,t)求这个分数的和。<br />
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More compactly the betweenness can be represented as:<ref name="brandes">{{cite journal |last1 = Brandes |first1 = Ulrik | year=2001 |title = A faster algorithm for betweenness centrality | journal = Journal of Mathematical Sociology| volume=25|issue = 2 | pages=163–177| url = http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.11.2024 | accessdate = October 11, 2011| format = PDF | doi=10.1080/0022250x.2001.9990249|citeseerx = 10.1.1.11.2024 }}</ref><br />
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More compactly the betweenness can be represented as:<br />
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更确切地说,中介性可以表示为:<br />
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:<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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<math>C_B(v)= \sum_{s \neq v \neq t \in V}\frac{\sigma_{st}(v)}{\sigma_{st}}</math><br />
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{ math > c _ b (v) = sum _ { s neq v neq t in v } frac { sigma _ st }(v)}{ sigma _ st } </math > <br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including ''v'', which for [[Digraph (mathematics)|directed graphs]] is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected [[Star (graph theory)|star graph]], the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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where <math>\sigma_{st}</math> is total number of shortest paths from node <math>s</math> to node <math>t</math> and <math>\sigma_{st}(v)</math> is the number of those paths that pass through <math>v</math>. The betweenness may be normalised by dividing through the number of pairs of vertices not including v, which for directed graphs is <math>(n-1)(n-2)</math> and for undirected graphs is <math>(n-1)(n-2)/2</math>. For example, in an undirected star graph, the center vertex (which is contained in every possible shortest path) would have a betweenness of <math>(n-1)(n-2)/2</math> (1, if normalised) while the leaves (which are contained in no shortest paths) would have a betweenness of 0.<br />
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其中 < math > sigma { st } </math > 是从节点 < math > s </math > 到节点 < math > t </math > 的最短路径总数,< math > sigma { st }(v) </math > 是通过 < math > v </math > 的路径数。中介性也许可以通过除以不包括V的顶点对的数目被规范化,对于有向图是 < math > (n-1)(n-2) </math > ,对于无向图是 < math > (n-1)(n-2)/2 </math > 。例如,在一个无向星图中,中心顶点(包含在每个可能的最短路径中)的中介性为 < math > (n-1)(n-2)/2 </math > (1,如果标准化) ,而叶节点(包含在没有最短路径中)的中介性为0。<br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires [[Big O notation|<math>O(V^3)</math>]] time with the [[Floyd–Warshall algorithm]]. However, on sparse graphs, [[Johnson's algorithm]] may be more efficient, taking [[Big O notation|<math>O(V^2 \log V + V E)</math>]] time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm<ref name=brandes/> which takes [[Big O notation|<math>O(V E)</math>]] time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<ref name="brandes" /><br />
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From a calculation aspect, both betweenness and closeness centralities of all vertices in a graph involve calculating the shortest paths between all pairs of vertices on a graph, which requires <math>O(V^3)</math> time with the Floyd–Warshall algorithm. However, on sparse graphs, Johnson's algorithm may be more efficient, taking <math>O(V^2 \log V + V E)</math> time. In the case of unweighted graphs the calculations can be done with Brandes' algorithm which takes <math>O(V E)</math> time. Normally, these algorithms assume that graphs are undirected and connected with the allowance of loops and multiple edges. When specifically dealing with network graphs, often graphs are without loops or multiple edges to maintain simple relationships (where edges represent connections between two people or vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice.<br />
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从计算的角度来看,图中所有顶点的中介中心性和紧密中心性都涉及到计算图中所有顶点对之间的最短路径,采用<math>O(V^3)</math>时间和 弗洛伊德-沃肖尔 Floyd-Warshall算法。然而,对于稀疏图,约翰逊 Johnson算法的效率可能更高,采用 < math > o (v ^ 2 log v + v e) </math > 时间。在不加权图的情况下,可以用布兰德斯 Brandes 的算法进行计算<ref name=brandes/>,该算法需要 < math > o (v e) </math > 时间。一般情况下,这些算法假定图是无向的,并且连通图中允许有圈和多条边。当专门处理网络图时,图通常没有环或多条边来维持简单的关系(其中的边表示两个人或顶点之间的联系)。在这种情况下,使用 Brandes 的算法将最终的中心性分数除以2来计算每条被重复计算的最短路径。<ref name="brandes" /><br />
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==Eigenvector centrality==<br />
=='''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
{{main|Eigenvector centrality}}<br />
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'''Eigenvector centrality''' (also called '''eigencentrality''') is a measure of the influence of a [[node (networking)|node]] in a [[network (mathematics)|network]]. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/> [[Google]]'s [[PageRank]] and the [[Katz centrality]] are variants of the eigenvector centrality.<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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Eigenvector centrality (also called eigencentrality) is a measure of the influence of a node in a network. It assigns relative scores to all nodes in the network based on the concept that connections to high-scoring nodes contribute more to the score of the node in question than equal connections to low-scoring nodes.<br />
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特征向量中心性 (也称为特征中心性)是对网络中节点影响的一种度量。它将相对得分分配给网络中的所有节点,这是基于这样一个概念: 连接得分高的节点比连接得分低的节点对得分贡献更大。<ref>{{cite journal|title = The mathematics of networks|url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf|author = M. E. J. Newman|accessdate = 2006-11-09}}</ref><ref name="Christian F. A. Negre, Uriel N. Morzan, Heidi P. Hendrickson, Rhitankar Pal, George P. Lisi, J. Patrick Loria, Ivan Rivalta, Junming Ho, Victor S. Batista. 2018 E12201--E12208"/>谷歌的网页排名和卡兹中心性是特征向量中心性的变体。<ref name="ams">{{Cite web | url=http://www.ams.org/samplings/feature-column/fcarc-pagerank | title=American Mathematical Society}}</ref><br />
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=== Using the adjacency matrix to find eigenvector centrality ==<br />
==使用'''<font color="#ff8000"> 邻接矩阵The adjacency matrix</font>'''发现'''<font color="#ff8000">特征向量中心性 Eigenvector centrality</font>'''==<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the [[adjacency matrix]], i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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For a given graph <math>G:=(V,E)</math> with <math>|V|</math> number of vertices let <math>A = (a_{v,t})</math> be the adjacency matrix, i.e. <math>a_{v,t} = 1</math> if vertex <math>v</math> is linked to vertex <math>t</math>, and <math>a_{v,t} = 0</math> otherwise. The relative centrality score of vertex <math>v</math> can be defined as:<br />
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对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math >的顶点数 让 < math > a = (a { v,t }) </math > 成为邻接矩阵。即,如果顶点 < math > > v </math > 与 math > t </math > 相连,而 < math > a { v,t } = 0 </math > 不然。顶点 < math > v </math > 的相对中心性评分可以定义为:<br />
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:<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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<math>x_v = \frac{1}{\lambda} \sum_{t \in M(v)}x_t = \frac{1}{\lambda} \sum_{t \in G} a_{v,t}x_t</math><br />
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在 m (v)} x _ t = frac {1}{ lambda } sum { t in g } a { v,t } x _ t </math > <br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the [[eigenvector]] equation<br />
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where <math>M(v)</math> is a set of the neighbors of <math>v</math> and <math>\lambda</math> is a constant. With a small rearrangement this can be rewritten in vector notation as the eigenvector equation<br />
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其中 < math > m (v) </math > 是 < math >的相邻集合,而< math > > lambda </math >是一个常量。通过一个小的重新排列,这可以用向量符号重写为特征向量方程。<br />
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:<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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<math>\mathbf{Ax} = {\lambda}\mathbf{x}</math><br />
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[ math > mathbf { Ax } = { lambda } mathbf { x } </math > <br />
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In general, there will be many different [[eigenvalue]]s <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the [[Perron–Frobenius theorem]]. This greatest eigenvalue results in the desired centrality measure.<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref> The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices ''n''. [[Power iteration]] is one of many [[eigenvalue algorithm]]s that may be used to find this dominant eigenvector.<ref name="ams" /> Furthermore, this can be generalized so that the entries in ''A'' can be real numbers representing connection strengths, as in a [[stochastic matrix]].<br />
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In general, there will be many different eigenvalues <math>\lambda</math> for which a non-zero eigenvector solution exists. Since the entries in the adjacency matrix are non-negative, there is a unique largest eigenvalue, which is real and positive, by the Perron–Frobenius theorem. This greatest eigenvalue results in the desired centrality measure. The <math>v^{th}</math> component of the related eigenvector then gives the relative centrality score of the vertex <math>v</math> in the network. The eigenvector is only defined up to a common factor, so only the ratios of the centralities of the vertices are well defined. To define an absolute score one must normalise the eigenvector, e.g., such that the sum over all vertices is 1 or the total number of vertices n. Power iteration is one of many eigenvalue algorithms that may be used to find this dominant eigenvector. Furthermore, this can be generalized so that the entries in A can be real numbers representing connection strengths, as in a stochastic matrix.<br />
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一般情况下,存在许多不同的特征值< math > > lambda </math >,对于这些特征值存在一个非零特征向量解。由于邻接矩阵中的项是非负的,所以由 佩龙-弗罗贝尼乌斯 Perron- Frobenius定理得出,它有一个唯一的正实数最大特征值。由这个最大的特征值得出期望的中心性度量。<ref>{{cite journal | author = M. E. J. Newman | title = The mathematics of networks | url = http://www-personal.umich.edu/~mejn/papers/palgrave.pdf | accessdate = 2006-11-09}}</ref>相关特征向量的 < math > v ^ { th } </math > 分量给出了网络中顶点 < math > v </math > 的相对中心性评分。特征向量只定义了一个公共因子,所以只有顶点中心性的比例是明确定义的。要定义一个绝对分数,必须对特征向量进行标准化,例如,使所有顶点的和为1或顶点的总数n。幂迭代是许多特征值算法之一,可以用来找到这个主要特征向量。<ref name="ams" />此外,这推广,使得 A中的项可以是表示连接强度的实数,就像在'''<font color="#ff8000"> 随机矩阵 Stochastic matrix</font>'''中一样。<br />
<br />
==Katz centrality==<br />
=='''<font color="#ff8000"> 卡兹中心性 Katz centrality</font>'''==<br />
{{main|Katz centrality}}<br />
<br />
'''Katz centrality'''<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref> is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
<br />
Katz centrality is a generalization of degree centrality. Degree centrality measures the number of direct neighbors, and Katz centrality measures the number of all nodes that can be connected through a path, while the contributions of distant nodes are penalized. Mathematically, it is defined as<br />
<br />
卡兹中心性<ref>Katz, L. 1953. A New Status Index Derived from Sociometric Index. Psychometrika, 39–43.</ref>是度中心性的推广。度中心性度量的是直接相邻节点的数量,卡兹中心性度量的是通过一条路径可以连接的所有节点的数量,而远处节点的贡献会受到'''<font color="#32CD32"> '削弱 Penalized</font>''。在数学上,它被定义为<br />
<br />
<br />
:<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
<br />
<math>x_i = \sum_{k=1}^{\infin}\sum_{j=1}^N \alpha^k (A^k)_{ji}</math><br />
<br />
[数学][数学]<br />
<br />
<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
<br />
where <math>\alpha</math> is an attenuation factor in <math>(0,1)</math>.<br />
<br />
其中 < math > alpha </math > 是 < math > (0,1) </math > 中的衰减因子。<br />
<br />
<br />
<br />
Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
<br />
Katz centrality can be viewed as a variant of eigenvector centrality. Another form of Katz centrality is<br />
<br />
卡兹中心性可以看作是特征向量中心性的一种变体。卡兹中心性的另一种形式是<br />
<br />
<br />
<br />
:<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
<br />
<math>x_i = \alpha \sum_{j =1}^N a_{ij}(x_j+1).</math><br />
<br />
(x _ j + 1) <br />
<br />
<br />
<br />
Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
<br />
Compared to the expression of eigenvector centrality, <math>x_j</math> is replaced by <math>x_j+1.</math><br />
<br />
与特征向量中心性的表达式相比,< math > x _ j </math > 被 < math > x _ j + 1所代替<br />
<br />
<br />
<br />
It is shown that<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref> the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
<br />
It is shown that the principal eigenvector (associated with the largest eigenvalue of <math>A</math>, the adjacency matrix) is the limit of Katz centrality as <math>\alpha</math> approaches <math>\tfrac{1}{\lambda}</math> from below.<br />
<br />
结果表明,<ref>{{cite journal | last1 = Bonacich | first1 = P | year = 1991 | title = Simultaneous group and individual centralities | url = | journal = Social Networks | volume = 13 | issue = 2| pages = 155–168 | doi=10.1016/0378-8733(91)90018-o}}</ref>主特征向量(与 < math > a </math > ,邻接矩阵的最大特征值相关)是卡兹中心性的极限,当 < math > alpha </math > 从下接近 < math > tfrac {1}{ lambda } </math >时 。<br />
<br />
== PageRank centrality ==<br />
=='''<font color="#ff8000"> 网页排名中心性 PageRank centrality </font>'''==<br />
<br />
{{main|PageRank}}'''[[PageRank]]''' satisfies the following equation<br />
<br />
PageRank satisfies the following equation<br />
<br />
网页排名满足下面的等式<br />
<br />
<br />
<br />
:<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
<br />
<math>x_i = \alpha \sum_{j } a_{ji}\frac{x_j}{L(j)} + \frac{1-\alpha}{N},</math><br />
<br />
1-alpha { n } ,</math > <br />
<br />
<br />
<br />
where<br />
<br />
where<br />
<br />
其中<br />
<br />
<br />
<br />
:<math>L(j) = \sum_{i} a_{ji}</math><br />
<br />
<math>L(j) = \sum_{i} a_{ji}</math><br />
<br />
[ math > l (j) = sum { i } a { ji } </math > <br />
<br />
<br />
<br />
is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
<br />
is the number of neighbors of node <math>j</math> (or number of outbound links in a directed graph). Compared to eigenvector centrality and Katz centrality, one major difference is the scaling factor <math>L(j)</math>. Another difference between PageRank and eigenvector centrality is that the PageRank vector is a left hand eigenvector (note the factor <math>a_{ji}</math> has indices reversed).<br />
<br />
是节点 < math > j </math > (或有向图中出站链接的数量)的相邻节点数量。与特征向量中心性和卡兹中心性相比,尺度因子 < math > l (j) </math > 是一个主要的区别。网页排名中心性和特征向量中心性的另一个区别是网页排名中心性向量是一个左手特征向量(注意因子 < math > a _ { ji } </math >具有相反的索引)。<ref>[http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf How does Google rank webpages?] {{webarchive | url= https://web.archive.org/web/20120131083328/http://scenic.princeton.edu/network20q/lectures/Q3_notes.pdf |date=January 31, 2012 }} 20Q: About Networked Life</ref><br />
<br />
<br />
==Percolation centrality==<br />
=='''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''==<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
A slew of centrality measures exist to determine the ‘importance’ of a single node in a complex network. However, these measures quantify the importance of a node in purely topological terms, and the value of the node does not depend on the ‘state’ of the node in any way. It remains constant regardless of network dynamics. This is true even for the weighted betweenness measures. However, a node may very well be centrally located in terms of betweenness centrality or another centrality measure, but may not be ‘centrally’ located in the context of a network in which there is percolation. Percolation of a ‘contagion’ occurs in complex networks in a number of scenarios. For example, viral or bacterial infection can spread over social networks of people, known as contact networks. The spread of disease can also be considered at a higher level of abstraction, by contemplating a network of towns or population centres, connected by road, rail or air links. Computer viruses can spread over computer networks. Rumours or news about business offers and deals can also spread via social networks of people. In all of these scenarios, a ‘contagion’ spreads over the links of a complex network, altering the ‘states’ of the nodes as it spreads, either recoverably or otherwise. For example, in an epidemiological scenario, individuals go from ‘susceptible’ to ‘infected’ state as the infection spreads. The states the individual nodes can take in the above examples could be binary (such as received/not received a piece of news), discrete (susceptible/infected/recovered), or even continuous (such as the proportion of infected people in a town), as the contagion spreads. The common feature in all these scenarios is that the spread of contagion results in the change of node states in networks. Percolation centrality (PC) was proposed with this in mind, which specifically measures the importance of nodes in terms of aiding the percolation through the network. This measure was proposed by Piraveenan et al.<br />
<br />
在复杂网络中,存在大量的中心性度量来确定单个节点的“重要性”。然而,这些度量单纯从拓扑学的角度来量化节点的重要性,节点的值并不以任何方式依赖于节点的状态。不管网络动态如何,它都保持不变。即使对于加权的两者之间的度量也是如此。然而,一个节点可能很好地位于中介中心性或其他中心性度量的中心位置,但可能不是位于有渗滤的网络的上下文中的中心位置。在许多情况下,复杂网络中都会出现“传染”的渗滤现象。例如,病毒或细菌感染可以通过人们的社交网络传播,也就是所谓的接触网络。还可以在更高的抽象层次上考虑疾病的传播问题,设想通过公路、铁路或空中连接起来的城镇或人口中心网络。计算机病毒可以通过计算机网络传播。关于商业活动和交易的谣言或新闻也可以通过人们的社交网络传播。在所有这些情况下,一种“传染病”在一个复杂网络的链接上传播,随着它的传播,无论是可恢复的还是不可恢复的,都会改变节点的“状态”。例如,在流行病学方案中,随着感染扩散,个人从”易感”状态转变为”受感染”状态。在上面的例子中,随着传染的扩散,每个节点可以采取的状态可以是二进制的(例如接收/没有接收到一条新闻)、离散的(易感/受感染/康复) ,甚至是连续的(例如一个城镇中受感染的人的比例) 。这些情景的共同特点是,传染的扩散导致网络中节点状态的改变。'''<font color="#ff8000"> 渗滤中心性 Percolation centrality</font>'''(PC)就是基于这个思想而提出的,它特别地度量了节点在协助网络渗滤方面的重要性。这种度量是由皮拉维南 piraveanan等人提出的。<ref name="piraveenan2013">{{cite journal |last1 = Piraveenan |first1 = M. |last2 = Prokopenko |first2 = M.|last3 = Hossain|first3 = L. |year=2013| title = Percolation Centrality: Quantifying Graph-Theoretic Impact of Nodes during Percolation in Networks | journal = PLOS One | volume=8 | issue=1 | doi=10.1371/journal.pone.0053095 | pages=e53095 | pmid=23349699 | pmc=3551907| bibcode=2013PLoSO...853095P }}</ref><br />
<br />
<br />
<br />
<br />
'''Percolation centrality''' is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
Percolation centrality is defined for a given node, at a given time, as the proportion of ‘percolated paths’ that go through that node. A ‘percolated path’ is a shortest path between a pair of nodes, where the source node is percolated (e.g., infected). The target node can be percolated or non-percolated, or in a partially percolated state.<br />
<br />
渗滤中心性定义为在给定时间内一个给定节点的渗滤路径的比例。“渗滤路径”是一对节点之间的最短路径,其中源节点被渗滤(例如,被感染)。目标节点可以是渗滤的或非渗滤的,或处于部分渗滤状态。<br />
<br />
<br />
<br />
:<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
<br />
<math>PC^t(v)= \frac{1}{N-2}\sum_{s \neq v \neq r}\frac{\sigma_{sr}(v)}{\sigma_{sr}}\frac{{x^t}_s}{{\sum {[{x^t}_i}]}-{x^t}_v}</math><br />
<br />
< math > PC ^ t (v) = frac {1}{ N-2} sum { s neq v neq r } frac { sigma { sr }(v)}{ sigma { sr }} frac { x ^ t }{ sum {[{ x ^ t } i }}}]}}-{ x ^ t }{ v } </math > <br />
<br />
<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
where <math>\sigma_{sr}</math> is total number of shortest paths from node <math>s</math> to node <math>r</math> and <math>\sigma_{sr}(v)</math> is the number of those paths that pass through <math>v</math>. The percolation state of the node <math>i</math> at time <math>t</math> is denoted by <math>{x^t}_i</math> and two special cases are when <math>{x^t}_i=0</math> which indicates a non-percolated state at time <math>t</math> whereas when <math>{x^t}_i=1</math> which indicates a fully percolated state at time <math>t</math>. The values in between indicate partially percolated states ( e.g., in a network of townships, this would be the percentage of people infected in that town).<br />
<br />
其中 < math > σ { sr } </math > 是从节点 < math > s </math > 到节点 < math > r </math >的最短路径的总数, < math > sigma { sr }(v) </math > 是通过 < math > v </math > 的路径的总数。在时间 < math > t </math > 时,节点< math > i</math >的渗滤状态用 < math > { x ^ t } _ i </math > 表示,两个特殊情况是当 < math > { x ^ t } _ i = 0 </math > 表示在时间上是非渗滤状态,而当 < math > < x ^ t </math > i = 1 </math > 表示在时间上是完全渗滤状态。两者之间的值表示部分渗滤状态(例如,在一个城镇网络中,这是该城镇感染者的百分比)。<br />
<br />
<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in [[Big O notation|<math>O(NM)</math>]] time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is [[Big O notation|<math>O(N^3)</math>]].<br />
<br />
The attached weights to the percolation paths depend on the percolation levels assigned to the source nodes, based on the premise that the higher the percolation level of a source node is, the more important are the paths that originate from that node. Nodes which lie on shortest paths originating from highly percolated nodes are therefore potentially more important to the percolation. The definition of PC may also be extended to include target node weights as well. Percolation centrality calculations run in <math>O(NM)</math> time with an efficient implementation adopted from Brandes' fast algorithm and if the calculation needs to consider target nodes weights, the worst case time is <math>O(N^3)</math>.<br />
<br />
渗流路径的权重取决于分配给源节点的渗滤水平,前提是源节点的渗滤水平越高,源节点的路径就越重要。因此,位于源自高渗滤节点的最短路径上的节点可能对渗滤更为重要。PC 的定义也可以扩展到包括目标节点的权重。渗滤中心性计算运行在 < math > o (NM) </math > 时间,高效的实现采用了布兰德斯快速算法,如果计算需要考虑目标节点的权重,最坏情况下时间为 < math > o (n ^ 3) </math > 。<br />
<br />
==Cross-clique centrality==<br />
=='''<font color="#ff8000">跨团中心性 Cross-clique centrality</font>'''==<br />
'''Cross-clique centrality''' of a single node in a complex graph determines the connectivity of a node to different [[clique (graph theory)|clique]]s. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in <ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref> but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
Cross-clique centrality of a single node in a complex graph determines the connectivity of a node to different cliques. A node with high cross-clique connectivity facilitates the propagation of information or disease in a graph. Cliques are subgraphs in which every node is connected to every other node in the clique. The cross-clique connectivity of a node <math>v</math> for a given graph <math>G:=(V,E)</math> with <math>|V|</math> vertices and <math>|E|</math> edges, is defined as <math>X(v)</math> where <math>X(v)</math> is the number of cliques to which vertex <math>v</math> belongs. This measure was used in but was first proposed by Everett and Borgatti in 1998 where they called it clique-overlap centrality.<br />
<br />
复杂图中单个节点的跨团中心性决定了一个节点与不同团的连通性。具有高度跨团连通性的节点有利于信息或疾病在图中的传播。团是一种'''<font color="#ff8000"> 子图 Subgraphs</font>''',团中的每个节点都与团中的其他节点相连。对于一个给定的图 g: = (v,e) </math > 与 < math > | v | </math > 顶点和 < math > | e | </math > 边的跨团连通性,定义为 < math > x (v) </math > x (v) </math > 其中 < math > x (v) </math > 是 < math > v </math > 所属的顶点团数。这个度量应用日久,<ref name="xssworms">{{cite journal |last1 = Faghani|first1 = Mohamamd Reza| year=2013| title = A Study of XSS Worm Propagation and Detection Mechanisms in Online Social Networks | journal = IEEE Transactions on Information Forensics and Security|volume = 8|issue = 11|pages = 1815–1826|doi = 10.1109/TIFS.2013.2280884}}</ref>但是在1998年由埃弗莱特 Everett 和博加提 Borgatti 首次提出,他们称之为'''<font color="#ff8000"> 派系重叠中心性 Clique-overlap centrality</font>'''。<br />
<br />
==Freeman centralization==<br />
=='''<font color="#ff8000"> 弗里曼集中度Freeman centralization</font>'''==<br />
<br />
The '''centralization''' of any network is a measure of how central its most central node is in relation to how central all the other nodes are.<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref> Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size.<ref name="Freeman1979"/> Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
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The centralization of any network is a measure of how central its most central node is in relation to how central all the other nodes are. Centralization measures then (a) calculate the sum in differences in centrality between the most central node in a network and all other nodes; and (b) divide this quantity by the theoretically largest such sum of differences in any network of the same size. Thus, every centrality measure can have its own centralization measure. Defined formally, if <math>C_x(p_i)</math> is any centrality measure of point <math>i</math>, if <math>C_x(p_*)</math> is the largest such measure in the network, and if:<br />
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任何网络的集中度都是衡量其最核心的节点相对于其他所有节点的集聚程度的标准。<ref name="Freeman1979">{{citation | journal = Social Networks | last1 = Freeman | first1 = Linton C. | year = 1979 | volume = 1 | issue = 3 | pages = 215–239 | title = centrality in social networks: Conceptual clarification | url = http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | doi = 10.1016/0378-8733(78)90021-7 | citeseerx = 10.1.1.227.9549 | access-date = 2014-07-31 | archive-url = https://web.archive.org/web/20160222033108/http://leonidzhukov.ru/hse/2013/socialnetworks/papers/freeman79-centrality.pdf | archive-date = 2016-02-22 | url-status = dead }}</ref>集中度的度量方法是: (a)计算网络中最中心的节点与所有其他节点之间的中心性差异之和; (b)将这个数量除以理论上相同规模的任何网络中这种差异之和的最大值。<ref name="Freeman1979"/>因此,每个中心性度量都可以有自己的集中度度量。正式定义,如果 < math > c _ x (p _ i) </math > 是点 < math > i </math > 的中心性度量,如果 < math > c _ x (p _ *) </math > 是网络中最大的中心性度量,如果:<br />
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:<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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<math>\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)</math><br />
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< math > max sum { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i) </math > <br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<ref name="Freeman1979"/><br />
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is the largest sum of differences in point centrality <math>C_x</math> for any graph with the same number of nodes, then the centralization of the network is:<br />
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是具有相同节点数的任何图的点中心性的最大差值之和,然后网络集中度是:<br />
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:<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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<math>C_x=\frac{\sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}{\max \sum_{i=1}^{N} C_x(p_*)-C_x(p_i)}.</math><br />
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< math > c _ x = frac { sum _ { i = 1} ^ { n } c _ x (p _ *)-c _ x (p _ i)}{ max sum _ { i = 1 ^ { n } c _ x (p _ *)-c _ x (p _ i)} . </math ><br />
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== Dissimilarity based centrality measures ==<br />
==基于相异性的中心性度量==<br />
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[[File:Srep17095-f1.jpg|thumbnail|In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.]]<br />
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In the illustrated network, green and red nodes are the most dissimilar because they do not share neighbors between them. So, the green one contributes more to the centrality of the red one than the gray ones, because the red one can access to the blue ones only through the green, and the gray nodes are redundant for the red one, because it can access directly to each gray node without any intermediary.<br />
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在图示的网络中,绿色节点和红色节点最不相似,因为它们之间不共享相邻节点。因此,绿色的节点比灰色的节点对红色节点的中心性的贡献更大,因为红色的节点只能通过绿色访问蓝色的节点,而灰色的节点对于红色的节点是多余的,因为它可以直接访问每个灰色的节点,而不需要任何中介。<br />
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In order to obtain better results in the ranking of the nodes of a given network, in <ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref> are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with [[eigenvector centrality]], calculating the centrality of each node through the solution of the eigenvalue problem<br />
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In order to obtain better results in the ranking of the nodes of a given network, in are used dissimilarity measures (specific to the theory of classification and data mining) to enrich the centrality measures in complex networks. This is illustrated with eigenvector centrality, calculating the centrality of each node through the solution of the eigenvalue problem<br />
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为了在给定网络节点的排序中获得更好的结果,<ref>{{Cite journal|title = Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|journal = Scientific Reports|date = 2015-11-25|pmc = 4658528|pmid = 26603652|volume = 5|doi = 10.1038/srep17095|first = A. J.|last = Alvarez-Socorro|first2 = G. C.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz|pages=17095|bibcode = 2015NatSR...517095A}}</ref>在复杂网络中使用了相异性度量(特定于分类和数据挖掘理论)来丰富中心性度量。用特征向量中心性来说明,通过求解特征值问题来计算每个节点的中心性。<br />
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:<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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<math>W\mathbf{c}=\lambda \mathbf{c}</math><br />
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数学,数学<br />
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where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary [[Matrix similarity|dissimilarity]] matrix, defined through a dissimilitary measure, e.g., [[Jaccard index|Jaccard]] dissimilarity given by<br />
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where <math>W_{ij}=A_{ij}D_{ij}</math> (coordinate-to-coordinate product) and <math>D_{ij}</math> is an arbitrary dissimilarity matrix, defined through a dissimilitary measure, e.g., Jaccard dissimilarity given by<br />
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这里 < math > w { ij } = a { ij } d { ij } </math > (coordinate-to-coordinate product)和 < math > d { ij } </math > 是一个任意的不相似矩阵,通过一个相异性度量来定义,例如,杰卡德 Jaccard相异性由以下给出。<br />
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:<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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<math>D_{ij}=1-\dfrac{|V^{+}(i)\cap V^{+}(j)|}{|V^{+}(i)\cup V^{+}(j)|}</math><br />
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1-dfrac { | v ^ { + }(i) cap v ^ { + }(j) | }{ | v ^ { + }(i) cup v ^ { + }(j) | } </math > <br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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Where this measure permits us to quantify the topological contribution (which is why is called contribution centrality) of each node to the centrality of a given node, having more weight/relevance those nodes with greater dissimilarity, since these allow to the given node access to nodes that which themselves can not access directly.<br />
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这种度量允许我们量化每个节点对给定节点中心性的拓扑贡献(这就是为什么我们称之为贡献中心性) ,对那些相异性较大的节点有更多的权重/相关性,因为这些节点允许给定的节点访问那些它们自己不能直接访问的节点。<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the [[Perron–Frobenius theorem]] to ensure that the above problem has a unique solution for ''λ'' = ''λ<sub>max</sub>'' with '''c''' non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
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Is noteworthy that <math>W</math> is non-negative because <math>A</math> and <math>D</math> are non-negative matrices, so we can use the Perron–Frobenius theorem to ensure that the above problem has a unique solution for λ = λ<sub>max</sub> with c non-negative, allowing us to infer the centrality of each node in the network. Therefore, the centrality of the i-th node is<br />
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值得注意的是,< math > w </math > 是非负的,因为 < math > a </math > 和 < math > d </math > 都是非负矩阵,所以我们可以使用Perron–Frobenius定理来确保上述问题对于 c 非负的 = < sub > max </sub > 有唯一的解,这样我们就可以推断出网络中每个节点的中心性。因此,i-th 节点的中心性为<br />
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:<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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<math>c_i=\dfrac{1}{n}\sum_{j=1}^{n}W_{ij}c_{j}, \,\,\,\,\,\, j=1,\cdots,n</math><br />
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1{ n } sum { j = 1} ^ { n } w { ij } c { j } ,,,,,j = 1,cdots,n </math > <br />
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where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in <ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref> obtaining improved results in the studied cases.<br />
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where <math>n</math> is the number of the nodes in the network. Several dissimilarity measures and networks were tested in obtaining improved results in the studied cases.<br />
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其中 < math > n </math > 是网络中的节点数。在所研究的案例中,为了获得改进的结果,测试了一些相异性度量和网络被测试。<ref>{{Cite web|url = http://www.nature.com/article-assets/npg/srep/2015/151125/srep17095/extref/srep17095-s1.pdf|title = Supplementary Information for Eigencentrality based on dissimilarity measures reveals central nodes in complex networks|date = |website = |publisher = Nature Publishing Group|last = Alvarez-Socorro|first = A.J.|last2 = Herrera-Almarza|first3 = L. A.|last3 = González-Díaz}}</ref><br />
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==Extensions==<br />
==扩展==<br />
Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality<ref>{{cite journal | last1 = Braha | first1 = D. | last2 = Bar-Yam | first2 = Y. | year = 2006 | title = From Centrality to Temporary Fame: Dynamic Centrality in Complex Networks | url = | journal = Complexity | volume = 12 | issue = 2| pages = 59–63 | doi=10.1002/cplx.20156| arxiv = physics/0611295 | bibcode = 2006Cmplx..12b..59B }}</ref> in the context of time-dependent and temporal networks.<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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Empirical and theoretical research have extended the concept of centrality in the context of static networks to dynamic centrality in the context of time-dependent and temporal networks.<br />
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经验和理论研究已经将静态网络中的中心性概念扩展到时间依赖网络和时间网络中的动态中心性。<ref>{{cite journal | last1 = Hill | first1 = S.A. | last2 = Braha | first2 = D. | year = 2010 | title = Dynamic Model of Time-Dependent Complex Networks | url = | journal = Physical Review E | volume = 82 | issue = 4| page = 046105 | doi=10.1103/physreve.82.046105| pmid = 21230343 | arxiv = 0901.4407 | bibcode = 2010PhRvE..82d6105H }}</ref><ref>Gross, T. and Sayama, H. (Eds.). 2009. ''Adaptive Networks: Theory, Models and Applications.'' Springer.</ref><ref>Holme, P. and Saramäki, J. 2013. ''Temporal Networks.'' Springer.</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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For generalizations to weighted networks, see Opsahl et al. (2010).<br />
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对加权网络的推广,见 Opsahl 等人。(2010). <ref>{{cite journal | last1 = Opsahl | first1 = Tore | last2 = Agneessens | first2 = Filip | last3 = Skvoretz | first3 = John | title = Node centrality in weighted networks: Generalizing degree and shortest paths | doi = 10.1016/j.socnet.2010.03.006 | year = 2010 | pages = 245–251 | volume = 32 | journal = Social Networks | url = http://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | issue = 3 | access-date = 2010-04-23 | archive-url = https://web.archive.org/web/20180226080331/https://toreopsahl.com/2010/04/21/article-node-centrality-in-weighted-networks-generalizing-degree-and-shortest-paths/ | archive-date = 2018-02-26 | url-status = dead }}</ref><br />
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The concept of centrality was extended to a group level as well. For example, '''group betweenness''' centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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The concept of centrality was extended to a group level as well. For example, group betweenness centrality shows the proportion of geodesics connecting pairs of non-group members that pass through the group.<br />
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中心性的概念也扩展到了群体层次。例如,组间的中介中心性显示了连接穿过组的成对非组成员的测地线的比例。<ref name="group1">Everett, M. G. and Borgatti, S. P. (2005). Extending centrality. In P. J. Carrington, J. Scott and S. Wasserman (Eds.), ''Models and methods in social network analysis'' (pp. 57–76). New York: Cambridge University Press.</ref><ref name="group2">Puzis, R., Yagil, D., Elovici, Y., Braha, D. (2009).[http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf Collaborative attack on Internet users’ anonymity] {{Webarchive|url=https://web.archive.org/web/20131207133417/http://necsi.edu/affiliates/braha/Internet_Research_Anonimity.pdf |date=2013-12-07 }}, ''Internet Research'' '''19'''(1)</ref><br />
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==See also==<br />
==又及==<br />
* [[Alpha centrality]]<br />
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* [[Core–periphery structure]]<br />
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* [[Distance (graph theory)|Distance in graphs]]<br />
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*阿尔法中心性<br />
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*核心—外围结构<br />
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*距离(图理论)图中的距离<br />
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==Notes and references==<br />
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{{Reflist}}<br />
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==Further reading==<br />
拓展阅读<br />
* Koschützki, D.; Lehmann, K. A.; Peeters, L.; Richter, S.; Tenfelde-Podehl, D. and Zlotowski, O. (2005) Centrality Indices. In Brandes, U. and Erlebach, T. (Eds.) ''Network Analysis: Methodological Foundations'', pp.&nbsp;16–61, LNCS 3418, Springer-Verlag.<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Centrality]]. Its edit history can be viewed at [[网络中心性/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E9%87%8D%E5%B0%BE%E5%88%86%E5%B8%83&diff=21361重尾分布2021-01-26T14:27:48Z<p>Vicky:/* Subexponential distributions 次指数分布 */</p>
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<div>此词条Jie翻译。已由Smile审校。<br />
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{{too technical|date=May 2020}}<br />
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{{mergefrom|Fat-tailed distribution|date=May 2020}}<br />
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In [[probability theory]], '''heavy-tailed distributions''' are [[probability distribution]]s whose tails are not exponentially bounded:<ref name="Asmussen">{{Cite book | doi = 10.1007/0-387-21525-5_10 | first = S. R. | last = Asmussen| chapter = Steady-State Properties of GI/G/1 | title = Applied Probability and Queues | series = Stochastic Modelling and Applied Probability | volume = 51 | pages = 266–301 | year = 2003 | isbn = 978-0-387-00211-8 | pmid = | pmc = }}</ref> that is, they have heavier tails than the [[exponential distribution]]. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy.<br />
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In probability theory, heavy-tailed distributions are probability distributions whose tails are not exponentially bounded: that is, they have heavier tails than the exponential distribution. In many applications it is the right tail of the distribution that is of interest, but a distribution may have a heavy left tail, or both tails may be heavy.<br />
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在概率论中,<font color="#ff8000">重尾分布 Heavy-tailed distributions</font>是指其尾部呈现出不受指数限制的概率分布<ref name="Asmussen">{{Cite book | doi = 10.1007/0-387-21525-5_10 | first = S. R. | last = Asmussen| chapter = Steady-State Properties of GI/G/1 | title = Applied Probability and Queues | series = Stochastic Modelling and Applied Probability | volume = 51 | pages = 266–301 | year = 2003 | isbn = 978-0-387-00211-8 | pmid = | pmc = }}</ref>:也就是说,它们的尾部比<font color="#ff8000">指数分布 exponential distribution </font> “重”。在许多应用中,关注的是分布的右尾,但是分布的左尾可能也很重,或者两个尾都很重。<br />
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There are three important subclasses of heavy-tailed distributions: the [[fat-tailed distribution]]s, the [[long-tailed distribution]]s and the '''subexponential distributions'''. In practice, all commonly used heavy-tailed distributions belong to the subexponential class.<br />
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There are three important subclasses of heavy-tailed distributions: the fat-tailed distributions, the long-tailed distributions and the subexponential distributions. In practice, all commonly used heavy-tailed distributions belong to the subexponential class.<br />
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重尾分布有三个重要的子类:<font color="#ff8000">胖尾分布 Fat-tailed distribution</font>,<font color="#ff8000">长尾分布 Long-tailed distribution</font>和<font color="#ff8000">次指数分布 Subexponential distributions</font>。实际上,所有常用的重尾分布都属于<font color="#ff8000">次指数分布类 subexponential class </font>。<br />
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There is still some discrepancy over the use of the term '''heavy-tailed'''. There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their power [[Moment (mathematics)|moments]] finite; and some others to those distributions that do not have a finite [[variance]]. The definition given in this article is the most general in use, and includes all distributions encompassed by the alternative definitions, as well as those distributions such as [[log-normal]] that possess all their power moments, yet which are generally considered to be heavy-tailed. (Occasionally, heavy-tailed is used for any distribution that has heavier tails than the normal distribution.)<br />
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There is still some discrepancy over the use of the term heavy-tailed. There are two other definitions in use. Some authors use the term to refer to those distributions which do not have all their power moments finite; and some others to those distributions that do not have a finite variance. The definition given in this article is the most general in use, and includes all distributions encompassed by the alternative definitions, as well as those distributions such as log-normal that possess all their power moments, yet which are generally considered to be heavy-tailed. (Occasionally, heavy-tailed is used for any distribution that has heavier tails than the normal distribution.)<br />
<br />
在使用<font color="#ff8000">“重尾” Heavy-tailed</font>一词时仍存在一些歧义。于是就出现了另外两种定义。一些作者使用该术语来指代并非所有幂矩都是有限的那些分布,以及其它一些没有有限方差的分布。本文中给出的是最常用的定义,包括替代定义所涵盖的所有分布,以及具有所有幂矩的<font color="#ff8000">对数正态分布 long-normal distributions </font>,但通常被认为是重尾的。(有时“重尾”用于任何具有比正态分布更重的尾巴的分布。)<br />
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<br />
== Definitions 定义 ==<br />
<br />
=== Definition of heavy-tailed distribution 重尾分布的定义 ===<br />
<br />
The distribution of a [[random variable]] ''X'' with [[cumulative distribution function|distribution function]] ''F'' is said to have a heavy (right) tail if the [[moment generating function]] of ''X'', ''M<sub>X</sub>''(''t''), is infinite for all ''t''&nbsp;>&nbsp;0.<ref name="ReferenceA">Rolski, Schmidli, Scmidt, Teugels, ''Stochastic Processes for Insurance and Finance'', 1999</ref><br />
<br />
The distribution of a random variable X with distribution function F is said to have a heavy (right) tail if the moment generating function of X, MX(t), is infinite for all t&nbsp;>&nbsp;0.<br />
<br />
如果''X''的矩生成函数, ''M<sub>X</sub>''(''t'')对于所有''t''&nbsp;>&nbsp;0都是无限的,则具有分布函数''F''的随机变量''X''的分布被称为重尾(右)。<ref name="ReferenceA">Rolski, Schmidli, Scmidt, Teugels, ''Stochastic Processes for Insurance and Finance'', 1999</ref><br />
<br />
<br />
<br />
That means<br />
<br />
也就是说<br />
<br />
:<math><br />
<br />
\int_{-\infty}^\infty e^{t x} \,dF(x) = \infty \quad \mbox{for all } t>0.<br />
<br />
</math><br />
<br />
<br />
<br />
An implication of this is that<br />
<br />
这意味着<br />
<br />
:<math><br />
<br />
\lim_{x \to \infty} e^{t x}\Pr[X>x] = \infty \quad \mbox{for all } t>0.\,<br />
<br />
</math><br />
<br />
<br />
<br />
This is also written in terms of the tail distribution function<br />
<br />
也可以写成<font color="#ff8000">尾分布函数 the tail distribution function </font>:<br />
<br />
<math><br />
<br />
\overline{F}(x) ≡ \Pr[X>x]<br />
<br />
</math><br />
<br />
<br />
<br />
as<br />
<br />
:<math><br />
<br />
\lim_{x \to \infty} e^{t x}\overline{F}(x) = \infty \quad \mbox{for all } t >0.\,<br />
<br />
</math><br />
<br />
=== Definition of long-tailed distribution 长尾分布的定义 ===<br />
<br />
The distribution of a [[random variable]] ''X'' with [[cumulative distribution function|distribution function]] ''F'' is said to have a long right tail if for all ''t'' > 0,<br />
<br />
The distribution of a random variable X with distribution function F is said to have a long right tail[1] if for all t > 0,<br />
<br />
如果对于所有''t''>0,则称具有分布函数''F''的随机变量''X''的分布为有较长的右尾,<br />
<br />
:<math><br />
<br />
\lim_{x \to \infty} \Pr[X>x+t\mid X>x] =1, \,<br />
<br />
</math><br />
<br />
<br />
<br />
or equivalently<br />
或等同于<br />
<br />
:<math><br />
<br />
\overline{F}(x+t) \sim \overline{F}(x) \quad \mbox{as } x \to \infty. \,<br />
<br />
</math><br />
<br />
This has the intuitive interpretation for a right-tailed long-tailed distributed quantity that if the long-tailed quantity exceeds some high level, the probability approaches 1 that it will exceed any other higher level.<br />
<br />
This has the intuitive interpretation for a right-tailed long-tailed distributed quantity that if the long-tailed quantity exceeds some high level, the probability approaches 1 that it will exceed any other higher level.<br />
<br />
对于右尾长尾分布量具有直观的解释,即如果长尾量超过某个高水平,则概率将接近1,它将超过其他更高的水平。<br />
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<br />
<br />
All long-tailed distributions are heavy-tailed, but the converse is false, and it is possible to construct heavy-tailed distributions that are not long-tailed.<br />
<br />
All long-tailed distributions are heavy-tailed, but the converse is false, and it is possible to construct heavy-tailed distributions that are not long-tailed.<br />
<br />
所有长尾分布都是重尾分布,但反过来不一定成立,且可以构造出非长尾分布的重尾分布。<br />
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<br />
=== Subexponential distributions 次指数分布 ===<br />
<br />
Subexponentiality is defined in terms of [[Convolution of probability distributions|convolutions of probability distributions]]. For two independent, identically distributed [[random variables]] <math> X_1,X_2</math> with common distribution function <math>F</math> the convolution of <math>F</math> with itself, <math>F^{*2}</math> is convolution square, using [[Lebesgue–Stieltjes integration]], by:<br />
<br />
Subexponentiality is defined in terms of [[Convolution of probability distributions|convolutions of probability distributions]]. For two independent, identically distributed [[random variables]] <math> X_1,X_2</math> with common distribution function <math>F</math> the convolution of <math>F</math> with itself, <math>F^{*2}</math> is convolution square, using [[Lebesgue–Stieltjes integration]], by:<br />
<br />
次指数性是根据概率分布的<font color="#ff8000">卷积 Convolution </font>定义的。对于具有共同分布函数<math>F</math>的两个独立且分布均匀的随机变量<math> X_1,X_2</math>,<math>F</math>与自身的卷积,<math>F^{*2}</math>是卷积的平方,使用Lebesgue–Stieltjes积分,方法如下:<br />
<br />
<br />
:<math><br />
\Pr[X_1+X_2 \leq x] = F^{*2}(x) = \int_{0}^x F(x-y)\,dF(y),<br />
</math><br />
<br />
<br />
and the ''n''-fold convolution <math>F^{*n}</math> is defined inductively by the rule:<br />
<br />
''n''倍卷积<math>F^{*n}</math>定义如下:<br />
<br />
<br />
:<math><br />
F^{*n}(x) = \int_{0}^x F(x-y)\,dF^{*n-1}(y).<br />
</math><br />
<br />
<br />
The tail distribution function <math>\overline{F}</math> is defined as <math>\overline{F}(x) = 1-F(x)</math>.<br />
<br />
尾分布函数<math>\overline{F}</math>定义为<math>\overline{F}(x) = 1-F(x)</math>。<br />
<br />
<br />
A distribution <math>F</math> on the positive half-line is subexponential<ref name="Asmussen"/><ref>{{Cite web|url=https://www.researchgate.net/publication/242637603_A_Theorem_on_Sums_of_Independent_Positive_Random_Variables_and_Its_Applications_to_Branching_Random_Processes|title=A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random Processes|last=Chistyakov|first=V. P.|date=1964|website=ResearchGate|language=en|archive-url=|archive-date=|access-date=April 7, 2019}}</ref><ref>{{Cite web|url=https://projecteuclid.org/download/pdf_1/euclid.aop/1176996225|title=The Class of Subexponential Distributions|last=Teugels|first=Jozef L.|authorlink=|date=1975|website=|publisher=Annals of Probability|publication-place=[[KU Leuven|University of Louvain]]|archive-url=|archive-date=|access-date=April 7, 2019}}</ref> if<br />
<br />
如果满足以下条件,则正半线上的分布<math>F</math>为次指数<ref name="Asmussen"/><ref>{{Cite web|url=https://www.researchgate.net/publication/242637603_A_Theorem_on_Sums_of_Independent_Positive_Random_Variables_and_Its_Applications_to_Branching_Random_Processes|title=A Theorem on Sums of Independent Positive Random Variables and Its Applications to Branching Random Processes|last=Chistyakov|first=V. P.|date=1964|website=ResearchGate|language=en|archive-url=|archive-date=|access-date=April 7, 2019}}</ref><ref>{{Cite web|url=https://projecteuclid.org/download/pdf_1/euclid.aop/1176996225|title=The Class of Subexponential Distributions|last=Teugels|first=Jozef L.|authorlink=|date=1975|website=|publisher=Annals of Probability|publication-place=[[KU Leuven|University of Louvain]]|archive-url=|archive-date=|access-date=April 7, 2019}}</ref><br />
<br />
<br />
:<math><br />
\overline{F^{*2}}(x) \sim 2\overline{F}(x) \quad \mbox{as } x \to \infty. <br />
</math><br />
<br />
<br />
This implies<ref name="Embrechts">{{cite book |author1=Embrechts P. |author2=Klueppelberg C. |author3=Mikosch T. |title=Modelling extremal events for insurance and finance |publisher=Springer | series = Stochastic Modelling and Applied Probability|location=Berlin |year=1997 | volume=33| doi = 10.1007/978-3-642-33483-2|isbn=978-3-642-08242-9 }}</ref> that, for any <math>n \geq 1</math>,<br />
<br />
这意味着<ref name="Embrechts">{{cite book |author1=Embrechts P. |author2=Klueppelberg C. |author3=Mikosch T. |title=Modelling extremal events for insurance and finance |publisher=Springer | series = Stochastic Modelling and Applied Probability|location=Berlin |year=1997 | volume=33| doi = 10.1007/978-3-642-33483-2|isbn=978-3-642-08242-9 }}</ref>,对于任何<math>n \geq 1</math>,<br />
<br />
<br />
:<math><br />
\overline{F^{*n}}(x) \sim n\overline{F}(x) \quad \mbox{as } x \to \infty. <br />
</math><br />
<br />
The probabilistic interpretation<ref name="Embrechts"/> of this is that, for a sum of <math>n</math> [[statistical independence|independent]] [[random variables]] <math>X_1,\ldots,X_n</math> with common distribution <math>F</math>,<br />
<br />
对此的概率解释<ref name="Embrechts"/>是,对于具有共同分布<math>F</math>的<math>n</math>个独立随机变量<math>X_1,\ldots,X_n</math>的总和<br />
<br />
<br />
:<math><br />
\Pr[X_1+ \cdots +X_n>x] \sim \Pr[\max(X_1, \ldots,X_n)>x] \quad \text{as } x \to \infty. <br />
</math><br />
<br />
This is often known as the principle of the single big jump<ref>{{Cite journal | last1 = Foss | first1 = S. | last2 = Konstantopoulos | first2 = T. | last3 = Zachary | first3 = S. | doi = 10.1007/s10959-007-0081-2 | title = Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments | journal = Journal of Theoretical Probability| volume = 20 | issue = 3 | pages = 581 | year = 2007 | arxiv = math/0509605| pmid = | url = http://www.math.nsc.ru/LBRT/v1/foss/fkz_revised.pdf| pmc = | citeseerx = 10.1.1.210.1699 }}</ref> or catastrophe principle.<ref>{{cite web| url = http://rigorandrelevance.wordpress.com/2014/01/09/catastrophes-conspiracies-and-subexponential-distributions-part-iii/ | title = Catastrophes, Conspiracies, and Subexponential Distributions (Part III) | first = Adam | last = Wierman | authorlink = Adam Wierman | date = January 9, 2014 | accessdate = January 9, 2014 | website = Rigor + Relevance blog | publisher = RSRG, Caltech}}</ref><br />
<br />
这通常被称为<font color="#ff8000">单跳 single big jump</font><ref>{{Cite journal | last1 = Foss | first1 = S. | last2 = Konstantopoulos | first2 = T. | last3 = Zachary | first3 = S. | doi = 10.1007/s10959-007-0081-2 | title = Discrete and Continuous Time Modulated Random Walks with Heavy-Tailed Increments | journal = Journal of Theoretical Probability| volume = 20 | issue = 3 | pages = 581 | year = 2007 | arxiv = math/0509605| pmid = | url = http://www.math.nsc.ru/LBRT/v1/foss/fkz_revised.pdf| pmc = | citeseerx = 10.1.1.210.1699 }}</ref>或<font color="#ff8000">突变理论 catastrophe principle</font> <ref>{{cite web| url = http://rigorandrelevance.wordpress.com/2014/01/09/catastrophes-conspiracies-and-subexponential-distributions-part-iii/ | title = Catastrophes, Conspiracies, and Subexponential Distributions (Part III) | first = Adam | last = Wierman | authorlink = Adam Wierman | date = January 9, 2014 | accessdate = January 9, 2014 | website = Rigor + Relevance blog | publisher = RSRG, Caltech}}</ref>。<br />
<br />
<br />
<br />
A distribution <math>F</math> on the whole real line is subexponential if the distribution<br />
<math>F I([0,\infty))</math> is.<ref>{{cite journal | last = Willekens | first = E. | title = Subexponentiality on the real line | journal = Technical Report | publisher = K.U. Leuven | year = 1986}}</ref> Here <math>I([0,\infty))</math> is the [[indicator function]] of the positive half-line. Alternatively, a random variable <math>X</math> supported on the real line is subexponential if and only if <math>X^+ = \max(0,X)</math> is subexponential.<br />
<br />
如果分布<math>F I([0,\infty))</m4ath>为实数,则<math>F</math>为整个实数上的次指数分布。<ref>{{cite journal | last = Willekens | first = E. | title = Subexponentiality on the real line | journal = Technical Report | publisher = K.U. Leuven | year = 1986}}</ref>此时<math>I([0,\infty))</math>是正半轴的指标函数。或者,当且仅当<math>X^+ = \max(0,X)</math>是次指数时,实数上支持的随机变量<math>X</math>才是次指数。<br />
<br />
<br />
<br />
All subexponential distributions are long-tailed, but examples can be constructed of long-tailed distributions that are not subexponential.<br />
<br />
所有次指数分布都是长尾分布,但可以构造出非次指数分布的长尾分布的示例。<br />
<br />
== Common heavy-tailed distributions 常见的重尾分布 ==<br />
<br />
All commonly used heavy-tailed distributions are subexponential.<ref name="Embrechts"/><br />
<br />
Those that are one-tailed include:<br />
*the [[Pareto distribution]];<br />
*the [[Log-normal distribution]];<br />
*the [[Lévy distribution]];<br />
*the [[Weibull distribution]] with shape parameter greater than 0 but less than 1;<br />
*the [[Burr distribution]];<br />
*the [[log-logistic distribution]];<br />
*the [[log-gamma distribution]];<br />
*the [[Fréchet distribution]];<br />
*the [[log-Cauchy distribution]], sometimes described as having a "super-heavy tail" because it exhibits [[logarithmic growth|logarithmic decay]] producing a heavier tail than the Pareto distribution.<ref>{{cite book|title=Laws of Small Numbers: Extremes and Rare Events|author=Falk, M., Hüsler, J. & Reiss, R.|page=80|year=2010|publisher=Springer|isbn=978-3-0348-0008-2}}</ref><ref>{{cite web|title=Statistical inference for heavy and super-heavy tailed distributions|url=http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf|author=Alves, M.I.F., de Haan, L. & Neves, C.|date=March 10, 2006|access-date=November 1, 2011|archive-url=https://web.archive.org/web/20070623175435/http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf|archive-date=June 23, 2007|url-status=dead}}</ref><br />
<br />
Those that are two-tailed include:<br />
*The [[Cauchy distribution]], itself a special case of both the stable distribution and the t-distribution;<br />
*The family of [[stable distributions]],<ref>{{cite web |author=John P. Nolan | title=Stable Distributions: Models for Heavy Tailed Data| year=2009 | url=http://academic2.american.edu/~jpnolan/stable/chap1.pdf | accessdate=2009-02-21}}</ref> excepting the special case of the normal distribution within that family. Some stable distributions are one-sided (or supported by a half-line), see e.g. [[Lévy distribution]]. See also ''[[financial models with long-tailed distributions and volatility clustering]]''.<br />
*The [[Student's t-distribution|t-distribution]].<br />
*The skew lognormal cascade distribution.<ref>{{cite web | author=Stephen Lihn | title=Skew Lognormal Cascade Distribution | year=2009 | url=http://www.skew-lognormal-cascade-distribution.org/ | access-date=2009-06-12 | archive-url=https://web.archive.org/web/20140407075213/http://www.skew-lognormal-cascade-distribution.org/ | archive-date=2014-04-07 | url-status=dead }}</ref><br />
<br />
<br />
All commonly used heavy-tailed distributions are subexponential.[6]<br />
<br />
所有常用的重尾分布都是次指数的。<ref name="Embrechts"/><br />
<br />
Those that are one-tailed include:<br />
单尾的包括:<br />
* <font color="#ff8000">帕累托分布 Pareto distribution</font>;<br />
* <font color="#ff8000">对数正态分布 Log-normal distribution</font>;<br />
* <font color="#ff8000">莱维分布 Lévy distribution</font>;<br />
* 形状参数大于0但小于1的<font color="#ff8000">韦布尔分布 Weibull distribution</font>;<br />
* <font color="#ff8000">伯尔分布 Burr distribution</font>;<br />
* <font color="#ff8000">对数逻辑分布 log-logistic distribution</font>;<br />
* <font color="#ff8000">对数伽玛分布 log-gamma distribution</font>;<br />
* <font color="#ff8000">弗雷歇分布 Fréchet distribution</font>;<br />
* <font color="#ff8000">对数柯西分布 log-Cauchy distribution</font>,有时被描述为“超重尾”分布,因为它表现出对数衰减,从而产生比帕累托分布更重的尾。<ref>{{cite book|title=Laws of Small Numbers: Extremes and Rare Events|author=Falk, M., Hüsler, J. & Reiss, R.|page=80|year=2010|publisher=Springer|isbn=978-3-0348-0008-2}}</ref><ref>{{cite web|title=Statistical inference for heavy and super-heavy tailed distributions|url=http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf|author=Alves, M.I.F., de Haan, L. & Neves, C.|date=March 10, 2006|access-date=November 1, 2011|archive-url=https://web.archive.org/web/20070623175435/http://docentes.deio.fc.ul.pt/fragaalves/SuperHeavy.pdf|archive-date=June 23, 2007|url-status=dead}}</ref><br />
* <br />
Those that are two-tailed include:<br />
双尾的包括:<br />
* <font color="#ff8000">柯西分布 Cauchy distribution</font>本身就是稳定分布和t分布的特例;<br />
* <font color="#ff8000">稳定分布族 The family of stable distributions</font><ref>{{cite web |author=John P. Nolan | title=Stable Distributions: Models for Heavy Tailed Data| year=2009 | url=http://academic2.american.edu/~jpnolan/stable/chap1.pdf | accessdate=2009-02-21}}</ref>,但该族中正态分布的特殊情况除外。一些稳定的分布是单面的(或有半线的支持),例如莱维分布。另请参见具有长尾分布和波动性聚类的财务模型。<br />
* t分布<br />
*<font color="#ff8000">偏对数正态级联分布 The skew lognormal cascade distribution</font>。<ref>{{cite web | author=Stephen Lihn | title=Skew Lognormal Cascade Distribution | year=2009 | url=http://www.skew-lognormal-cascade-distribution.org/ | access-date=2009-06-12 | archive-url=https://web.archive.org/web/20140407075213/http://www.skew-lognormal-cascade-distribution.org/ | archive-date=2014-04-07 | url-status=dead }}</ref><br />
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<br />
<br />
<br />
== Relationship to fat-tailed distributions 与胖尾分布的关系 ==<br />
A [[fat-tailed distribution]] is a distribution for which the probability density function, for large x, goes to zero as a power <math>x^{-a}</math>. Since such a power is always bounded below by the probability density function of an exponential distribution, fat-tailed distributions are always heavy-tailed. Some distributions, however, have a tail which goes to zero slower than an exponential function (meaning they are heavy-tailed), but faster than a power (meaning they are not fat-tailed). An example is the [[log-normal distribution]] <ref>{{Contradict-inline|article=fat-tailed distribution|reason=Fat-tailed page says log-normals are in fact fat-tailed.|date=June 2019}}</ref>. Many other heavy-tailed distributions such as the [[log-logistic distribution|log-logistic]] and [[Pareto distribution|Pareto]] distribution are, however, also fat-tailed.<br />
<br />
胖尾分布是这样的分布,对于较大的x,概率密度函数为<math>x^{-a}</math>趋于零。由于这样的幂总是受到指数分布概率密度函数的限制,因此,胖尾分布始终是重尾分布。但是,某些分布的尾部趋近于零的速率比指数函数慢(表示它们是重尾),而比幂快(表示它们不是胖尾)。例如对数正态分布<ref>{{Contradict-inline|article=fat-tailed distribution|reason=Fat-tailed page says log-normals are in fact fat-tailed.|date=June 2019}}</ref>。当然,许多其他的重尾分布,例如对数逻辑分布和帕累托分布也属于胖尾分布。<br />
<br />
<br />
<br />
== Estimating the tail-index{{definition|date=January 2018}} 尾指数估计 ==<br />
<br />
There are parametric (see Embrechts et al.<ref name="Embrechts"/>) and non-parametric (see, e.g., Novak<ref name="Novak2011">{{cite book<br />
| author=Novak S.Y. <br />
| title=Extreme value methods with applications to finance<br />
| year=2011<br />
| series=London: CRC<br />
| isbn=978-1-43983-574-6 <br />
}}</ref>) approaches to the problem of the tail-index estimation.<br />
<br />
对于尾指数估计的问题,有参数方法(参见Emprechts等人<ref name="Embrechts"/>)和非参数方法(例如,Novak<ref name="Novak2011">{{cite book<br />
| author=Novak S.Y. <br />
| title=Extreme value methods with applications to finance<br />
| year=2011<br />
| series=London: CRC<br />
| isbn=978-1-43983-574-6 <br />
}}</ref>)两种。<br />
<br />
<br />
<br />
To estimate the tail-index using the parametric approach, some authors employ [[GEV distribution]] or [[Pareto distribution]]; they may apply the maximum-likelihood estimator (MLE).<br />
<br />
为了使用参数化方法估计尾指数,有些作者采用了GEV分布或帕累托分布;他们可能会运用极大似然估计方法(MLE)。<br />
<br />
<br />
<br />
=== Pickand's tail-index estimator Pickand的尾指数估算器===<br />
<br />
With <math>(X_n , n \geq 1)</math> a random sequence of independent and same density function <math>F \in D(H(\xi))</math>, the Maximum Attraction Domain<ref name=Pickands>{{cite journal|last=Pickands III|first=James|title=Statistical Inference Using Extreme Order Statistics|journal=The Annals of Statistics|date=Jan 1975|volume=3|issue=1|pages=119–131|jstor=2958083|doi=10.1214/aos/1176343003|doi-access=free}}</ref> of the generalized extreme value density <math> H </math>, where <math>\xi \in \mathbb{R}</math>. If <math>\lim_{n\to\infty} k(n) = \infty </math> and <math>\lim_{n\to\infty} \frac{k(n)}{n}= 0</math>, then the ''Pickands'' tail-index estimation is<ref name="Embrechts"/><ref name="Pickands"/><br />
<br />
对于<math>(X_n , n \geq 1)</math>的独立且相同的密度函数<math>F \in D(H(\xi))</math>的随机序列,是<font color="#ff8000">广义极值密度 the generalized extreme value density </font><math>H</math>的<font color="#ff8000">最大吸引域 the Maximum Attraction Domain </font><ref name=Pickands>{{cite journal|last=Pickands III|first=James|title=Statistical Inference Using Extreme Order Statistics|journal=The Annals of Statistics|date=Jan 1975|volume=3|issue=1|pages=119–131|jstor=2958083|doi=10.1214/aos/1176343003|doi-access=free}}</ref>,其中<math>\xi \in \mathbb{R}</math>。如果<math>\lim_{n\to\infty} k(n) = \infty </math>和<math>\lim_{n\to\infty} \frac{k(n)}{n}= 0</math>,则Pickands尾部指数估计为<ref name="Embrechts"/><ref name="Pickands"/><br />
<br />
<br />
:<math><br />
\xi^\text{Pickands}_{(k(n),n)} =\frac{1}{\ln 2} \ln \left( \frac{X_{(n-k(n)+1,n)} - X_{(n-2k(n)+1,n)}}{X_{(n-2k(n)+1,n)} - X_{(n-4k(n)+1,n)}}\right)<br />
</math><br />
<br />
<br />
where <math>X_{(n-k(n)+1,n)}=\max \left(X_{n-k(n)+1},\ldots ,X_{n}\right)</math>. This estimator converges in probability to <math>\xi</math>.<br />
<br />
其中<math>X_{(n-k(n)+1,n)}=\max \left(X_{n-k(n)+1},\ldots ,X_{n}\right)</math>。 此估计量的概率收敛到<math>\xi</math>。<br />
<br />
<br />
<br />
=== Hill's tail-index estimator 希尔 Hill的尾指数估算器 ===<br />
<br />
Let <math>(X_t , t \geq 1)</math> be a sequence of independent and identically distributed random variables with distribution function <math>F \in D(H(\xi))</math>, the maximum domain of attraction of the [[generalized extreme value distribution]] <math> H </math>, where <math>\xi \in \mathbb{R}</math>. The sample path is <math>{X_t: 1 \leq t \leq n}</math> where <math>n</math> is the sample size. If <br />
<math>\{k(n)\}</math> is an intermediate order sequence, i.e. <math>k(n) \in \{1,\ldots,n-1\}, </math>, <math>k(n) \to \infty</math> and <math>k(n)/n \to 0</math>, then the Hill tail-index estimator is<ref>Hill B.M. (1975) A simple general approach to inference about the tail of a distribution. Ann. Stat., v. 3, 1163–1174.</ref><br />
<br />
令<math>(X_t , t \geq 1)</math>为具有分布函数<math>F \in D(H(\xi))</math>独立且均匀分布的随机变量序列,其分布函数为广义极值分布<math> H </math>的最大吸引域,其中<math>\xi \in \mathbb{R}</math>。样本路径为<math>{X_t: 1 \leq t \leq n}</math>,其中<math>n</math>为样本大小。 如果<math>\{k(n)\}</math>是中间阶数序列,即<math>k(n) \in \{1,\ldots,n-1\}, </math>,<math>k(n) \to \infty</math>和<math>k(n)/n \to 0</math>,则Hill尾指数估计器为<ref>Hill B.M. (1975) A simple general approach to inference about the tail of a distribution. Ann. Stat., v. 3, 1163–1174.</ref>:<br />
<br />
<br />
: <math><br />
\xi^\text{Hill}_{(k(n),n)} = \left(\frac 1 {k(n)} \sum_{i=n-k(n)+1}^n \ln(X_{(i,n)}) - \ln (X_{(n-k(n)+1,n)})\right)^{-1},<br />
</math><br />
<br />
<br />
where <math>X_{(i,n)}</math> is the <math>i</math>-th [[order statistic]] of <math>X_1, \dots, X_n</math>.<br />
This estimator converges in probability to <math>\xi</math>, and is asymptotically normal provided <math>k(n) \to \infty </math> is restricted based on a higher order regular variation property<ref>Hall, P.(1982) On some estimates of an exponent of regular variation. J. R. Stat. Soc. Ser. B., v. 44, 37–42.</ref> <br />
.<ref>Haeusler, E. and J. L. Teugels (1985) On asymptotic normality of Hill's estimator for the exponent of regular variation. Ann. Stat., v. 13, 743–756.</ref> Consistency and asymptotic normality extend to a large class of dependent and heterogeneous sequences,<ref>Hsing, T. (1991) On tail index estimation using dependent data. Ann. Stat., v. 19, 1547–1569.</ref><ref>Hill, J. (2010) On tail index estimation for dependent, heterogeneous data. Econometric Th., v. 26, 1398–1436.</ref> irrespective of whether <math>X_t</math> is observed, or a computed residual or filtered data from a large class of models and estimators, including mis-specified models and models with errors that are dependent.<ref>Resnick, S. and Starica, C. (1997). Asymptotic behavior of Hill’s estimator for autoregressive data. Comm. Statist. Stochastic Models 13, 703–721.</ref><ref>Ling, S. and Peng, L. (2004). Hill’s estimator for the tail index of an ARMA model. J. Statist. Plann. Inference 123, 279–293.</ref><ref>Hill, J. B. (2015). Tail index estimation for a filtered dependent time series. Stat. Sin. 25, 609–630.</ref><br />
<br />
其中<math>X_{(i,n)}</math>是<math>X_1, \dots, X_n</math>的第<math>i</math>次序统计量。该估计量依概率收敛于<math>\xi</math>,并且在基于高阶的正则变化性质的情况下,是限制<math>k(n) \to \infty </math>的渐近正态<ref>Hall, P.(1982) On some estimates of an exponent of regular variation. J. R. Stat. Soc. Ser. B., v. 44, 37–42.</ref>.<ref>Haeusler, E. and J. L. Teugels (1985) On asymptotic normality of Hill's estimator for the exponent of regular variation. Ann. Stat., v. 13, 743–756.</ref>。一致性和渐近正态性适用于一大类相关序列和异类序列<ref>Hsing, T. (1991) On tail index estimation using dependent data. Ann. Stat., v. 19, 1547–1569.</ref><ref>Hill, J. (2010) On tail index estimation for dependent, heterogeneous data. Econometric Th., v. 26, 1398–1436.</ref>,而不管是否观测到<math>X_t</math>,或者来自大量模型和估计量(包括错误指定的模型和具有相关误差的模型)计算出的残差或筛选数据。<ref>Resnick, S. and Starica, C. (1997). Asymptotic behavior of Hill’s estimator for autoregressive data. Comm. Statist. Stochastic Models 13, 703–721.</ref><ref>Ling, S. and Peng, L. (2004). Hill’s estimator for the tail index of an ARMA model. J. Statist. Plann. Inference 123, 279–293.</ref><ref>Hill, J. B. (2015). Tail index estimation for a filtered dependent time series. Stat. Sin. 25, 609–630.</ref><br />
<br />
<br />
<br />
=== Ratio estimator of the tail-index 尾部指数的比率估计器 ===<br />
<br />
The ratio estimator (RE-estimator) of the tail-index was introduced by Goldie <br />
and Smith.<ref>Goldie C.M., Smith R.L. (1987) Slow variation with remainder:<br />
theory and applications. Quart. J. Math. Oxford, v. 38, 45–71.</ref> <br />
It is constructed similarly to Hill's estimator but uses a non-random "tuning parameter".<br />
<br />
尾指数的比率估计器(RE估计器)由Goldie和Smith提出<ref>Goldie C.M., Smith R.L. (1987) Slow variation with remainder:<br />
theory and applications. Quart. J. Math. Oxford, v. 38, 45–71.</ref>。它的构造类似于Hill估计器,但使用了非随机的“调整参数”<br />
<br />
<br />
<br />
A comparison of Hill-type and RE-type estimators can be found in Novak.<ref name="Novak2011"/><br />
<br />
在Novak中可以找到Hill型和RE型估计量的比较。<ref name="Novak2011"/><br />
<br />
=== Software 应用软件===<br />
* [http://www.cs.bu.edu/~crovella/aest.html aest], [[C (programming language)|C]] tool for estimating the heavy-tail index.<ref>{{Cite journal | last1 = Crovella | first1 = M. E. | last2 = Taqqu | first2 = M. S. | title = Estimating the Heavy Tail Index from Scaling Properties| journal = Methodology and Computing in Applied Probability | volume = 1 | pages = 55–79 | year = 1999 | doi = 10.1023/A:1010012224103 | url = http://www.cs.bu.edu/~crovella/paper-archive/aest.ps| pmid = | pmc = }}</ref><br />
<br />
* 用于估计重尾指数的软件[http://www.cs.bu.edu/~crovella/aest.html aest]和C。<ref>{{Cite journal | last1 = Crovella | first1 = M. E. | last2 = Taqqu | first2 = M. S. | title = Estimating the Heavy Tail Index from Scaling Properties| journal = Methodology and Computing in Applied Probability | volume = 1 | pages = 55–79 | year = 1999 | doi = 10.1023/A:1010012224103 | url = http://www.cs.bu.edu/~crovella/paper-archive/aest.ps| pmid = | pmc = }}</ref><br />
<br />
== Estimation of heavy-tailed density 重尾密度的估计 ==<br />
<br />
Nonparametric approaches to estimate heavy- and superheavy-tailed probability density functions were given in <br />
Markovich.<ref name="Markovich2007">{{cite book<br />
| author=Markovich N.M. <br />
| title=Nonparametric Analysis of Univariate Heavy-Tailed data: Research and Practice<br />
| year=2007<br />
| series=Chitester: Wiley<br />
| isbn=978-0-470-72359-3<br />
}}</ref> These are approaches based on variable bandwidth and long-tailed kernel estimators; on the preliminary data transform to a new random variable at finite or infinite intervals which is more convenient for the estimation and then inverse transform of the obtained density estimate; and "piecing-together approach" which provides a certain parametric model for the tail of the density and a non-parametric model to approximate the mode of the density. Nonparametric estimators require an appropriate selection of tuning (smoothing) parameters like a bandwidth of kernel estimators and the bin width of the histogram. The well known data-driven methods of such selection are a cross-validation and its modifications, methods based on the minimization of the mean squared error (MSE) and its asymptotic and their upper bounds.<ref name="WandJon1995">{{cite book<br />
| author=Wand M.P., Jones M.C. <br />
| title=Kernel smoothing<br />
| year=1995<br />
| series=New York: Chapman and Hall<br />
| isbn=978-0412552700<br />
}}</ref> A discrepancy method which uses well-known nonparametric statistics like Kolmogorov-Smirnov's, von Mises and Anderson-Darling's ones as a metric in the space of distribution functions (dfs) and quantiles of the later statistics as a known uncertainty or a discrepancy value can be found in.<ref name="Markovich2007"/> Bootstrap is another tool to find smoothing parameters using approximations of unknown MSE by different schemes of re-samples selection, see e.g.<ref name="Hall1992">{{cite book<br />
| author=Hall P. <br />
| title=The Bootstrap and Edgeworth Expansion<br />
| year=1992<br />
| series=Springer<br />
| isbn=9780387945088<br />
}}</ref><br />
<br />
Markovich中给出了估计重尾和超重尾概率密度函数的非参数方法。<ref name="Markovich2007">{{cite book<br />
| author=Markovich N.M. <br />
| title=Nonparametric Analysis of Univariate Heavy-Tailed data: Research and Practice<br />
| year=2007<br />
| series=Chitester: Wiley<br />
| isbn=978-0-470-72359-3<br />
}}</ref>这些是基于<font color="#ff8000">可变带宽 variable bandwidth</font>和<font color="#ff8000">长尾核估计器 long-tailed kernel estimators</font>的方法。将初步数据以有限或无限间隔变换为新的随机变量,这样更便于估计,然后对获得的密度估计进行逆变换;以及“拼合方法”,它为密度的尾部提供了确定的参数模型,并为近似密度模型提供了非参数模型。非参数估计器需要适当选择调整(平滑)参数,例如内核估计器的带宽和直方图的组距。这种选择大众化数据驱动方法是基于均方误差(MSE)及其渐近或上限的最小化的交叉验证及修改方法。<ref name="WandJon1995">{{cite book<br />
| author=Wand M.P., Jones M.C. <br />
| title=Kernel smoothing<br />
| year=1995<br />
| series=New York: Chapman and Hall<br />
| isbn=978-0412552700<br />
}}</ref>可以找到一种差异方法,通过使用著名的非参数统计数据(例如Kolmogorov-Smirnov's,von Mises和Anderson-Darling的统计量)作为分布函数(dfs)空间中的度量,并将后来的统计量的分位数作为已知的不确定性或差异值。<ref name="Markovich2007"/><font color="#ff8000">自助法 Bootstrap</font>是另一种工具,可以通过不同的重抽样方案使用未知MSE的近似值来查找平滑参数。<ref name="Hall1992">{{cite book<br />
| author=Hall P. <br />
| title=The Bootstrap and Edgeworth Expansion<br />
| year=1992<br />
| series=Springer<br />
| isbn=9780387945088<br />
}}</ref><br />
<br />
<br />
<br />
== See also 其他参考资料 ==<br />
*[[Leptokurtic distribution]]<br />
*[[Generalized extreme value distribution]]<br />
*[[Outlier]]<br />
*[[Long tail]]<br />
*[[Power law]]<br />
*[[Seven states of randomness]]<br />
*[[Fat-tailed distribution]]<br />
**[[Taleb distribution]] and [[Holy grail distribution]]<br />
<br />
<br />
* <font color="#ff8000">尖峭态分布 Leptokurtic distribution</font><br />
* <font color="#ff8000">广义极值分布 Generalized extreme value distribution</font><br />
* <font color="#ff8000">离群值 Outlier</font><br />
* <font color="#ff8000">长尾 Long tail</font><br />
* <font color="#ff8000">幂律 Power law</font><br />
* <font color="#ff8000">随机的七个状态 Seven states of randomness</font><br />
* <font color="#ff8000">胖尾分布 Fat-tailed distribution</font><br />
**<font color="#ff8000">塔勒布分布 Taleb distribution</font>和<font color="#ff8000">圣杯分布 Holy grail distribution</font><br />
<br />
<br />
<br />
== References 参考文献 ==<br />
<br />
<references/><br />
<br />
[[Category:Tails of probability distributions]]<br />
[[Category:Types of probability distributions]]<br />
[[Category:Actuarial science]]<br />
[[Category:Risk]]<br />
<br />
<br />
<br />
Category:Tails of probability distributions<br />
<br />
类别: 概率分布的尾部<br />
<br />
*the [[Burr distribution]];<br />
<br />
Category:Types of probability distributions<br />
<br />
类别: 概率分布的类型<br />
<br />
*the [[log-logistic distribution]];<br />
<br />
Category:Actuarial science<br />
<br />
类别: 精算<br />
<br />
*the [[log-gamma distribution]];<br />
<br />
Category:Risk<br />
<br />
类别: 风险<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Heavy-tailed distribution]]. Its edit history can be viewed at [[重尾分布/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E6%9C%89%E6%95%88%E5%9C%BA%E8%AE%BA&diff=21306有效场论2021-01-25T12:21:43Z<p>Vicky:/* Other examples其他例子 */</p>
<hr />
<div>此词条由Henry初次翻译。<br />
{{More footnotes|date=May 2013}}<br />
已由三奇同学完成第一次审校。<br />
{{More footnotes|date=January 2021}}<br />
<br />
{{Quantum field theory|cTopic=Some models}}<br />
<br />
In [[physics]], an '''effective field theory''' is a type of approximation, or [[effective theory]], for an underlying physical theory, such as a [[quantum field theory]] or a [[statistical mechanics]] model. An effective field theory includes the appropriate [[degrees of freedom (physics and chemistry)|degrees of freedom]] to describe physical phenomena occurring at a chosen [[length scale]] or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies). Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales. Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in [[particle physics]], [[statistical mechanics]], [[condensed matter physics]], [[general relativity]], and [[hydrodynamics]]. They simplify calculations, and allow treatment of [[Dissipative system|dissipation]] and [[radiation]] effects.<ref>{{Cite journal|doi=10.1103/PhysRevLett.110.174301|pmid=23679733|url=http://authors.library.caltech.edu/38643/1/PhysRevLett.110.174301.pdf|title=Classical Mechanics of Nonconservative Systems|journal=Physical Review Letters|volume=110|issue=17|pages=174301|year=2013|last1=Galley|first1=Chad R.|s2cid=14591873|access-date=2014-03-03|archive-url=https://web.archive.org/web/20140303174914/http://authors.library.caltech.edu/38643/1/PhysRevLett.110.174301.pdf|archive-date=2014-03-03|url-status=dead}}</ref><ref>{{Cite journal |arxiv = 1402.2610|last1 = Birnholtz|first1 = Ofek|title = Radiation reaction at the level of the action|journal = International Journal of Modern Physics A|volume = 29|issue = 24|pages = 1450132|last2 = Hadar|first2 = Shahar|last3 = Kol|first3 = Barak|year = 2014|doi = 10.1142/S0217751X14501322|s2cid = 118541484}}</ref><br />
<br />
In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies). Intuitively, one averages over the behavior of the underlying theory at shorter length scales to derive what is hoped to be a simplified model at longer length scales. Effective field theories typically work best when there is a large separation between length scale of interest and the length scale of the underlying dynamics. Effective field theories have found use in particle physics, statistical mechanics, condensed matter physics, general relativity, and hydrodynamics. They simplify calculations, and allow treatment of dissipation and radiation effects.<br />
<br />
在物理学中,<font color="#ff8000"> 有效场论Effective field theory</font>是一种有效的近似理论,用于基础的物理理论,比如量子场论或者统计力学模型理论。有效场论用适当的自由度来描述特定距离尺度或能量尺度下发生的物理现象,而忽略在较小尺度上的子结构和自由度(或者相仿地,在较高的能量上)。直观地说,一个人可以用较短的长度尺度对潜在理论的结果取平均,从而得出一个在较长长度尺度下的简化模型。当研究者感兴趣的尺度与相互作用的基本尺度存在较大差异时,有效场论是最实用的。有效场论已经在粒子物理学、统计力学、凝聚态物理学、广义相对论和流体力学中得到了应用。它们简化了计算,并可以处理耗散和辐射效应。<br />
<br />
<br />
<br />
==The renormalization group重整化群 ==<br />
<br />
Presently, effective field theories are discussed in the context of the [[renormalization group]] (RG) where the process of ''integrating out'' short distance degrees of freedom is made systematic. Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through an RG analysis. This method also lends credence to the main technique of constructing effective field theories, through the analysis of [[symmetry|symmetries]]. If there is a single mass scale '''M''' in the ''microscopic'' theory, then the effective field theory can be seen as an expansion in '''1/M'''. The construction of an effective field theory accurate to some power of '''1/M''' requires a new set of free parameters at each order of the expansion in '''1/M'''. This technique is useful for [[scattering]] or other processes where the maximum momentum scale '''k''' satisfies the condition '''k/M≪1'''. Since effective field theories are not valid at small length scales, they need not be [[Renormalization#Renormalizability|renormalizable]]. Indeed, the ever expanding number of parameters at each order in '''1/M''' required for an effective field theory means that they are generally not renormalizable in the same sense as [[quantum electrodynamics]] which requires only the renormalization of two parameters.<br />
<br />
Presently, effective field theories are discussed in the context of the renormalization group (RG) where the process of integrating out short distance degrees of freedom is made systematic. Although this method is not sufficiently concrete to allow the actual construction of effective field theories, the gross understanding of their usefulness becomes clear through an RG analysis. This method also lends credence to the main technique of constructing effective field theories, through the analysis of symmetries. If there is a single mass scale M in the microscopic theory, then the effective field theory can be seen as an expansion in 1/M. The construction of an effective field theory accurate to some power of 1/M requires a new set of free parameters at each order of the expansion in 1/M. This technique is useful for scattering or other processes where the maximum momentum scale k satisfies the condition k/M≪1. Since effective field theories are not valid at small length scales, they need not be renormalizable. Indeed, the ever expanding number of parameters at each order in 1/M required for an effective field theory means that they are generally not renormalizable in the same sense as quantum electrodynamics which requires only the renormalization of two parameters.<br />
<br />
目前,有效场论是在<font color="#ff8000"> 重整化群Renormalization group</font>(RG)的背景下讨论的,重整化群使短距离自由度的积分过程变得系统化。尽管这种方法不够具体,无法实际构建有效场论,但通过RG分析,对其有用性的总体理解变得清晰。通过对对称性的分析,该方法也为构造有效场论的主要技术提供了依据。如果微观理论中只有一个质量尺度M,因此,有效场论可以看作是1/M的展开式。建立精确到1/M幂次的有效场理论需要在1/M阶展开的每一阶上都有一组新的自由参数。这种方法对于散射或其他最大动量标度k满足条件k/M≪1的过程是有用的。由于有效场论在小尺度下是无效的,所以它们不必是可重整化的。事实上,随着阶次升高,有效场论要求的参数数目不断增加,这意味着它们通常不像只需要两个参数即可重整化的量子电动力学那样可重整化。<br />
<br />
<br />
<br />
==Examples of effective field theories有效场理论实例==<br />
<br />
===Fermi theory of beta decay贝塔衰变的费米理论 ===<br />
<br />
The best-known example of an effective field theory is the [[Fermi's interaction|Fermi theory of beta decay]]. This theory was developed during the early study of weak decays of [[Atomic nucleus|nuclei]] when only the [[hadron]]s and [[lepton]]s undergoing weak decay were known. The typical [[elementary particle reaction|reactions]] studied were:<br />
<br />
The best-known example of an effective field theory is the Fermi theory of beta decay. This theory was developed during the early study of weak decays of nuclei when only the hadrons and leptons undergoing weak decay were known. The typical reactions studied were:<br />
<br />
有效场理论最著名的例子是贝塔衰变费米理论。这个理论是在早期研究弱衰变核时发展起来的,当时物理学家只知道经历弱衰变的强子和轻子。研究的典型反应有:<br />
<br />
<br />
<br />
::<math><br />
<br />
<math><br />
<br />
《数学》<br />
<br />
\begin{align}<br />
<br />
\begin{align}<br />
<br />
开始{ align }<br />
<br />
n & \to p+e^-+\overline\nu_e \\<br />
<br />
n & \to p+e^-+\overline\nu_e \\<br />
<br />
N & to p + e ^-+ overline nu _ e<br />
<br />
\mu^- & \to e^-+\overline\nu_e+\nu_\mu.<br />
<br />
\mu^- & \to e^-+\overline\nu_e+\nu_\mu.<br />
<br />
Mu ^-& to e ^-+ overline nu _ e + nu _ mu.<br />
<br />
\end{align}<br />
<br />
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This theory posited a pointlike interaction between the four [[fermion]]s involved in these reactions. The theory had great [[phenomenology (particle physics)|phenomenological]] success and was eventually understood to arise from the [[gauge theory]] of [[electroweak interaction]]s, which forms a part of the [[standard model]] of particle physics. In this more fundamental theory, the interactions are mediated by a [[flavour (particle physics)|flavour]]-changing [[gauge boson]], the W<sup>±</sup>. The immense success of the Fermi theory was because the W particle has mass of about 80 [[GeV]], whereas the early experiments were all done at an energy scale of less than 10 [[MeV]]. Such a separation of scales, by over 3 orders of magnitude, has not been met in any other situation as yet.<br />
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This theory posited a pointlike interaction between the four fermions involved in these reactions. The theory had great phenomenological success and was eventually understood to arise from the gauge theory of electroweak interactions, which forms a part of the standard model of particle physics. In this more fundamental theory, the interactions are mediated by a flavour-changing gauge boson, the W<sup>±</sup>. The immense success of the Fermi theory was because the W particle has mass of about 80 GeV, whereas the early experiments were all done at an energy scale of less than 10 MeV. Such a separation of scales, by over 3 orders of magnitude, has not been met in any other situation as yet.<br />
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这一理论假定参与这些反应的四个费米子之间的点状相互作用,在现象学上取得了巨大的成功,成为描述弱电相互作用的规范理论,它构成了粒子物理学标准模型的一部分。在这个更基本的理论中,相互作用是由一个可以改变味的规范玻色子w±介导的。费米理论的巨大成功是因为 w 粒子的质量约为80gev,而早期的实验都是在能量小于10mev 的情况下进行的。这种差距超过了3个数量级,其他任何实验都难以达到。。<br />
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===BCS theory of superconductivityBCS超导理论 ===<br />
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Another famous example is the [[BCS theory]] of [[superconductivity]]. Here the underlying theory is of [[electron]]s in a [[metal]] interacting with lattice vibrations called [[phonon]]s. The phonons cause attractive interactions between some electrons, causing them to form [[Cooper pair]]s. The length scale of these pairs is much larger than the wavelength of phonons, making it possible to neglect the dynamics of phonons and construct a theory in which two electrons effectively interact at a point. This theory has had remarkable success in describing and predicting the results of experiments on superconductivity.<br />
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Another famous example is the BCS theory of superconductivity. Here the underlying theory is of electrons in a metal interacting with lattice vibrations called phonons. The phonons cause attractive interactions between some electrons, causing them to form Cooper pairs. The length scale of these pairs is much larger than the wavelength of phonons, making it possible to neglect the dynamics of phonons and construct a theory in which two electrons effectively interact at a point. This theory has had remarkable success in describing and predicting the results of experiments on superconductivity.<br />
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另一个著名的例子是超导现象的 BCS 理论。这里的基本理论是金属中的电子与声子相互作用。声子在一些电子之间引起吸引力的相互作用,导致它们形成库珀对。库珀对的长度比声子的波长大得多,因此可以忽略声子的动力学,建立两个电子在同一点上有效相互作用的理论。这个理论在描述和预测超导现象的实验结果方面取得了显著的成功。<br />
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===Effective Field Theories in Gravity重力中的有效场理论 ===<br />
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[[General relativity]] itself is expected to be the low energy effective field theory of a full theory of [[quantum gravity]], such as [[string theory]] or [[Loop Quantum Gravity]]. The expansion scale is the [[Planck mass]].<br />
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General relativity itself is expected to be the low energy effective field theory of a full theory of quantum gravity, such as string theory or Loop Quantum Gravity. The expansion scale is the Planck mass.<br />
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<font color="#ff8000"> 广义相对论General relativity</font>本身有望成为完整的量子引力理论的低能有效场论,如弦论或回圈量子重力理论。膨胀尺度是普朗克质量。<br />
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Effective field theories have also been used to simplify problems in General Relativity, in particular in calculating the [[gravitational wave]] signature of inspiralling finite-sized objects.<ref>{{Cite journal |arxiv = hep-th/0409156|last1 = Goldberger|first1 = Walter|title = An Effective Field Theory of Gravity for Extended Objects|journal = Physical Review D|volume = 73|issue = 10|last2 = Rothstein|first2 = Ira|year = 2004|doi = 10.1103/PhysRevD.73.104029|s2cid = 54188791}}</ref> The most common EFT in GR is "[[Non-Relativistic General Relativity]]" (NRGR),<ref>[http://online.kitp.ucsb.edu/online/numrel-m08/buonanno/pdf1/Porto_NumRelData_KITP.pdf]</ref><ref>{{Cite journal |arxiv = 0712.4116|last1 = Kol|first1 = Barak|title = Non-Relativistic Gravitation: From Newton to Einstein and Back|journal = Classical and Quantum Gravity|volume = 25|issue = 14|pages = 145011|last2 = Smolkin|first2 = Lee|year = 2008|doi = 10.1088/0264-9381/25/14/145011|s2cid = 119216835}}</ref><ref>{{Cite journal |arxiv = gr-qc/0511061|last1 = Porto|first1 = Rafael A|title = Post-Newtonian corrections to the motion of spinning bodies in NRGR|journal = Physical Review D|volume = 73|issue = 104031|pages = 104031|year = 2006|doi = 10.1103/PhysRevD.73.104031|s2cid = 119377563}}</ref> which is similar to the [[post-Newtonian expansion]].<ref>{{Cite journal |doi = 10.1103/PhysRevD.88.104037|title = Theory of post-Newtonian radiation and reaction|journal = Physical Review D|volume = 88|issue = 10|pages = 104037|year = 2013|last1 = Birnholtz|first1 = Ofek|last2 = Hadar|first2 = Shahar|last3 = Kol|first3 = Barak|arxiv = 1305.6930|s2cid = 119170985}}</ref> Another common GR EFT is the Extreme Mass Ratio (EMR), which in the context of the inspiralling problem is called [[Extreme mass ratio inspiral|EMRI]].<br />
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Effective field theories have also been used to simplify problems in General Relativity, in particular in calculating the gravitational wave signature of inspiralling finite-sized objects. The most common EFT in GR is "Non-Relativistic General Relativity" (NRGR), which is similar to the post-Newtonian expansion. Another common GR EFT is the Extreme Mass Ratio (EMR), which in the context of the inspiralling problem is called EMRI.<br />
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有效场论也被用来简化广义相对论中的问题,特别是在计算有限大小的物体的引力波特征时。GR 中最常见的 EFT 是“非相对论广义相对论”(NRGR) ,它类似于后牛顿力学近似方法。另一个常见的 GR EFT 是极端质量比(EMR) ,在激励问题的背景下被称为 EMRI。<br />
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===Other examples其他例子===<br />
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Presently, effective field theories are written for many situations.<br />
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Presently, effective field theories are written for many situations.<br />
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目前,有效场理论是针对多种情况而编写的。<br />
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*One major branch of [[nuclear physics]] is [[quantum hadrodynamics]], where the interactions of [[hadron]]s are treated as a field theory, which should be derivable from the underlying theory of [[quantum chromodynamics]]. Quantum hadrodynamics is the theory of the [[nuclear force]], similarly to quantum chromodynamics being the theory of the [[strong interaction]] and quantum electrodynamics being the theory of the [[electromagnetic force]]. Due to the smaller separation of length scales here, this effective theory has some classificatory power, but not the spectacular success of the Fermi theory.<br />
*[[量子物理]]的一个主要分支是[[量子强子动力学]],其中[[强子]]的相互作用被视为场理论,它应该从[[量子色动力学]]的基础理论中衍生出来。量子强子动力学是[[核力]]的理论,类似于量子色动力学是[[强相互作用]的理论,量子电动力学是[[电磁力]的理论。由于长度尺度的分离较小,这一有效理论具有一定的分类能力,但没有费米理论的惊人成功。<br />
*In [[particle physics]] the effective field theory of [[Quantum chromodynamics|QCD]] called [[chiral perturbation theory]] has had better success.<ref>{{Cite journal |arxiv = hep-ph/9311274|last1 = Leutwyler|first1 = H|title = On the Foundations of Chiral Perturbation Theory|journal = Annals of Physics|volume = 235|pages = 165–203|year = 1994|doi = 10.1006/aphy.1994.1094|s2cid = 16739698}}</ref> This theory deals with the interactions of [[hadron]]s with [[pion]]s or [[kaon]]s, which are the [[Goldstone boson]]s of [[spontaneous chiral symmetry breaking]]. The expansion parameter is the [[pion]] energy/momentum.<br />
在[[粒子物理]]中,[[量子色动力学| QCD]]中称为[[手征微扰理论]的有效场论有更好的表现成功。这一理论研究[[强子]]s与[[π]]s或[[kaon]]s的相互作用,它们是[[自发手征对称性破坏]]的[[金石玻色子]]s。膨胀参数是[[pion]]能量/动量。<br />
*For [[hadron]]s containing one heavy [[quark]] (such as the [[bottom quark|bottom]] or [[Charm quark|charm]]), an effective field theory which expands in powers of the quark mass, called the [[heavy quark effective theory]] (HQET), has been found useful.<br />
对于含有一个重的[[夸克]]的[[强子]]s(例如[[底夸克|底]]或[[粲夸克|粲]]),一种以夸克质量为幂展开的有效场论,称为[[重夸克有效理论](HQET)。<br />
*For [[hadron]]s containing two heavy quarks, an effective field theory which expands in powers of the [[relative velocity]] of the heavy quarks, called [[non-relativistic QCD]] (NRQCD), has been found useful, especially when used in conjunctions with [[lattice QCD]].<br />
*对于含有两个重夸克的[[强子]],以重夸克的[[相对速度]]为幂展开的有效场论很实用,称为[[非相对论性QCD]](NRQCD),特别是在与[[晶格QCD]]结合时。 <br />
*For [[hadron]] reactions with light energetic ([[collinear]]) particles, the interactions with low-energetic (soft) degrees of freedom are described by the [[soft-collinear effective theory]] (SCET).<br />
对于与光能([[共线]])粒子的[[强子]]反应,用[[软共线有效理论]](SCET)描述了与低能(软)自由度的相互作用。 <br />
*Much of [[condensed matter physics]] consists of writing effective field theories for the particular property of matter being studied.<br />
*许多[[凝聚态物理]]都是为所研究的物质的特殊性质建立有效理论。<br />
*[[Hydrodynamics]] can also be treated using Effective Field Theories<ref>{{Cite journal |arxiv = 1211.6461|last1 = Endlich|first1 = Solomon|title = Dissipation in the effective field theory for hydrodynamics: First order effects|journal = Physical Review D|volume = 88|issue = 10|pages = 105001|last2 = Nicolis|first2 = Alberto|last3 = Porto|first3 = Rafael|last4 = Wang|first4 = Junpu|year = 2013|doi = 10.1103/PhysRevD.88.105001|s2cid = 118441607}}</ref><br />
[流体力学]也可以使用有效场论进行处理<br />
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==See also参见==<br />
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*[[Form factor (quantum field theory)]]<br />
形状因子(量子场论)<br />
*[[Renormalization group]]<br />
重整化群 <br />
*[[Quantum field theory]]<br />
量子场论<br />
*[[Quantum triviality]]<br />
量子平凡性<br />
*[[Ginzburg–Landau theory]]<br />
金茨堡-兰道理论<br />
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==References参考==<br />
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{{Reflist}}<br />
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==External links外部链接==<br />
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*{{cite arxiv |eprint=hep-ph/9806303|last1=Birnholtz|first1=Ofek|title=Effective Field Theory|last2=Hadar|first2=Shahar|last3=Kol|first3=Barak|year=1998}}<br />
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*{{cite journal |doi=10.1016/S1355-2198(01)00005-3 |url=http://philsci-archive.pitt.edu/93/1/Hartmann.pdf|title=Effective Field Theories, Reductionism and Scientific Explanation|journal=Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics|volume=32|issue=2|pages=267–304|year=2001|last1=Hartmann|first1=Stephan}}<br />
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*{{Cite journal |arxiv=hep-ph/9703290|last1=Birnholtz|first1=Ofek|title=Aspects of Heavy Quark Theory|journal= Annual Review of Nuclear and Particle Science|volume=47|pages=591–661|last2=Hadar|first2=Shahar|last3=Kol|first3=Barak|year=1997|doi=10.1146/annurev.nucl.47.1.591|s2cid=13843227}}<br />
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*[http://www.fuw.edu.pl/~dobaczew/maub-42w/node18.html Effective field theory] (Interactions, Symmetry Breaking and Effective Fields - from Quarks to Nuclei. an Internet Lecture by Jacek Dobaczewski)<br />
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范畴: 量子场论<br />
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[[Category:Statistical mechanics]]<br />
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类别: 统计力学<br />
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[[Category:Renormalization group]]<br />
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Category:Renormalization group<br />
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类别: 重整化群<br />
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[[Category:Nuclear physics]]<br />
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[[Category:Condensed matter physics]]<br />
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Category:Condensed matter physics<br />
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类别: 凝聚态物理学<br />
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<small>This page was moved from [[wikipedia:en:Effective field theory]]. Its edit history can be viewed at [[有效场论/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%9B%9A%E5%BE%92%E5%9B%B0%E5%A2%83&diff=21305囚徒困境2021-01-25T12:06:14Z<p>Vicky:/* Stochastic iterated prisoner's dilemma */</p>
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<div>此词条由Henry初步翻译。已由Smile审校。<br />
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{{short description|Canonical example of a game analyzed in game theory}}<br />
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The '''prisoner's dilemma''' is a standard example of a game analyzed in [[game theory]] that shows why two completely [[Rationality#Economics|rational]] individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by [[Merrill Flood]] and [[Melvin Dresher]] while working at [[RAND Corporation|RAND]] in 1950. [[Albert W. Tucker]] formalized the game with prison sentence rewards and named it "prisoner's dilemma",<ref>Poundstone, 1992</ref> presenting it as follows:<br />
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The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", prensenting it as follows:<br />
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<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>是<font color="#ff8000"> 博弈论game theory</font>分析博弈的一个代表性例子,它揭示了为什么两个完全理性的个体可能不会合作,即使这样做符合他们的最大利益。它最初是由梅里尔·弗勒德 Merrill Flood和 梅文·加舍尔 Melvin Dresher于1950年在兰德公司工作时构建的。阿尔伯特.W.塔克 Albert W. Tucker将这种博弈以监禁刑罚奖励的方式正式化,并将其命名为囚徒困境,具体阐述如下:<br />
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{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
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{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
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* If A and B each betray the other, each of them serves two years in prison<br />
* If A betrays B but B remains silent, A will be set free and B will serve three years in prison<br />
* If A remains silent but B betrays A, A will serve three years in prison and B will be set free<br />
* If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).}}<br />
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{{一个犯罪团伙的两名成员被捕入狱。每个囚犯都被单独监禁,与他人无法沟通。检察官缺乏足够的证据来对这两个人定罪,但有足够的证据以较低的罪名定罪。同时,检察官向每个犯人提供了一个交易。每个囚犯都有机会出卖对方,证明对方犯下的罪行,或者他们可以合作,保持沉默。可能的结果有:<br />
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*如果A和B都背叛了对方,他们都会在监狱服刑两年。<br />
*如果A背叛了B但B保持沉默,A会被无罪释放而B会服刑三年。<br />
*如果A保持沉默但B背叛了A,A会服刑三年而B会无罪释放。<br />
*如果A和B都保持沉默,他们就只用服刑一年(以较低的罪名)。}}<br />
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It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref> In reality, humans display a [[systemic bias]] towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action.<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref> This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref> The prisoner's dilemma became the focus of extensive experimental research.<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
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It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other. In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action. This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome. The prisoner's dilemma became the focus of extensive experimental research. <br />
<br />
这意味着,囚犯除了监禁刑罚之外,没有机会奖励或惩罚他们的同伴,他们的决定也不会影响他们未来的声誉。因为背叛一个同伴比与他们合作能得到更大的回报,所以所有纯粹理性的、自私自利的囚犯都会背叛对方,这意味着,对于两个纯粹理性的囚犯来说,唯一可能的结果就是他们相互背叛。<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref>实际上,尽管“理性的”自利行为的简单模型已经预测到了这一点,但人类在这种和类似的博弈中仍然表现出对合作行为的<font color="#ff8000">系统性偏差 systemic bias </font>。<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref>自从在兰德公司首次进行这项测试以来,人们就已经知道了这种对合作的偏见; 参与测试的秘书们相互信任,为了最好的共同的目标而努力。<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref>囚徒困境成为大量实验研究的焦点。<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
<br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by [[backward induction]]) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<br />
<br />
一个扩展的<font color="#ff8000">重复iterated</font>版本的博弈由此衍生出来。在这个版本中,经典博弈会在在同一组囚犯之间重复进行,他们不断有机会为了之前的决定对其他囚犯进行惩罚。如果参与者知道博弈的次数,那么(通过<font color="#ff8000">逆向归纳法 backward induction </font>)两个经典的理性的玩家就会因为和在单次博弈中相同的原因反复背叛对方。在无限次或未知次数的博弈中,没有固定的最优策略,因而,举办囚徒困境竞赛来竞争和检验这种情况下的算法。<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
<br />
<br />
The prisoner's dilemma game can be used as a model for many [[#Real-life examples|real world situations]] involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activitie <br />
<br />
囚徒困境博弈可以作为许多现实中涉及合作行为的模型。在非正式用法中,“囚徒困境”一词可适用于不严格符合经典或重复博弈的形式标准的情况: 例如,两个实体可以从合作中获得巨大利益或者会因为合作失败而遭受损失,但发现协调他们的活动很困难或者代价昂贵(并非是不可能的)。<br />
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<br />
<br />
==Strategy for the prisoner's dilemma==<br />
囚徒困境的策略<br />
<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
两名囚犯被分开关押在各自的房间里,不能相互交流。<br />
<br />
The normal game is shown below:<br />
<br />
The normal game is shown below:<br />
<br />
正常的博弈如下:<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class“ wikitable”<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! {{diagonal split header|<br />Prisoner A|Prisoner B}} !! Prisoner B stays silent<br>(''cooperates'') !! Prisoner B betrays<br>(''defects'')<br />
<br />
! !! Prisoner B stays silent<br>(cooperates) !! Prisoner B betrays<br>(defects)<br />
<br />
! {{diagonal split header|<br />犯人A|犯人B}}!!犯人B保持沉默<br>(''合作'') !! 犯人B背叛<br>(''背叛'')<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A stays silent<br>(''cooperates'')<br />
<br />
! Prisoner A stays silent<br>(cooperates)<br />
<br />
!犯人 a 保持沉默<br>(''合作'')<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
|每人服刑1年||囚犯 A: 3年<br />囚犯 B: 无罪释放<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A betrays<br>(''defects'')<br />
<br />
! Prisoner A betrays<br>(defects)<br />
<br />
!犯人A背叛<br>(''背叛'')<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
|囚犯 A: 获释<br />囚犯 B: 3年||每人服刑2年<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by [[Dilemma#Use in logic|dilemma]]: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by dilemma: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
假设两个囚犯都了解博弈的本质,对彼此不忠诚,且在博弈之外没有机会得到报复或奖励。那么不管对方怎么决定,每个犯人背叛对方都会得到更高的奖励(“叛变”)。推理涉及一个进退两难的论点:B 要么合作,要么叛变。如果B合作,A 应该叛变,因为得到释放总比服刑1年好。如果 B叛变,A也应该叛变,因为服刑2年总比服刑3年好。所以不管怎样,A都应该叛变。并行推理表明B应该选择叛变。<br />
<br />
<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a [[dominant strategy]]. Mutual defection is the only strong [[Nash equilibrium]] in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a dominant strategy. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
因为不管对方的选择如何,背叛总是比合作带来更好的回报,所以这是一个<font color="#ff8000">占优策略 dominant strategy</font>。相互背叛是博弈中唯一的强<font color="#ff8000">纳什均衡点 dominant strategy </font>(即每个参与者单方面的改变策略只能使自己的情况变糟)。因此,困境在于,虽然相互合作比相互背叛产生更好的结果,但它却不是理性的结果,因为从自我利益的角度来看,合作的选择是非理性的。<br />
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<br />
<br />
==Generalized form==<br />
<font color="#ff8000">广泛形态 Generalized form </font><br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
传统囚徒困境的结构可以从其最初的囚徒环境中概括出来。假设两个玩家用红色和蓝色表示,并且每个玩家选择“合作”或“背叛”。<br />
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<br />
<br />
If both players cooperate, they both receive the reward ''R'' for cooperating. If both players defect, they both receive the punishment payoff ''P''. If Blue defects while Red cooperates, then Blue receives the temptation payoff ''T'', while Red receives the "sucker's" payoff, ''S''. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff ''S'', while Red receives the temptation payoff ''T''.<br />
<br />
If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the tem punishment payoffptation payoff T.<br />
<br />
如果两个玩家合作,他们都会因为合作而获得奖励''R''。如果两个参与人都叛变,他们都会受到惩罚''P''。 如果蓝方叛变而红方合作,那么蓝方得到诱惑回报''T'',而红方受到“上当受骗者”损失''S''。同样地,如果蓝方合作而红方叛变,那么蓝方得到上当受骗者的损失''S'',而红方得到诱惑支付''T''。<br />
<br />
<br />
<br />
This can be expressed in [[Normal-form game|normal form]]:<br />
<br />
This can be expressed in normal form:<br />
<br />
这可以用标准形式的博弈来表示:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
| + <font color="#ff8000">正则 PD 支付矩阵 Canonical PD payoff matrix </font> <br />
<br />
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
! {{diagonal split header|{{color|#009|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
要成为强意义下的囚徒困境博弈,收益必须满足以下条件:<br />
<br />
<br />
<br />
:{{tmath|T > R > P > S}}<br />
<br />
<br />
<br />
The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents.<br />
<br />
The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents.<br />
<br />
回报关系{{tmath|R > P}}意味着相互合作优于相互背叛,然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。<br />
<br />
<br />
<br />
===Special case: donation game===<br />
特例:<font color="#ff8000">捐赠博弈 donation game </font><br />
<br />
The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus<br />
<br />
The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus<br />
<br />
捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式,在这种博弈中,合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b'',而叛变意味着什么也不提供。收益矩阵如下:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
! {{diagonal split header|{{navy (color)|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section).<br />
<br />
Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section).<br />
<br />
请注意{{tmath|2R>T+S}}(即{{tmath|2(b-c)>b-c}})这使得捐赠博弈成为一个重复博弈(见下一节)。<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything.<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.<br />
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捐赠博弈可能适用于市场。假设种植者X 种橘子,种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b'',“b”比橙子的边际效用''c''高,因为X有橙子剩余而没有苹果。同样地,对于苹果种植者Y来说,橙子的边际效用是''b'',而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子,并且每个人都完成了交易,那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货,那么这个违约者将得到''b''的收益,而合作者将失去''c''的收益。 如果两者都违约,那么谁也不会得到或失去任何东西。<br />
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==The iterated prisoner's dilemma==<br />
<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma </font> {{more citations needed section|date=November 2012}}<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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如果两个参与者连续进行多次囚徒困境博弈,他们记住对手先前的行动并相应地改变策略,这种博弈被称为重复囚徒困境。<br />
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In addition to the general form above, the iterative version also requires that {{tmath|2R > T + S}}, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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In addition to the general form above, the iterative version also requires that , to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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除了上面的一般形式之外,重复版本还要求{{tmath|2R > T + S}},防止交替合作和背叛比相互合作有更大的回报。<br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "[[Peace war game|peace-war game]]".<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "peace-war game".<br />
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重复囚徒困境博弈是人类合作与信任的理论基础。假设博弈可以为两个需要信任的人之间的交易建模,那么群体中的合作行为也可以由多个参与者重复的博弈模型来建模。因此,这些年来,它吸引了许多学者。1975年,葛夫曼 Grofman和普尔 Pool估计专门撰写有关该领域的学术文章超过2000篇。重复囚徒困境也被称为“和平-战争博弈”。<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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If the game is played exactly ''N'' times and both players know this, then it is optimal to defect in all rounds. The only possible [[Nash equilibrium]] is to always defect. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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If the game is played exactly N times and both players know this, then it is optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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如果这个游戏正好玩了N次,并且两个玩家都知道这一点,那么在所有回合中最佳的策略就是叛变。唯一可能的纳什均衡点就是永远叛变。证明是通过归纳法证出来的: 不妨假设一个人在最后一回合叛变,因为对手之后没有机会反击。因此,双方都会在最后一个回合叛变。所以玩家同样也会在倒数第二回合时叛变,因为无论采取什么策略,对手都会在倒数第一回合叛变,依此类推。如果博弈次数未知但次数有限的情况也同样如此。<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The [[superrational]] strategy in the iterated prisoner's dilemma with fixed ''N'' is to cooperate against a superrational opponent, and in the limit of large ''N'', experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoner's dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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与标准的囚徒困境不同,在重复囚徒困境中,叛变策略是严重违反直觉的,以至于不能很好地预测人类玩家的行为。然而,在标准的经济理论中,这是唯一正确的答案。具有固定次数 N的重复囚徒困境中的<font color="#ff8000">超理性 superrational</font>策略是与超理性对手进行合作,在N很大的限制下,实验结果的策略与超理性结果的策略一致,而不是博弈论的理性结果。<br />
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For [[cooperation]] to emerge between game theoretic rational players, the total number of rounds ''N'' must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by [[Robert Aumann]] in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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For cooperation to emerge between game theoretic rational players, the total number of rounds N must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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为了使合作在博弈论的理性参与者之间出现,参与者必须不知道回合总数N。在这种情况下,“总是叛变”可能不再是一个严格占优策略,而只是一个纳什均衡。罗伯特·奥曼 Robert Aumann在1959年的一篇论文中表明,理性参与者在无限多次的博弈中通过反复互动可以维持合作的结果。<br />
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According to a 2019 experimental study in the ''American Economic Review'' which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, [[Tit for tat|tit-for-tat]], and [[Grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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According to a 2019 experimental study in the American Economic Review which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, tit-for-tat, and Grim trigger. Which strategy the subjects chose depended on the parameters of the game.<br />
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根据《美国经济评论》于2019年进行的一项实验研究,该实验中通过完美的监控测试了现实中被用在重复囚徒困境情况下的策略,监测选择的策略总是背叛,针锋相对的和 <font color="#ff8000"> 冷酷触发策略 Grim trigger</font>。受试者选择的策略取决于博弈的参数。<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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===Strategy for the iterated prisoner's dilemma===<br />
重复囚徒困境下的策略<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by [[Robert Axelrod]] in his book ''[[The Evolution of Cooperation]]'' (1984). In it he reports on a tournament he organized of the ''N'' step prisoner's dilemma (with ''N'' fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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Interest in the iterated prisoner's dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In it he reports on a tournament he organized of the N step prisoner's dilemma (with N fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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罗伯特·阿克塞尔罗德 Robert Axelrod在他的著作《合作的进化》(1984)中激起了人们对重复囚徒困境(IPD)的兴趣。在这篇文章中,他报道了自己组织的固定N次囚徒困境的比赛,参与者必须一次又一次地选择他们的共同策略,并且要记住他们之前的遭遇。阿克塞尔罗德邀请世界各地的学术界同仁设计计算机策略来参加IPD锦标赛。输入的程序在算法复杂性、最初敌意、宽恕能力等方面有很大差异。<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more [[altruism|altruistic]] strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by [[natural selection]].<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.<br />
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阿克塞尔罗德发现,当这些遭遇长时间在许多玩家身上重复发生时,每个玩家都有不同的策略,从长远来看,贪婪策略往往表现得非常糟糕,而更加利他的策略表现得更好,这完全是根据自身利益来判断的。他利用这一结果揭示了通过自然选择,从最初纯粹自私行为向利他行为进化的可能机制。<br />
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The winning [[deterministic algorithm|deterministic]] strategy was tit for tat, which [[Anatol Rapoport]] developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of [[BASIC]], and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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The winning deterministic strategy was tit for tat, which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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最终获胜的决定性策略是针锋相对策略,这是阿纳托尔·拉波波特 Anatol Rapoport开发并参加比赛的策略。这是所有参赛程序中最简单的一个,只有四行 BASIC 语言,并且赢得了比赛。策略很简单,就是在游戏的第一次重复中进行合作; 在此之后,玩家将执行做他的对手在前一步中所做的事情。根据具体情况,一个稍微好一点的策略可以是“带着宽恕之心针锋相对”。当对手叛变时,在下一次博弈中,玩家有时还是会合作,但概率很小(大约1-5%)。这允许博弈偶尔能从陷入叛变循环中恢复过来。确切的概率取决于对手的安排。<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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通过分析得分最高的战略,阿克塞尔罗德阐述了战略成功的几个必要条件。<br />
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; Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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;友好:最重要的条件是策略必须是好的,也就是说,它不会在对手之前叛变(这有时被称为“乐观”算法)。几乎所有得分最高的策略都是友好的; 因此,一个纯粹的自私策略不会为了纯粹自身的利益而“欺骗”对手。<br />
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; Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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;报复:然而,阿克塞尔罗德认为,成功的战略决不能是盲目的乐观主义。它有时必须进行报复。非报复策略的一个例子就是永远合作。这是一个非常糟糕的选择,因为“肮脏”的策略会无情地利用这些玩家。<br />
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; Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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;宽容: 成功的策略也必须是宽容的。虽然玩家会报复,但如果对手不继续叛变,他们将再次回到合作的状态。这阻止了长时间的报复和反报复,最大限度地提高积分。<br />
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; Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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;不嫉妒: 最后一个品质是不嫉妒,不强求比对手得分更多。<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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对于一次性的囚徒困境博弈,最优(点数最大化)策略就是简单的叛变; 正如上面所说,无论对手的构成如何,这都是正确的。然而,在重复囚徒困境博弈中,最优策略取决于可能的对手的策略,以及他们对叛变和合作的反应。例如,考虑一个群体,其中每个人每次都会叛变,只有一个人遵循针锋相对的策略。那个人就会由于第一回合的失利而处于轻微的不利地位。在这样一个群体中,个体的最佳策略是每次都叛变。在一定比例的总是选择背叛的玩家和其余组成选择针锋相对策略的玩家的人群中,个人的最佳策略取决于这一比例和博弈的次数。<br />
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In the strategy called Pavlov, [[win-stay, lose-switch]], faced with a failure to cooperate, the player switches strategy the next turn.<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref> In certain circumstances,{{specify|date=November 2012}} Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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In the strategy called Pavlov, win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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在所谓的<font color="#ff8000">巴甫洛夫策略 Pavlov strategy</font>中,<font color="#ff8000">去输存赢 win-stay, lose-switch</font>,面对一次合作失败,玩家将在下一次变换策略。<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref>在某些情况下,{{specify|date=November 2012}}巴甫洛夫通过使用类似策略给与合作者优惠待遇打败了其他所有策略。<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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得出最佳策略通常有两种方法:<br />
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* [[Bayesian Nash equilibrium]]: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit for tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.{{efn|1=For example see the 2003 study<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref> for discussion of the concept and whether it can apply in real [[economic]] or strategic situations.}}<br />
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<font color="#ff8000">贝叶斯纳什均衡 Bayesian Nash equilibrium</font>:如果可以确定对立策略的统计分布(例如,50%针锋相对,50%总是合作),那么,可以通过分析得出最佳的反策略{{efn|1=例如2003年的研究<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref>讨论这一概念以及它是否可以应用于实际经济或战略情况。}}<br />
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* [[Monte Carlo method|Monte Carlo]] simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a [[genetic algorithm]] for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit for tat players (see for instance Chess 1988),{{Clarify|date=August 2016}} but no analytic proof exists that this will always occur.<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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<font color="#ff8000">蒙特卡洛方法 Monte Carlo method </font>已经对种群进行了模拟,分数低的个体死亡,分数高的个体繁殖(<font color="#ff8000">遗传算法 genetic algorithm </font>用于寻找一个最佳策略)。最终群体中的算法组合通常取决于初始总体的组合。引入突变(繁殖过程中的随机变异)可以减少对初始种群的依赖性。使用这种系统进行经验性实验往往会为针锋相对的玩家带来麻烦(见Chess 1988),{{Clarify|date=August 2016}},但是没有分析证据表明这种情况会一直发生。<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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Although tit for tat is considered to be the most [[robust]] basic strategy, a team from [[Southampton University]] in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start.<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref> Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show [[University of Southampton]]'s strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between [[computer program|software strategies]] (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian [[Evolutionarily stable strategy|ESS]] simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. [[Richard Dawkins]] showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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Although tit for tat is considered to be the most robust basic strategy, a team from Southampton University in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between software strategies (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian ESS simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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尽管针锋相对被认为是最有力的基本策略,来自英格兰南安普敦大学的一个团队在20周年的重复囚徒困境竞赛中提出了一个新策略,这个策略被证明比针锋相对更为成功。这种策略依赖于程序之间的串通,以获得单个程序的最高分数。这所大学提交了60个程序,这些程序的设计目的是在比赛开始时通过一系列的5到10个动作来互相认识。<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref>一旦认识建立,一个程序总是合作,另一个程序总是叛变,保证叛变者得到最多的分数。如果这个程序意识到它正在和一个非南安普顿的球员比赛,它会不断地叛变,试图最小化与之竞争的程序的得分。因此,2004年囚徒困境锦标赛的结果显示了南安普敦大学战略位居前三名,尽管它比冷酷战略赢得更少,输的更多。(在囚徒困境锦标赛中,比赛的目的不是“赢”比赛——这一点频繁叛变很容易实现)。此外,即使没有软件策略之间的暗中串通(南安普顿队利用了这一点) ,针锋相对并不总是任何特定锦标赛的绝对赢家; 更准确地说,它是在一系列锦标赛中的长期结果超过了它的竞争对手。(在任何一个事件中,一个给定的策略可以比针锋相对稍微更好地适应竞争,但是针锋相对更稳健)。这同样适用于带有宽恕变量的针锋相对,和其他最佳策略: 在任何特定的一天,他们可能不会“赢得”一个特定的混合反战略。另一种方法是使用达尔文 Darwinian的<font color="#ff8000"> ESS模拟 ESS simulation</font>。在这样的模拟中,针锋相对几乎总是占主导地位,尽管讨厌的策略会在人群中漂移,因为使用针锋相对策略的人群可以通过非报复性的好策略进行渗透,这反过来使他们容易成为讨厌策略的猎物。理查德·道金斯 Richard Dawkins指出,在这里,没有静态的混合策略会形成一个稳定的平衡,系统将始终在边界之间振荡。这种策略最终在比赛中获得了前三名的成绩,或者是接近垫底的成绩。<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of [[minmaxing]]). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book ''[[The Selfish Gene]]'', pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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这种策略利用了这样一个事实,即在这场特殊的比赛中允许多个参赛项目,并且团队的表现由得分最高的项目来衡量(这意味着使用自我牺牲的项目是一种分数最大化的形式)。在一个只能控制一个玩家的比赛中,针锋相对当然是一个更好的策略。由于这一新规则的存在,与阿克塞尔罗德的具有深远影响的竞赛相比,这种竞赛在分析单个主体策略时也就没有什么理论意义。然而,它为在分析多主体框架下,特别是在存在干扰的情况下,如何实现协作策略提供了基础。事实上,早在这场新规则锦标赛开始之前,道金斯就在他的《自私的基因》一书中指出,如果允许多次参赛,这种策略就有可能获胜,但他说,如果提交这种策略的话,阿克塞尔罗德很可能不会允许。因为它依赖于规避囚徒困境的规则,即两个参与者之间不允许交流,南安普顿的项目可以说在开场的“十步舞”中就是这样做以认识对方的; 这只是强调了交流在改变游戏平衡方面的价值。<br />
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===Stochastic iterated prisoner's dilemma===<br />
随机重复囚徒困境<br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities".<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref> In an encounter between player ''X'' and player ''Y'', ''X'' 's strategy is specified by a set of probabilities ''P'' of cooperating with ''Y''. ''P'' is a function of the outcomes of their previous encounters or some subset thereof. If ''P'' is a function of only their most recent ''n'' encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that ''X'' will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which ''X'' cooperated and ''Y'' defected, then <math>P_{cd}</math> is the probability that ''X'' will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as ''P''={1,0,1,0}, in which ''X'' responds as ''Y'' did in the previous encounter. Another is the [[win–stay, lose–switch]] strategy written as ''P''={1,0,0,1}, in which ''X'' responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<ref name="Press2012"/><br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player X and player Y, X 's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which X cooperated and Y defected, then <math>P_{cd}</math> is the probability that X will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as P={1,0,1,0}, in which X responds as Y did in the previous encounter. Another is the win–stay, lose–switch strategy written as P={1,0,0,1}, in which X responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<br />
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在随机重复<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>博弈中,策略由“合作概率”来确定。<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref>在玩家''X''和玩家''Y''之间的遭遇中,''X''的策略由一组与''Y''合作的概率''P''确定,''P''是他们之前遭遇的结果的函数,或者是其中的一些子集。如果''P''只是它们最近遇到次数 ''n''的函数,那么它被称为“记忆-n”策略。我们可以由四个联合概率指定一个记忆-1策略: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>,其中<math>P_{ab}</math>是在当前遭遇中基于先前联合的概率。如果每个概率都是1或0,这种策略称为确定性策略。确定性策略的一个例子是针锋相对策略,写成 p {1,0,1,0} ,其中 x 的反应和 y 在前一次遭遇中的反应一样。另一种是胜-保持-败-转换策略,它被写成 p {1,0,0,1} ,在这种策略中,如果 x 获得胜利(即:cc 或 dc),x会做出与上一次遭遇一样的反应 ,但如果失败,x会改变策略(即cd 或 dd)。研究表明,对于任何一种记忆-n 策略,存在一个相应的记忆-1策略,这个策略给出相同的统计结果,因此只需要考虑记忆-1策略。<ref name="Press2012"/><br />
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If we define ''P'' as the above 4-element strategy vector of ''X'' and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of ''Y'', a transition matrix ''M'' may be defined for ''X'' whose ''ij'' th entry is the probability that the outcome of a particular encounter between ''X'' and ''Y'' will be ''j'' given that the previous encounter was ''i'', where ''i'' and ''j'' are one of the four outcome indices: ''cc'', ''cd'', ''dc'', or ''dd''. For example, from ''X'' 's point of view, the probability that the outcome of the present encounter is ''cd'' given that the previous encounter was ''cd'' is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for ''Q'' are from ''Y'' 's point of view: a ''cd'' outcome for ''X'' is a ''dc'' outcome for ''Y''.) Under these definitions, the iterated prisoner's dilemma qualifies as a [[stochastic process]] and ''M'' is a [[stochastic matrix]], allowing all of the theory of stochastic processes to be applied.<ref name="Press2012"/><br />
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If we define P as the above 4-element strategy vector of X and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of Y, a transition matrix M may be defined for X whose ij th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X 's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for Q are from Y 's point of view: a cd outcome for X is a dc outcome for Y.) Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.<br />
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如果我们将''P''定义为''X''的上述4元策略向量,并将<math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math>定义为''Y''的4元策略向量,则对于''X''可以定义一个转移矩阵''M'',其第ij项是''X''和''Y''之间特定相遇的结果为j的概率,给定i,其中i和j是cc、cd、dc或dd 四个结果索引中的一个。例如,从''X''的角度来看,如果给定''cd'',那么这次的结果是''cd''的概率等于<math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>。(''Q''的指标是 从''Y''的角度: ''X''的''cd''结果是''Y''的''dc''结果)在这些定义下,重复的囚徒困境被定义为一个随机过程,''M''是一个随机矩阵,允许应用所有的随机过程理论。<ref name="Press2012"/><br />
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One result of stochastic theory is that there exists a stationary vector ''v'' for the matrix ''M'' such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that ''v'' is normalized so that the sum of its four components is unity. The ''ij'' th entry in <math>M^n</math> will give the probability that the outcome of an encounter between ''X'' and ''Y'' will be ''j'' given that the encounter ''n'' steps previous is ''i''. In the limit as ''n'' approaches infinity, ''M'' will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing ''j'' which will be independent of ''i''. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that ''v'' is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to ''v''. Thus the stationary vector specifies the equilibrium outcome probabilities for ''X''. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From ''X'' 's point of view), the equilibrium payoffs for ''X'' and ''Y'' can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.<br />
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One result of stochastic theory is that there exists a stationary vector v for the matrix M such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij th entry in <math>M^n</math> will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j which will be independent of i. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to v. Thus the stationary vector specifies the equilibrium outcome probabilities for X. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From X 's point of view), the equilibrium payoffs for X and Y can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies P and Q to be compared for their long term payoffs.<br />
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随机理论的一个结果是,矩阵''M''存在一个平稳向量''v''使得<math>v\cdot M=v</math>成立。一般地,我们可以指定''v''是标准化的,因此它的4个组成部分之和为1。the equilibrium payoffs for and can now be specified as and, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.第''ij''项<math>M^n</math>给出了''X''和''Y''相遇的结果的概率为''j'',给定前面相遇''n''步的概率是''i''。当''n''趋于无穷时,''M''收敛于一个具有固定值的矩阵,并且''j''趋向一个长期概率,与''i''独立。换句话说, <math>M^\infty</math>的行将是相同的,从而给出了重复囚徒困境的长期均衡结果概率,而不需要明确地计算大量的相互作用。可以看出,''v''是<math>M^n</math>特别是<math>M^\infty</math>, 的平稳向量,因此<math>M^\infty</math>的每一行都等于''v''。因此平稳向量指定了''X''的均衡结果概率。定义<math>S_x=\{R,S,T,P\}</math>和<math>S_y=\{R,T,S,P\}</math>作为{cc,cd,dc,dd}结果的短期收益向量(从''X''的角度来看) ,现在可以将''X''和''Y''的均衡收益指定为<math>s_x=v\cdot S_x</math>和<math>s_y=v\cdot S_y</math>,使得''P''、''Q''两种策略的长期收益可以比较。<br />
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====Zero-determinant strategies====<br />
<font color="#ff8000">零决定策略 Zero-determinant strategies</font><br />
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[[File:IPD Venn.svg|right|thumb|upright=2.5|The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram]]. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and [[weak selection]]. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and weak selection. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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<font color="#ff8000">维恩图 Venn diagram</font>中讨论了<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma</font>(IPD)中零决定策略(ZD)、合作策略和背叛策略之间的关系。合作策略总是与其他合作策略相互配合,而背叛策略总是与其他背叛策略相抵触。这两种策略都包都含在强选择下稳健的策略子集,这意味着当它们驻留在一个种群中时,没有选择其他的记忆-1策略来入侵此策略。只有合作策略包含在始终稳健的策略子集,意味着无论选择强项还是弱项,都不会选择其他任何记忆-1策略来入侵和替换此策略。零决定策略和良好的合作策略之间的交集是一组宽松的零决定策略。勒索策略是零决定策略和非稳健背叛策略的交集。针锋相对是合作、背叛和零决定策略的交集。<br />
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In 2012, [[William H. Press]] and [[Freeman Dyson]] published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies.<ref name="Press2012"/> The long term payoffs for encounters between ''X'' and ''Y'' can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector ''v''. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in ''f'', it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where ''U''={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector v. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in f, it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where U={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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2012年,威廉·H·普莱斯 William H. Press和弗里曼·戴森 Freeman Dyson针对随机重复囚徒困境提出了一类新的策略,称为“零决定”策略。<ref name="Press2012"/>''X''和''Y''之间的长期收益可以表示为一个矩阵的决定因素,它是两个策略和短期收益向量的函数: <math>s_x=D(P,Q,S_x)</math>和<math>s_y=D(P,Q,S_y)</math>,不涉及平稳向量''v''。 由于行列式函数<math>s_y=D(P,Q,f)</math>在''f''中是线性的,因此可以推出<math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math>(其中''U''={1,1,1,1})。任何策略的<math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math>被定义为零决定策略,长期收益服从关系式<math>\alpha s_x+\beta s_y+\gamma=0</math>。<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of [[ultimatum game]]. Specifically, ''X'' is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of ''Y'' 's strategy, offering an opportunity for ''X'' to "extort" player ''Y'' (and vice versa). (It turns out that if ''X'' tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.<ref name="Press2012"/>)<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of Y 's strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.)<br />
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针锋相对是一种零决定策略,在不获得超越其他玩家优势的意义下是“公平”的。然而,零决定策略空间还包含这样的策略:在两个玩家的情况下,可以允许一个玩家单方面设置另一个玩家的分数,或者强迫进化的玩家获得比他自己的分数低一些的收益。被勒索的玩家可能会背叛,但会因此获得较低的回报并且受到伤害。因此,勒索的解决方案将重复囚徒困境转化为一种<font color="#ff8000">最后通牒博弈 ultimatum game </font>。具体来说,''X''能够选择一种策略,对于这种策略,<math>D(P,Q,\beta S_y+\gamma U)=0</math>单方面地将<math>s_y</math>设置为一个特定值范围内的特定值,与''Y''的策略无关,为''X''提供了“勒索”玩家''Y''的机会(反之亦然)。(事实证明,如果''X''试图将<math>s_x</math>设置为一个特定的值,那么可能的范围要小得多,只包括完全合作或完全叛变。<ref name="Press2012"/>)<br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not [[evolutionarily stable strategy|evolutionarily stable]]. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<br />
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重复囚徒困境的一个扩展是进化的随机重复囚徒困境,其中允许特定策略的相对丰度改变,更成功的策略相对增加。这个过程可以通过让不太成功的玩家模仿更成功的策略,或者通过从游戏中淘汰不太成功的玩家,同时让更成功的玩家成倍增加。研究表明,不公平的零决定策略不是进化稳定策略。关键的直觉告诉我们,进化稳定策略不仅要能够入侵另一个群体(这是勒索零决定策略可以做到的) ,而且还要在同类型的其他玩家面前表现良好(勒索零决定策略玩家表现不佳,因为他们减少了彼此的盈余)。<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and [[win–stay, lose–switch]] agents.<ref name=Hilbe2013 /><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.<br />
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理论和模拟证实,超过一个临界种群规模,零决定勒索在与更多合作策略的进化竞争中会失败,因此,种群越大,种群的平均收益就越大。此外,在某些情况下,勒索者甚至可能通过帮助打破统一的背叛者与使用“赢-保持-输”策略的转换玩家之间的对峙而促进合作。<ref name=Hilbe2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies ''is'' both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the [[Prisoner's dilemma#Special case: Donation game|donation game]] by Alexander Stewart and Joshua Plotkin in 2013.<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref> Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013)<ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<ref name=Stewart2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013) to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<br />
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虽然勒索零决定策略在人口众多的情况下并不稳定,但另一种宽松的零决定策略既稳定又稳健。事实上,当人口不算太少的时候,这些策略可以取代任何其他零决定策略,甚至在一系列针对重复囚徒困境的广泛通用策略(包括“获胜-保持-输”的转换策略)中表现良好。亚历山大·斯图尔特 Alexander Stewart和约书亚·普洛特金 Joshua Plotkin在2013年的捐赠博弈中证明了这一点。<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref>宽松的策略会与其他合作的玩家合作,面对背叛,慷慨的玩家比他的对手失去更多的效用。宽松策略是零决定策略和所谓的“好”策略的交集,阿金(2013) <ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.将这两种策略定义为玩家对过去的相互合作作出回应,并在至少获得合作预期收益的情况下平均分配预期收益的策略。在好的策略中,当总体不太小时,宽松(零决定)子集表现良好。如果总体很少,背叛策略往往占主导地位。<ref name=Stewart2013 /><br />
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===Continuous iterated prisoner's dilemma===<br />
<font color="#ff8000">连续重复囚徒困境 Continuous iterated prisoner's dilemma </font> <br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref> found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from [[Assortative mating|assorting]] with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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关于重复囚徒困境的研究大多集中在离散情况下,在这种情况下,参与者要么合作,要么背叛,因为这个模型分析起来比较简单。然而,一些研究人员已经研究了连续重复囚徒困境模型,在这个模型中,玩家能够对另一个玩家做出可变的贡献。乐 Le和博伊德 Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref>发现,在这种情况下,合作比离散重复的囚徒困境更难发展。这个结果的基本直觉很简单: 在一个持续的囚徒困境中,如果一个人群开始处于非合作均衡状态,那么与非合作者相比,合作程度稍高的玩家不会从相互配合中获益。相比之下,在离散的囚徒困境中,相对于非合作者,针锋相对的合作者在非合作均衡中相互配合会获得巨大的回报。由于自然界可以提供更多的机会来进行各种各样的合作,而不是严格地将合作或背叛分为两类,因此连续的囚徒困境可以帮助解释为什么现实生活中针锋相对的合作的例子在自然界中极其罕见。(例如,哈默斯坦 Hammerstein <ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)。<br />
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even though tit for tat seems robust in theoretical models.<br />
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even though tit for tat seems robust in theoretical models.<br />
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尽管在理论模型中,针锋相对策略似乎是稳健的。<br />
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===Emergence of stable strategies===<br />
<font color="#ff8000">稳定策略的出现 Emergence of stable strategies </font> <br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref> Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies. Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<br />
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玩家似乎不能协调相互合作,因此常常陷入劣等而稳定的背叛策略。这样,重复回合可以促进稳定策略的发展。<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref>重复回合往往产生新颖的策略,这对复杂的社会互动有影响。其中一个策略就是“赢-保持-输”的转变。这个策略比一个简单的针锋相对策略要好&nbsp;–也就是说,如果你能逃脱作弊的惩罚,就重复这个行为,如果你被抓住了,就改变策略。<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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这种针锋相对策略的唯一问题是它们很容易出现信号错误。当一个人因报复而作弊,而另一个人将其单纯解释为欺骗时,就会出现问题。结果,第二个人现在作弊,然后在接下来的连锁反应中开始了反复交替的作弊模式。<br />
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==Real-life examples==<br />
现实生活的例子<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the [[social science]]s such as [[economics]], [[politics]], and [[sociology]], as well as to the biological sciences such as [[ethology]] and [[evolutionary biology]]. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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囚犯的环境似乎是人为的,但实际上,在人类交往以及自然界的交互中有许多具有相同收益矩阵的例子。因此,囚徒困境是经济学、政治学、社会学等社会科学以及动物行为学、进化生物学等生物学研究的热点问题。许多自然过程都被抽象为生物进行无休止的囚徒困境博弈的模型。囚徒困境这种广泛的适用性让博弈变得非常重要。<br />
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===Environmental studies===<br />
环境研究<br />
In [[environmental studies]], the PD is evident in crises such as global [[climate change|climate-change]]. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb [[Carbon dioxide|{{Co2}}]] emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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In environmental studies, the PD is evident in crises such as global climate-change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide| emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<br />
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在环境研究中,囚徒困境在诸如全球气候变化等危机中显而易见。有人认为,所有国家都将从稳定的气候中受益,但是每一个国家通常都在限制二氧化碳排放方面犹豫不决。人们错误地认为,如果所有国家的行为都改变,任何一个国家保持目前的行为所带来的直接好处都会大于所谓的最终好处,这就解释了2007年气候变化方面的僵局。<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<br />
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气候变化政治与囚徒困境之间的一个重要区别是不确定性; 污染对气候变化的影响程度和速度尚不清楚。因此,政府面临的困境不同于囚徒困境,因为合作的回报是未知的。这种差异表明,各国之间的合作远远少于真正的重复囚徒困境中的合作,因此避免可能发生的气候灾难的可能性远远小于使用真正的重复囚徒困境博弈论情景分析<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of [[Michael Porter]]'s hypothesis, in which government regulation of competing firms is substantial.<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.<br />
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欧桑 Osang和南迪 Nandy (2003)提供了一个理论解释,并根据迈克尔·波特 Michael Porter的假设,即政府对竞争企业的监管是实质性的,证明了监管驱动的双赢局面。<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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===Animals===<br />
动物<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, [[guppy|guppies]] inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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许多动物的合作行为可以理解为囚徒困境的一个例子。通常动物会建立长期的伙伴关系,这种关系可以更具体地模拟为重复囚徒困境。例如,孔雀鱼成群结队地合作监察捕食者,它们被认为是在惩罚不合作的监察者。<br />
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[[Vampire bats]] are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<br />
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吸血蝙蝠是从事相互的食物交换的群居动物。应用囚徒困境收益可以帮助解释这种行为: <ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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* C/C: "Reward: I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much."<br />
* 合作/合作:"回报:我在不幸运的晚上得到了能让我果腹的血,那在幸运的晚上我也应该分出点血,那不会花费多少。"<br />
* D/C: "Temptation: You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night."<br />
* 背叛/合作:"诱惑:你在我的不幸的夜里救了我,但在我的幸运夜我不会给你血,那样我会活的更好。"<br />
* C/D: "Sucker's Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death."<br />
* 合作/叛变:"可怜者的回报:在我的幸运夜我救了你的命,但在我的不幸夜里你没有救我,我有饿死的风险。"<br />
* D/D: "Punishment: I don't have to pay the slight costs of feeding you on my good nights. But I run a real risk of starving on my poor nights."<br />
* 叛变/叛变:"惩罚:我在我的幸运夜里不必付出代价来救你,但我在我的不幸夜里有挨饿的风险。"<br />
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===Psychology===<br />
心理学<br />
In [[addiction]] research / [[behavioral economics]], [[George Ainslie (psychologist)|George Ainslie]] points out<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref> that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, ''defecting'' means ''relapsing'', and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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In addiction research / behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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在成瘾研究/行为经济学中,乔治·安斯利 George Ainslie指出<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref>,可以将成瘾视为成瘾者现在和未来自我之间的跨期囚徒困境问题。在这种情况下,背叛意味着复发,很容易看出,目前和未来都没有背叛是迄今为止最好的结果。如果一个人今天戒了,但在将来又复吸,这是最糟糕的结果&nbsp;–从某种意义上来说,今天戒瘾所包含的纪律和自我牺牲已经被“浪费”了,因为未来的复吸意味着瘾君子又回到了他开始的地方,他将被迫重新开始(这相当令人沮丧,也使得重新开始更加困难)。今天和明天复发是一个稍微“好一点”的结果,因为尽管瘾君子仍然上瘾,但他们没有努力去尝试停止。最后一种情况是,现在与成瘾斗争的任何人都会熟悉现在的成瘾行为,而在明天放弃。这里的问题是(和其他囚徒困境问题一样),背叛“今天”有一个明显的好处,但明天这个人将面临同样的囚徒困境问题,同样明显的好处是背叛,最终导致一连串无休止的背叛。<br />
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[[John Gottman]] in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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John Gottman in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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约翰·高特曼 John Gottman在他的研究《信任的科学》中将良好的关系定义为伙伴知道不进入(背叛,背叛)牢房中或者至少不要陷入这样的动态循环关系中。<br />
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===Economics===<br />
经济学<br />
The prisoner's dilemma has been called the ''[[Escherichia coli|E. coli]]'' of social psychology, and it has been used widely to research various topics such as [[Oligopoly|oligopolistic]] competition and collective action to produce a collective good.<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref> <br />
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The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good. <br />
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囚徒困境被称为社会心理学中的“大肠杆菌”,它被广泛用于研究寡头垄断竞争和集体行动来产生集体利益等问题。<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When [[cigarette advertising]] was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. <ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref> This analysis is likely to be pertinent in many other business situations involving advertising. <ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.<br />
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广告有时被认为是囚徒困境的一个真实例子。当香烟广告在美国是合法的时候,相互竞争的香烟制造商必须决定在广告上花多少钱。公司A的广告效果部分取决于公司B的广告效果。同样,公司B的广告带来的利润也受到公司A的广告影响。如果公司A和公司B都选择在给定的时间段内做广告,那么一家公司的广告就会抵消另一方的广告,倘若收入保持不变,费用就会因广告成本而增加。两家公司都将从广告减少中获益。然而,如果B公司选择不做广告,A公司就可以通过广告获得巨大的利益。尽管如此,一家公司的最佳广告数量仍取决于另一家公司的广告投放量。由于最佳策略取决于其他公司的选择,因此这里没有占主导地位的策略,这使得它与囚徒困境略有不同。但结果是相似的,如果两家公司的广告都少于均衡状态,他们的处境会更好。有时合作行为确实会在商业环境中出现。例如,香烟制造商支持立法禁止香烟广告,因为这将降低成本并增加整个行业的利润。<ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref>这种分析可能适用于许多其他涉及广告的商业情况。<ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref> <br />
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Without enforceable agreements, members of a [[cartel]] are also involved in a (multi-player) prisoner's dilemma.<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. [[Anti-trust]] authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for [[consumer]]s.<br />
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Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.<br />
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没有可强制执行的协议,卡特尔 cartel的成员国也会陷入(多玩家)囚徒困境。<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> “合作”通常意味着将价格保持在预先商定的最低水平。“背叛”意味着低于最低价格水平销售,并立即从其他卡特尔成员那里获得业务(和利润)。反垄断机构希望潜在的卡特尔成员相互背叛,确保消费者获得尽可能低的价格。<br />
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===Sport===<br />
运动<br />
[[Doping in sport]] has been cited as an example of a prisoner's dilemma.<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Doping in sport has been cited as an example of a prisoner's dilemma.<br />
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体育运动中的兴奋剂被认为是囚徒困境的一个例子。<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<ref name="wired" /><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<br />
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两名参赛运动员可以选择使用非法或危险药物来提高成绩。如果两个运动员都没有服用这种药物,那么他们都不会获得优势。如果只有一个人这样做,那么这个运动员就比他们的竞争对手获得了明显的优势,但由于法律或服用药物的医疗风险,这种优势会减少。然而,如果两名运动员都服用了这种药物,那么好处就被抵消了,只剩下风险,这使得他们的处境比没有服用兴奋剂的情况更加糟糕。<ref name="wired" /><br />
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===International politics===<br />
国际政治<br />
In [[international politics|international political theory]], the Prisoner's Dilemma is often used to demonstrate the coherence of [[strategic realism]], which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given [[anarchy (international relations)|international anarchy]]. A classic example is an arms race like the [[Cold War]] and similar conflicts.<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref> During the Cold War the opposing alliances of [[NATO]] and the [[Warsaw Pact]] both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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In international political theory, the Prisoner's Dilemma is often used to demonstrate the coherence of strategic realism, which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given international anarchy. A classic example is an arms race like the Cold War and similar conflicts. During the Cold War the opposing alliances of NATO and the Warsaw Pact both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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在国际政治理论中,囚徒困境经常被用来证明战略现实主义的一致性,这种战略现实主义认为,在国际关系中,由于国际无政府状态,所有国家(无论其国内政策或公开宣称的意识形态如何)都会为了自身的理性利益来行动。一个典型的例子是类似冷战和类似冲突的军备竞赛。<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref>在冷战期间,北约和华约组织的对立联盟都可以选择武装或解除武装。从双方的观点来看,解除武装而对手继续武装可能会导致军事劣势和被歼灭。相反,如果选择武装而对手已经解除了武装,那么就会获得优势。如果双方都选择武装自己,那么任何一方都承担不起攻击对方的代价,但是双方都为发展和维持核武库付出了高昂的代价。如果双方都选择裁军,战争就可以避免,也不会有任何代价。<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a [[War of attrition (game)|war of attrition]] for the next thirty years until the Soviet Union could not withstand the economic cost.<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref> The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a war of attrition for the next thirty years until the Soviet Union could not withstand the economic cost. The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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虽然最好的结果是双方解除武装,但是双方的理性选择是武装起来,事实也的确如此。在接下来的三十年里,双方都在军事研究和武器装备的消耗战上投入了大量的资源,直到苏联无法承受经济损失。<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref>同样的逻辑也适用于任何类似的情况,无论是主权国家之间的经济竞争还是技术竞争。<br />
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===Multiplayer dilemmas===<br />
<font color="#ff8000">多玩家困境 Multiplayer dilemmas</font><br />
Many real-life dilemmas involve multiple players.<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref> Although metaphorical, [[Garrett Hardin|Hardin's]] [[tragedy of the commons]] may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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许多现实生活中的困境牵涉到多个参与者。<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref>尽管具有隐喻性,但哈丁的<font color="#ff8000">公地悲剧 tragedy of the commons</font>可以看作是囚徒困境多个参与者的一个例子: 每个村民做出选择是为了个人利益还是克制。对于一致(甚至频繁)叛变的集体回报是非常低的(代表了对“公共资源”的破坏)。大多数人可能会遇到的公地困境是在一个共用的房子里洗碗。通过不洗碗,个人可以节省时间,但如果每个居民都选择这种行为,那么集体的代价是任何人都没有干净的盘子。<br />
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The commons are not always exploited: [[William Poundstone]], in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to [[Excludability|take a paper without paying]] (''defecting'') but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by [[Elinor Ostrom]], winner of the 2009 [[Nobel Memorial Prize in Economic Sciences]], hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<br />
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公共资源并不总是被利用: 威廉·庞德斯通 William Poundstone在一本关于囚徒困境的书(见下文参考文献)中描述了新西兰的一种情况,信箱没有上锁。人们可以不付钱就拿报纸(背叛) ,但很少有人这样做,他们觉得如果他们不付钱,那么其他人也不会付钱,这会摧毁整个系统。2009年诺贝尔经济学奖获得者埃莉诺·奥斯特罗姆 Elinor Ostrom随后的研究认为公地悲剧过于简单化,其负面结果会受到外部影响。在没有复杂压力的情况下,团体之间为了共同利益进行沟通和管理,执行社会规范以保护资源并为团体实现最大利益,这是实现囚徒困境最佳结果的一个例子。<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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==Related games==<br />
相关博弈<br />
===Closed-bag exchange===<br />
<font color="#ff8000">封闭袋子交换 Closed-bag exchange </font><br />
[[File:Prisoner's Dilemma briefcase exchange (colorized).svg|thumb|The prisoner's dilemma as a briefcase exchange]]<br />
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The prisoner's dilemma as a briefcase exchange<br />
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囚徒困境是一个公文包式的交换<br />
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[[Douglas Hofstadter]]<ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref> once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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Douglas Hofstadter once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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侯世达 Douglas Hofstadter <ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref>曾经指出,人们通常会发现诸如囚徒困境的问题,比如,当它以一个简单囚徒困境博弈的形式,或者以权衡的方式表现出来时,会更容易理解。他使用的几个例子之一是“封闭袋子交换” :<br />
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{{quote|Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.}}<br />
两人相遇并交换包裹,事先知道一个包里装着钱,一个装着订单。任一玩家都可选择尊重交易,放入事先约定的东西;也可以选择背叛,交换空的公文包。<br />
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Defection always gives a game-theoretically preferable outcome.<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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Defection always gives a game-theoretically preferable outcome.<br />
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背叛总是会带来一个理论上更可取的结果。<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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===''Friend or Foe?''===<br />
朋友还是敌人?<br />
''[[Friend or Foe? (TV series)|Friend or Foe?]]'' is a game show that aired from 2002 to 2005 on the [[Game Show Network]] in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, ''Friend or Foe'' has a rewards model between prisoner's dilemma and the [[Chicken (game)|game of Chicken]].<br />
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Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.<br />
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朋友还是敌人?是一个竞赛节目,从2002年至2005年在美国的Game show Network播出。这是囚徒困境博弈在真人身上测试的一个例子,只是在人为的环境中。在游戏节目中,有三对选手参加比赛。当一对被淘汰时,他们会玩一个类似囚徒困境的游戏来决定奖金如何分配。如果他们都合作(朋友) ,他们分享奖金50-50。如果一方合作而另一方背叛(敌人) ,那么叛变者将得到所有的奖金,而合作者将一无所获。如果双方都背叛,那么双方都将一无所有。请注意,奖励矩阵与上面给出的标准矩阵略有不同,因为“双方都背叛”和“合作而对方背叛”情况下的奖励是相同的。与标准囚徒困境中的严格均衡相比,这使得“两个都背叛”情况成为一个弱均衡。如果一个参赛者知道他们的对手将投票给“敌人” ,那么他们自己的选择不会影响他们自己的奖金。从特定意义上讲,“朋友还是敌人”节目在囚徒困境和“胆小鬼”博弈之间有一个奖励模型。<br />
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The rewards matrix is<br />
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The rewards matrix is<br />
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奖励矩阵是<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Friend"<br />(cooperate)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Foe"<br />(defect)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"Friend"<br />(cooperate)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"Foe"<br />(defect)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"朋友"<br />(合作)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"敌人"<br />(背叛)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"朋友"<br />(合作)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"敌人"<br />(背叛)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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This payoff matrix has also been used on the [[United Kingdom|British]] [[television]] programmes ''Trust Me'', ''[[Shafted]]'', ''[[The Bank Job (TV series)|The Bank Job]]'' and ''[[Golden Balls]]'', and on the [[United States|American]] shows ''[[Bachelor Pad]]'' and ''[[Take It All (game show)|Take It All]]''. Game data from the ''[[Golden Balls]]'' series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls, and on the American shows Bachelor Pad and Take It All. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<br />
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英国电视节目《相信我》、《阴影》、《银行工作》和《黄金球》以及美国电视节目《单身公寓》和《全部拿走》也采用了这种奖励矩阵。一个经济学家团队分析了“金球奖”系列的游戏数据,他们发现,现实生活中,合作对于金额而言“惊人地高” ,但在游戏的背景下,相对较低。<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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===Iterated snowdrift===<br />
<font color="#ff8000">重复雪堆 Iterated snowdrift </font><br />
{{main|snowdrift game}}<br />
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Researchers from the [[University of Lausanne]] and the [[University of Edinburgh]] have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a [[chicken game]], it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a [[snowdrift]], each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
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Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
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来自洛桑大学和爱丁堡大学的研究人员认为,“重复雪堆游戏”可能更能反映现实世界的社会状况。虽然这个模型实际上是一个胆小鬼博弈。在这个模型中,由于背叛可以降低被剥削的风险,个体总是从合作选择中获益。这个雪堆游戏可以设想两个司机被困在雪堆的两侧,每个司机都可以选择铲雪清理道路,或者留在自己的车里。一个玩家的最高回报来自于让对手清除所有的积雪,但是仍然可以从对手的工作中得到回报。<br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<br />
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这可能更好地反映了现实世界的情景,研究人员举了两位科学家合作完成一份报告的例子,如果另一位科学家更加努力地工作,这两位科学家都会受益。“但当你的合作者不做任何工作时,你自己完成所有的工作可能会更好。你最终还是会完成一个项目。” <ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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{|<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ Example snowdrift payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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! Cooperates<br />
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| 200, 200 || 100, 300<br />
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! Defects<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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||<br />
<br />
{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ Example PD payouts (A, B)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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|-<br />
<br />
! Cooperates<br />
<br />
| 200, 200 || -100, 300<br />
<br />
|-<br />
<br />
! Defects<br />
<br />
| 300, -100 || 0, 0<br />
<br />
|}<br />
<br />
<br />
<br />
{|<br />
<br />
|-<br />
<br />
|<br />
<br />
{| class="wikitable" style="text-align: center;"<br />
<br />
|+ 重复雪堆的支出示例 (A, B)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
<br />
|-<br />
<br />
! 合作<br />
<br />
| 200, 200 || 100, 300<br />
<br />
|-<br />
<br />
! 背叛<br />
<br />
| 300, 100 || 0, 0<br />
<br />
|}<br />
<br />
||<br />
<br />
{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ 囚徒困境支出示例 (A, B)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
<br />
|-<br />
<br />
! 合作<br />
<br />
| 200, 200 || -100, 300<br />
<br />
|-<br />
<br />
! 背叛<br />
<br />
| 300, -100 || 0, 0<br />
<br />
|}<br />
<br />
<br />
<br />
<br />
===Coordination games===<br />
<font color="#ff8000">协调博弈 Coordination games</font><br />
{{main|coordination games}}<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local [[left- and right-hand traffic]] convention helps to co-ordinate their actions.<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.<br />
<br />
在协调博弈中,参与者必须协调自己的策略以获得一个好的结果。一个例子是两辆车在暴风雪中突然相遇,每辆车必须选择是左转还是右转。如果两辆车都向左转弯,或者都向右转弯,那么两辆车就不会相撞。当地的左右向交通惯例有助于协调他们的行动。<br />
<br />
<br />
<br />
Symmetrical co-ordination games include [[Stag hunt]] and [[Bach or Stravinsky]].<br />
<br />
Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.<br />
<br />
对称的协调游戏包括猎鹿 Stag hunt和巴赫 Bach或斯特拉文斯基 Stravinsky。<br />
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<br />
<br />
===Asymmetric prisoner's dilemmas===<br />
<br />
<font color="#ff8000">不对称的囚徒困境 Asymmetric prisoner's dilemmas</font><br />
<br />
A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an [[alibi]], whence the term "alibi game".<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
<br />
A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, whence the term "alibi game".<br />
<br />
一个更一般的博弈集是不对称的。就像在囚徒困境中一样,最好的结果是合作,而背叛是有动机的。与对称的囚徒困境不同的是一个玩家比另一个玩家有更多的损失或收获。这样的博弈被描述为囚徒困境,其中一个囚徒有不在场证明,这就是术语“不在场证明游戏”的由来。<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
<br />
<br />
<br />
In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
<br />
In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<br />
<br />
在实验中,在重复博弈中获得不均等收益的参与者可能会寻求利润最大化,但是前提是两个玩家都必须获得均等的收益。这可能会导致一个稳定的均衡策略,即弱势参与者在每隔X场博弈中都会背叛,而另一个参与者总是保持合作。这种行为可能取决于实验围绕公平的社会规范。<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
<br />
<br />
<br />
==Software==<br />
软件<br />
<br />
<br />
Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
<br />
Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
<br />
已经有一些可以用来运行囚徒困境模拟和比赛的软件包,其中一些有可用的源代码。<br />
<br />
* The source code for the [[The Evolution of Cooperation|second tournament]] run by Robert Axelrod (written by Axelrod and many contributors in [[Fortran]]) is available [http://www-personal.umich.edu/~axe/research/Software/CC/CC2.html online]<br />
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* [https://web.archive.org/web/19991010053242/http://www.lifl.fr/IPD/ipd.frame.html Prison], a library written in [[Java (programming language)|Java]], last updated in 1998<br />
<br />
* [https://github.com/Axelrod-Python/Axelrod Axelrod-Python], written in [[Python (programming language)|Python]]<br />
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* [http://selborne.nl/ipd/ play the Iterative Prisoner's Dilemma in the browser], play against strategies or let strategies play against other strategies<br />
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<br />
<br />
==In fiction==<br />
在小说中<br />
[[Hannu Rajaniemi]] set the opening scene of his ''[[The Quantum Thief]]'' trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in [[mathematical physics]]&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, ''[[The Fractal Prince]]'' and ''[[The Causal Angel]]'', published in 2012 and 2014, respectively.<br />
<br />
Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in mathematical physics&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.<br />
<br />
汉努·拉贾尼埃米 Hannu Rajaniemi将他的《量子窃贼》三部曲的开场场景设置在一个“囚徒困境”中。该系列的主题被描述为“双重宇宙的不足” ,最终的对手是一个叫做全面背叛者的角色。作为一个处理这个问题的艺术家,拉贾尼埃米尤其有趣,因为他是剑桥大学培养的数学家,拥有数学物理学博士学位——物质和信息的可互换性是这本书的一个主要特征,它发生在<font color="#ff8000">后奇点post-singularity</font>的未来。该系列的第一本书于2010年出版,其续集《分形王子》和《因果天使》分别于2012年和2014年出版。<br />
<br />
<br />
<br />
A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game ''[[Zero Escape: Virtue's Last Reward]]'' and a minor part in its 2016 sequel ''[[Zero Escape: Zero Time Dilemma]]''.<br />
<br />
A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.<br />
<br />
一个(重复)囚徒困境博弈的模型是2012年电子游戏《零度逃脱: 美德的最后奖励》的重点,也是2016年续集《零度逃脱: 极限脱出刻之困境》的一个次要部分。<br />
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<br />
<br />
In ''The Mysterious Benedict Society and the Prisoner's Dilemma'' by [[Trenton Lee Stewart]], the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
<br />
In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
<br />
在特伦顿·李·斯图尔特 Trenton Lee Stewart的《神秘的本尼迪克特社会和囚徒困境》中,主要角色从玩一个版本的游戏开始,然后一起逃离“监狱”。后来他们变成了真正的囚犯,再次越狱。<br />
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<br />
<br />
In ''[[The Adventure Zone]]: Balance'' during ''The Suffering Game'' subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
<br />
在冒险区: 苦难游戏的平衡中,玩家角色在他们在两个领域的时间内两次呈现出囚徒困境,一次是合作,一次是背叛。<br />
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<br />
<br />
In the 8th novel from the author James S. A. Corey [[Tiamat's Wrath]] . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. {{cn|date=April 2020}}<br />
<br />
In the 8th novel from the author James S. A. Corey Tiamat's Wrath . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. <br />
<br />
在作者詹姆斯·S·A·科里·提亚玛特 James S. A. Corey Tiamat的《愤怒》中的第八部小说中,温斯顿•杜阿尔特 Winston Duarte向他14岁的女儿特蕾莎 Teresa解释了她面临的囚徒困境,来训练她的战略思维能力。<br />
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<br />
==See also==<br />
请参阅<br />
{{div col|colwidth=18em}}<br />
<br />
* [[Abilene paradox]]<br />
<font color="#ff8000"> 阿背伦悖论</font><br />
* [[Centipede game]]<br />
<font color="#ff8000"> 蜈蚣博弈</font><br />
* [[Christmas truce]]<br />
<font color="#ff8000"> 圣诞休战</font><br />
* [[Folk theorem (game theory)]]<br />
<font color="#ff8000"> 无名氏定理(博弈论)/font><br />
* [[Free-rider problem]]<br />
<font color="#ff8000"> 搭便车问题</font><br />
* [[Hobbesian trap]]<br />
]<font color="#ff8000"> 霍布斯主义陷阱</font><br />
* [[Innocent prisoner's dilemma]]<br />
<font color="#ff8000"> 无辜囚徒困局</font><br />
* [[Liar Game]]<br />
<font color="#ff8000">说谎者博弈</font><br />
* [[Optional prisoner's dilemma]]<br />
<font color="#ff8000"> 可选择囚徒困境</font><br />
* [[Robert H. Frank#Prisoner's dilemma and cooperation|Prisoner's dilemma and cooperation]]<br />
罗伯特·H·弗兰克囚徒的困境和合作|<font color="#ff8000"> 囚徒困境</font>和合作<br />
* [[Public goods game]]<br />
<font color="#ff8000"> 公共商品博弈</font><br />
* [[Gift-exchange game]]<br />
<font color="#ff8000"> 互利博弈</font><br />
* [[Reciprocal altruism]]<br />
<font color="#ff8000"> 相互利他行为</font><br />
* [[Social preferences]]<br />
<font color="#ff8000"> 社会偏好</font><br />
* [[Swift trust theory]]<br />
<font color="#ff8000"> 快速信任理论</font><br />
* [[Unscrupulous diner's dilemma]]<br />
]<font color="#ff8000"> 无道德食客困境</font><br />
{{div col end}}<br />
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<br />
==References==<br />
==参考==<br />
{{notelist}}<br />
<br />
{{reflist|colwidth=30em}}<br />
<br />
<br />
<br />
==Further reading==<br />
==拓展阅读==<br />
{{refbegin|30em}}<br />
<br />
* [[S.M. Amadae|Amadae, S.]] (2016). 'Prisoner's Dilemma,' ''Prisoners of Reason.'' [[Cambridge University Press]], NY, pp.&nbsp;24–61.<br />
<br />
* {{cite book |first1=Robert |last1=Aumann |authorlink=Robert Aumann |chapter=Acceptable points in general cooperative ''n''-person games |editor1-first=R. D. |editor1-last=Luce |editor2-first=A. W. |editor2-last=Tucker |title=Contributions to the Theory 23 of Games IV |series=Annals of Mathematics Study |volume=40 |pages=287–324 |publisher=Princeton University Press |location=Princeton NJ |year=1959 |mr=0104521}}<br />
<br />
* [[Robert Axelrod|Axelrod, R.]] (1984). ''[[The Evolution of Cooperation]]''. {{isbn|0-465-02121-2}}<br />
<br />
* [[Cristina Bicchieri|Bicchieri, Cristina]] (1993). Rationality and Coordination. [[Cambridge University Press]].<br />
<br />
* {{cite journal |first1=David M. |last1=Chess |date=December 1988 |title=Simulating the evolution of behavior: the iterated prisoners' dilemma problem |url=http://www.complex-systems.com/pdf/02-6-4.pdf |journal=Complex Systems |volume=2 |issue=6 |pages=663–70}}<br />
<br />
* [[Melvin Dresher|Dresher, M.]] (1961). ''The Mathematics of Games of Strategy: Theory and Applications'' [[Prentice-Hall]], Englewood Cliffs, NJ.<br />
<br />
* Greif, A. (2006). ''Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.'' Cambridge University Press, [[Cambridge]], UK.<br />
<br />
* [[Anatol Rapoport|Rapoport, Anatol]] and Albert M. Chammah (1965). ''Prisoner's Dilemma''. [[University of Michigan Press]].<br />
<br />
{{refend}}<br />
<br />
<br />
<br />
==External links==<br />
外部链接<br />
*{{Commonscat-inline}}<br />
<br />
* [http://plato.stanford.edu/entries/prisoner-dilemma/ Prisoner's Dilemma (''Stanford Encyclopedia of Philosophy'')]<br />
<br />
* [http://www.msri.org/ext/larryg/pages/15.htm The Bowerbird's Dilemma] The Prisoner's Dilemma in ornithology&nbsp;– mathematical cartoon by Larry Gonick.<br />
<br />
* [https://www.youtube.com/watch?v=_1SEXTVsxjk The Prisoner's Dilemma] The Prisoner's Dilemma with Lego minifigures.<br />
<br />
* {{cite encyclopedia |last1=Dixit |first1=Avinash |authorlink1=Avinash Dixit |last2= Nalebuff |first2=Barry |authorlink2=Barry Nalebuff |editor=[[David R. Henderson]]|encyclopedia=[[Concise Encyclopedia of Economics]] |title=Prisoner's Dilemma |url=http://www.econlib.org/library/Enc/PrisonersDilemma.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}<br />
<br />
* [http://gametheory101.com/The_Prisoner_s_Dilemma.html Game Theory 101: Prisoner's Dilemma]<br />
<br />
* [https://www.youtube.com/watch?v=I71mjZefg8g Dawkins: Nice Guys Finish First]<br />
<br />
* [https://axelrod.readthedocs.io/en/stable/ Axelrod] Iterated Prisoner's Dilemma [[Python (programming language)|Python]] library<br />
<br />
* [http://gametheorygames.nl/index.html Play the Iterated Prisoner's Dilemma on gametheorygames.nl]<br />
<br />
* [https://web.archive.org/web/20141011014608/http://demo.otree.org/demo/Prisoner%27s+Dilemma/ Play Prisoner's Dilemma on ''oTree''] (N/A 11-5-17)<br />
<br />
* Nicky Case's [https://web.archive.org/web/20181229222135/https://ncase.me/trust/ Evolution of Trust], an example of the donation game<br />
<br />
* [http://iterated-prisoners-dilemma.info Iterated Prisoner's Dilemma online game] by Wayne Davis<br />
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{{Decision theory paradoxes}}<br />
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{{Game theory}}<br />
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{{Authority control}}<br />
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[[Category:Non-cooperative games]]<br />
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Category:Non-cooperative games<br />
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类别: 非合作性游戏<br />
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[[Category:Thought experiments]]<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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[[Category:Dilemmas]]<br />
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Category:Dilemmas<br />
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类别: 困境<br />
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[[Category:Environmental studies]]<br />
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Category:Environmental studies<br />
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类别: 环境研究<br />
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[[Category:Social psychology]]<br />
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Category:Social psychology<br />
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类别: 社会心理学<br />
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[[Category:Moral psychology]]<br />
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Category:Moral psychology<br />
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范畴: 道德心理学<br />
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<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Prisoner's dilemma]]. Its edit history can be viewed at [[囚徒困境/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%9B%9A%E5%BE%92%E5%9B%B0%E5%A2%83&diff=21303囚徒困境2021-01-25T11:49:24Z<p>Vicky:/* Stochastic iterated prisoner's dilemma */</p>
<hr />
<div>此词条由Henry初步翻译。已由Smile审校。<br />
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{{other uses}}<br />
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{{short description|Canonical example of a game analyzed in game theory}}<br />
<br />
{| class="wikitable floatright"<br />
<br />
|+ Prisoner's dilemma payoff matrix<br />
<br />
! {{diagonal split header|A|B}}<br />
<br />
! B stays<br />silent<br />
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! B<br />betrays<br />
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|-<br />
<br />
! A stays<br />silent <br />
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| {{diagonal split header|-1|-1|transparent}}<br />
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| {{diagonal split header|-3|0|transparent}}<br />
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|-<br />
<br />
! A<br />betrays<br />
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| {{diagonal split header|0|-3|transparent}}<br />
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| {{diagonal split header|-2|-2|transparent}}<br />
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|}<br />
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{| class="wikitable floatright"<br />
<br />
|+ <font color="#ff8000"> 囚徒困境支付矩阵 Prisoner's dilemma payoff matrix</font><br />
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! {{diagonal split header|A|B}}<br />
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! B 保持<br />缄默<br />
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! B<br />背叛<br />
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|-<br />
<br />
! A 保持<br />缄默 <br />
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| {{diagonal split header|-1|-1|transparent}}<br />
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| {{diagonal split header|-3|0|transparent}}<br />
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|-<br />
<br />
! A<br />背叛<br />
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| {{diagonal split header|0|-3|transparent}}<br />
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| {{diagonal split header|-2|-2|transparent}}<br />
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|}<br />
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<br />
The '''prisoner's dilemma''' is a standard example of a game analyzed in [[game theory]] that shows why two completely [[Rationality#Economics|rational]] individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by [[Merrill Flood]] and [[Melvin Dresher]] while working at [[RAND Corporation|RAND]] in 1950. [[Albert W. Tucker]] formalized the game with prison sentence rewards and named it "prisoner's dilemma",<ref>Poundstone, 1992</ref> presenting it as follows:<br />
<br />
The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", prensenting it as follows:<br />
<br />
<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>是<font color="#ff8000"> 博弈论game theory</font>分析博弈的一个代表性例子,它揭示了为什么两个完全理性的个体可能不会合作,即使这样做符合他们的最大利益。它最初是由梅里尔·弗勒德 Merrill Flood和 梅文·加舍尔 Melvin Dresher于1950年在兰德公司工作时构建的。阿尔伯特.W.塔克 Albert W. Tucker将这种博弈以监禁刑罚奖励的方式正式化,并将其命名为囚徒困境,具体阐述如下:<br />
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<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
* If A and B each betray the other, each of them serves two years in prison<br />
* If A betrays B but B remains silent, A will be set free and B will serve three years in prison<br />
* If A remains silent but B betrays A, A will serve three years in prison and B will be set free<br />
* If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).}}<br />
<br />
{{一个犯罪团伙的两名成员被捕入狱。每个囚犯都被单独监禁,与他人无法沟通。检察官缺乏足够的证据来对这两个人定罪,但有足够的证据以较低的罪名定罪。同时,检察官向每个犯人提供了一个交易。每个囚犯都有机会出卖对方,证明对方犯下的罪行,或者他们可以合作,保持沉默。可能的结果有:<br />
<br />
*如果A和B都背叛了对方,他们都会在监狱服刑两年。<br />
*如果A背叛了B但B保持沉默,A会被无罪释放而B会服刑三年。<br />
*如果A保持沉默但B背叛了A,A会服刑三年而B会无罪释放。<br />
*如果A和B都保持沉默,他们就只用服刑一年(以较低的罪名)。}}<br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref> In reality, humans display a [[systemic bias]] towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action.<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref> This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref> The prisoner's dilemma became the focus of extensive experimental research.<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other. In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action. This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome. The prisoner's dilemma became the focus of extensive experimental research. <br />
<br />
这意味着,囚犯除了监禁刑罚之外,没有机会奖励或惩罚他们的同伴,他们的决定也不会影响他们未来的声誉。因为背叛一个同伴比与他们合作能得到更大的回报,所以所有纯粹理性的、自私自利的囚犯都会背叛对方,这意味着,对于两个纯粹理性的囚犯来说,唯一可能的结果就是他们相互背叛。<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref>实际上,尽管“理性的”自利行为的简单模型已经预测到了这一点,但人类在这种和类似的博弈中仍然表现出对合作行为的<font color="#ff8000">系统性偏差 systemic bias </font>。<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref>自从在兰德公司首次进行这项测试以来,人们就已经知道了这种对合作的偏见; 参与测试的秘书们相互信任,为了最好的共同的目标而努力。<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref>囚徒困境成为大量实验研究的焦点。<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
<br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by [[backward induction]]) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<br />
<br />
一个扩展的<font color="#ff8000">重复iterated</font>版本的博弈由此衍生出来。在这个版本中,经典博弈会在在同一组囚犯之间重复进行,他们不断有机会为了之前的决定对其他囚犯进行惩罚。如果参与者知道博弈的次数,那么(通过<font color="#ff8000">逆向归纳法 backward induction </font>)两个经典的理性的玩家就会因为和在单次博弈中相同的原因反复背叛对方。在无限次或未知次数的博弈中,没有固定的最优策略,因而,举办囚徒困境竞赛来竞争和检验这种情况下的算法。<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
<br />
<br />
The prisoner's dilemma game can be used as a model for many [[#Real-life examples|real world situations]] involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activitie <br />
<br />
囚徒困境博弈可以作为许多现实中涉及合作行为的模型。在非正式用法中,“囚徒困境”一词可适用于不严格符合经典或重复博弈的形式标准的情况: 例如,两个实体可以从合作中获得巨大利益或者会因为合作失败而遭受损失,但发现协调他们的活动很困难或者代价昂贵(并非是不可能的)。<br />
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<br />
<br />
==Strategy for the prisoner's dilemma==<br />
囚徒困境的策略<br />
<br />
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Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
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两名囚犯被分开关押在各自的房间里,不能相互交流。<br />
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The normal game is shown below:<br />
<br />
The normal game is shown below:<br />
<br />
正常的博弈如下:<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class“ wikitable”<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! {{diagonal split header|<br />Prisoner A|Prisoner B}} !! Prisoner B stays silent<br>(''cooperates'') !! Prisoner B betrays<br>(''defects'')<br />
<br />
! !! Prisoner B stays silent<br>(cooperates) !! Prisoner B betrays<br>(defects)<br />
<br />
! {{diagonal split header|<br />犯人A|犯人B}}!!犯人B保持沉默<br>(''合作'') !! 犯人B背叛<br>(''背叛'')<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A stays silent<br>(''cooperates'')<br />
<br />
! Prisoner A stays silent<br>(cooperates)<br />
<br />
!犯人 a 保持沉默<br>(''合作'')<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
|每人服刑1年||囚犯 A: 3年<br />囚犯 B: 无罪释放<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A betrays<br>(''defects'')<br />
<br />
! Prisoner A betrays<br>(defects)<br />
<br />
!犯人A背叛<br>(''背叛'')<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
|囚犯 A: 获释<br />囚犯 B: 3年||每人服刑2年<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by [[Dilemma#Use in logic|dilemma]]: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by dilemma: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
假设两个囚犯都了解博弈的本质,对彼此不忠诚,且在博弈之外没有机会得到报复或奖励。那么不管对方怎么决定,每个犯人背叛对方都会得到更高的奖励(“叛变”)。推理涉及一个进退两难的论点:B 要么合作,要么叛变。如果B合作,A 应该叛变,因为得到释放总比服刑1年好。如果 B叛变,A也应该叛变,因为服刑2年总比服刑3年好。所以不管怎样,A都应该叛变。并行推理表明B应该选择叛变。<br />
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<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a [[dominant strategy]]. Mutual defection is the only strong [[Nash equilibrium]] in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a dominant strategy. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
因为不管对方的选择如何,背叛总是比合作带来更好的回报,所以这是一个<font color="#ff8000">占优策略 dominant strategy</font>。相互背叛是博弈中唯一的强<font color="#ff8000">纳什均衡点 dominant strategy </font>(即每个参与者单方面的改变策略只能使自己的情况变糟)。因此,困境在于,虽然相互合作比相互背叛产生更好的结果,但它却不是理性的结果,因为从自我利益的角度来看,合作的选择是非理性的。<br />
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<br />
<br />
==Generalized form==<br />
<font color="#ff8000">广泛形态 Generalized form </font><br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
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传统囚徒困境的结构可以从其最初的囚徒环境中概括出来。假设两个玩家用红色和蓝色表示,并且每个玩家选择“合作”或“背叛”。<br />
<br />
<br />
<br />
If both players cooperate, they both receive the reward ''R'' for cooperating. If both players defect, they both receive the punishment payoff ''P''. If Blue defects while Red cooperates, then Blue receives the temptation payoff ''T'', while Red receives the "sucker's" payoff, ''S''. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff ''S'', while Red receives the temptation payoff ''T''.<br />
<br />
If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the tem punishment payoffptation payoff T.<br />
<br />
如果两个玩家合作,他们都会因为合作而获得奖励''R''。如果两个参与人都叛变,他们都会受到惩罚''P''。 如果蓝方叛变而红方合作,那么蓝方得到诱惑回报''T'',而红方受到“上当受骗者”损失''S''。同样地,如果蓝方合作而红方叛变,那么蓝方得到上当受骗者的损失''S'',而红方得到诱惑支付''T''。<br />
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<br />
<br />
This can be expressed in [[Normal-form game|normal form]]:<br />
<br />
This can be expressed in normal form:<br />
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这可以用标准形式的博弈来表示:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
| + <font color="#ff8000">正则 PD 支付矩阵 Canonical PD payoff matrix </font> <br />
<br />
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
! {{diagonal split header|{{color|#009|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
要成为强意义下的囚徒困境博弈,收益必须满足以下条件:<br />
<br />
<br />
<br />
:{{tmath|T > R > P > S}}<br />
<br />
<br />
<br />
The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents.<br />
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The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents.<br />
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回报关系{{tmath|R > P}}意味着相互合作优于相互背叛,然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。<br />
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===Special case: donation game===<br />
特例:<font color="#ff8000">捐赠博弈 donation game </font><br />
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The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus<br />
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The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus<br />
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捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式,在这种博弈中,合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b'',而叛变意味着什么也不提供。收益矩阵如下:<br />
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{| class="wikitable" style="text-align:center"<br />
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! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}}<br />
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! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
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! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
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|-<br />
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! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
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| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|Defect}}<br />
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| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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{| class="wikitable" style="text-align:center"<br />
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! {{diagonal split header|{{navy (color)|蓝方}}|{{color|#900|红方}}}}<br />
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! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
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! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
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|-<br />
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! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
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| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|背叛}}<br />
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| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section).<br />
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Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section).<br />
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请注意{{tmath|2R>T+S}}(即{{tmath|2(b-c)>b-c}})这使得捐赠博弈成为一个重复博弈(见下一节)。<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything.<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.<br />
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捐赠博弈可能适用于市场。假设种植者X 种橘子,种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b'',“b”比橙子的边际效用''c''高,因为X有橙子剩余而没有苹果。同样地,对于苹果种植者Y来说,橙子的边际效用是''b'',而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子,并且每个人都完成了交易,那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货,那么这个违约者将得到''b''的收益,而合作者将失去''c''的收益。 如果两者都违约,那么谁也不会得到或失去任何东西。<br />
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==The iterated prisoner's dilemma==<br />
<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma </font> {{more citations needed section|date=November 2012}}<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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如果两个参与者连续进行多次囚徒困境博弈,他们记住对手先前的行动并相应地改变策略,这种博弈被称为重复囚徒困境。<br />
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In addition to the general form above, the iterative version also requires that {{tmath|2R > T + S}}, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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In addition to the general form above, the iterative version also requires that , to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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除了上面的一般形式之外,重复版本还要求{{tmath|2R > T + S}},防止交替合作和背叛比相互合作有更大的回报。<br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "[[Peace war game|peace-war game]]".<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "peace-war game".<br />
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重复囚徒困境博弈是人类合作与信任的理论基础。假设博弈可以为两个需要信任的人之间的交易建模,那么群体中的合作行为也可以由多个参与者重复的博弈模型来建模。因此,这些年来,它吸引了许多学者。1975年,葛夫曼 Grofman和普尔 Pool估计专门撰写有关该领域的学术文章超过2000篇。重复囚徒困境也被称为“和平-战争博弈”。<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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If the game is played exactly ''N'' times and both players know this, then it is optimal to defect in all rounds. The only possible [[Nash equilibrium]] is to always defect. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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If the game is played exactly N times and both players know this, then it is optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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如果这个游戏正好玩了N次,并且两个玩家都知道这一点,那么在所有回合中最佳的策略就是叛变。唯一可能的纳什均衡点就是永远叛变。证明是通过归纳法证出来的: 不妨假设一个人在最后一回合叛变,因为对手之后没有机会反击。因此,双方都会在最后一个回合叛变。所以玩家同样也会在倒数第二回合时叛变,因为无论采取什么策略,对手都会在倒数第一回合叛变,依此类推。如果博弈次数未知但次数有限的情况也同样如此。<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The [[superrational]] strategy in the iterated prisoner's dilemma with fixed ''N'' is to cooperate against a superrational opponent, and in the limit of large ''N'', experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoner's dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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与标准的囚徒困境不同,在重复囚徒困境中,叛变策略是严重违反直觉的,以至于不能很好地预测人类玩家的行为。然而,在标准的经济理论中,这是唯一正确的答案。具有固定次数 N的重复囚徒困境中的<font color="#ff8000">超理性 superrational</font>策略是与超理性对手进行合作,在N很大的限制下,实验结果的策略与超理性结果的策略一致,而不是博弈论的理性结果。<br />
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For [[cooperation]] to emerge between game theoretic rational players, the total number of rounds ''N'' must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by [[Robert Aumann]] in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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For cooperation to emerge between game theoretic rational players, the total number of rounds N must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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为了使合作在博弈论的理性参与者之间出现,参与者必须不知道回合总数N。在这种情况下,“总是叛变”可能不再是一个严格占优策略,而只是一个纳什均衡。罗伯特·奥曼 Robert Aumann在1959年的一篇论文中表明,理性参与者在无限多次的博弈中通过反复互动可以维持合作的结果。<br />
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According to a 2019 experimental study in the ''American Economic Review'' which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, [[Tit for tat|tit-for-tat]], and [[Grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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According to a 2019 experimental study in the American Economic Review which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, tit-for-tat, and Grim trigger. Which strategy the subjects chose depended on the parameters of the game.<br />
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根据《美国经济评论》于2019年进行的一项实验研究,该实验中通过完美的监控测试了现实中被用在重复囚徒困境情况下的策略,监测选择的策略总是背叛,针锋相对的和 <font color="#ff8000"> 冷酷触发策略 Grim trigger</font>。受试者选择的策略取决于博弈的参数。<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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===Strategy for the iterated prisoner's dilemma===<br />
重复囚徒困境下的策略<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by [[Robert Axelrod]] in his book ''[[The Evolution of Cooperation]]'' (1984). In it he reports on a tournament he organized of the ''N'' step prisoner's dilemma (with ''N'' fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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Interest in the iterated prisoner's dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In it he reports on a tournament he organized of the N step prisoner's dilemma (with N fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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罗伯特·阿克塞尔罗德 Robert Axelrod在他的著作《合作的进化》(1984)中激起了人们对重复囚徒困境(IPD)的兴趣。在这篇文章中,他报道了自己组织的固定N次囚徒困境的比赛,参与者必须一次又一次地选择他们的共同策略,并且要记住他们之前的遭遇。阿克塞尔罗德邀请世界各地的学术界同仁设计计算机策略来参加IPD锦标赛。输入的程序在算法复杂性、最初敌意、宽恕能力等方面有很大差异。<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more [[altruism|altruistic]] strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by [[natural selection]].<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.<br />
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阿克塞尔罗德发现,当这些遭遇长时间在许多玩家身上重复发生时,每个玩家都有不同的策略,从长远来看,贪婪策略往往表现得非常糟糕,而更加利他的策略表现得更好,这完全是根据自身利益来判断的。他利用这一结果揭示了通过自然选择,从最初纯粹自私行为向利他行为进化的可能机制。<br />
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The winning [[deterministic algorithm|deterministic]] strategy was tit for tat, which [[Anatol Rapoport]] developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of [[BASIC]], and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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The winning deterministic strategy was tit for tat, which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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最终获胜的决定性策略是针锋相对策略,这是阿纳托尔·拉波波特 Anatol Rapoport开发并参加比赛的策略。这是所有参赛程序中最简单的一个,只有四行 BASIC 语言,并且赢得了比赛。策略很简单,就是在游戏的第一次重复中进行合作; 在此之后,玩家将执行做他的对手在前一步中所做的事情。根据具体情况,一个稍微好一点的策略可以是“带着宽恕之心针锋相对”。当对手叛变时,在下一次博弈中,玩家有时还是会合作,但概率很小(大约1-5%)。这允许博弈偶尔能从陷入叛变循环中恢复过来。确切的概率取决于对手的安排。<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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通过分析得分最高的战略,阿克塞尔罗德阐述了战略成功的几个必要条件。<br />
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; Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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;友好:最重要的条件是策略必须是好的,也就是说,它不会在对手之前叛变(这有时被称为“乐观”算法)。几乎所有得分最高的策略都是友好的; 因此,一个纯粹的自私策略不会为了纯粹自身的利益而“欺骗”对手。<br />
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; Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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;报复:然而,阿克塞尔罗德认为,成功的战略决不能是盲目的乐观主义。它有时必须进行报复。非报复策略的一个例子就是永远合作。这是一个非常糟糕的选择,因为“肮脏”的策略会无情地利用这些玩家。<br />
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; Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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;宽容: 成功的策略也必须是宽容的。虽然玩家会报复,但如果对手不继续叛变,他们将再次回到合作的状态。这阻止了长时间的报复和反报复,最大限度地提高积分。<br />
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; Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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;不嫉妒: 最后一个品质是不嫉妒,不强求比对手得分更多。<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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对于一次性的囚徒困境博弈,最优(点数最大化)策略就是简单的叛变; 正如上面所说,无论对手的构成如何,这都是正确的。然而,在重复囚徒困境博弈中,最优策略取决于可能的对手的策略,以及他们对叛变和合作的反应。例如,考虑一个群体,其中每个人每次都会叛变,只有一个人遵循针锋相对的策略。那个人就会由于第一回合的失利而处于轻微的不利地位。在这样一个群体中,个体的最佳策略是每次都叛变。在一定比例的总是选择背叛的玩家和其余组成选择针锋相对策略的玩家的人群中,个人的最佳策略取决于这一比例和博弈的次数。<br />
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In the strategy called Pavlov, [[win-stay, lose-switch]], faced with a failure to cooperate, the player switches strategy the next turn.<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref> In certain circumstances,{{specify|date=November 2012}} Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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In the strategy called Pavlov, win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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在所谓的<font color="#ff8000">巴甫洛夫策略 Pavlov strategy</font>中,<font color="#ff8000">去输存赢 win-stay, lose-switch</font>,面对一次合作失败,玩家将在下一次变换策略。<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref>在某些情况下,{{specify|date=November 2012}}巴甫洛夫通过使用类似策略给与合作者优惠待遇打败了其他所有策略。<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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得出最佳策略通常有两种方法:<br />
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* [[Bayesian Nash equilibrium]]: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit for tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.{{efn|1=For example see the 2003 study<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref> for discussion of the concept and whether it can apply in real [[economic]] or strategic situations.}}<br />
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<font color="#ff8000">贝叶斯纳什均衡 Bayesian Nash equilibrium</font>:如果可以确定对立策略的统计分布(例如,50%针锋相对,50%总是合作),那么,可以通过分析得出最佳的反策略{{efn|1=例如2003年的研究<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref>讨论这一概念以及它是否可以应用于实际经济或战略情况。}}<br />
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* [[Monte Carlo method|Monte Carlo]] simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a [[genetic algorithm]] for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit for tat players (see for instance Chess 1988),{{Clarify|date=August 2016}} but no analytic proof exists that this will always occur.<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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<font color="#ff8000">蒙特卡洛方法 Monte Carlo method </font>已经对种群进行了模拟,分数低的个体死亡,分数高的个体繁殖(<font color="#ff8000">遗传算法 genetic algorithm </font>用于寻找一个最佳策略)。最终群体中的算法组合通常取决于初始总体的组合。引入突变(繁殖过程中的随机变异)可以减少对初始种群的依赖性。使用这种系统进行经验性实验往往会为针锋相对的玩家带来麻烦(见Chess 1988),{{Clarify|date=August 2016}},但是没有分析证据表明这种情况会一直发生。<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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Although tit for tat is considered to be the most [[robust]] basic strategy, a team from [[Southampton University]] in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start.<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref> Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show [[University of Southampton]]'s strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between [[computer program|software strategies]] (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian [[Evolutionarily stable strategy|ESS]] simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. [[Richard Dawkins]] showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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Although tit for tat is considered to be the most robust basic strategy, a team from Southampton University in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between software strategies (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian ESS simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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尽管针锋相对被认为是最有力的基本策略,来自英格兰南安普敦大学的一个团队在20周年的重复囚徒困境竞赛中提出了一个新策略,这个策略被证明比针锋相对更为成功。这种策略依赖于程序之间的串通,以获得单个程序的最高分数。这所大学提交了60个程序,这些程序的设计目的是在比赛开始时通过一系列的5到10个动作来互相认识。<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref>一旦认识建立,一个程序总是合作,另一个程序总是叛变,保证叛变者得到最多的分数。如果这个程序意识到它正在和一个非南安普顿的球员比赛,它会不断地叛变,试图最小化与之竞争的程序的得分。因此,2004年囚徒困境锦标赛的结果显示了南安普敦大学战略位居前三名,尽管它比冷酷战略赢得更少,输的更多。(在囚徒困境锦标赛中,比赛的目的不是“赢”比赛——这一点频繁叛变很容易实现)。此外,即使没有软件策略之间的暗中串通(南安普顿队利用了这一点) ,针锋相对并不总是任何特定锦标赛的绝对赢家; 更准确地说,它是在一系列锦标赛中的长期结果超过了它的竞争对手。(在任何一个事件中,一个给定的策略可以比针锋相对稍微更好地适应竞争,但是针锋相对更稳健)。这同样适用于带有宽恕变量的针锋相对,和其他最佳策略: 在任何特定的一天,他们可能不会“赢得”一个特定的混合反战略。另一种方法是使用达尔文 Darwinian的<font color="#ff8000"> ESS模拟 ESS simulation</font>。在这样的模拟中,针锋相对几乎总是占主导地位,尽管讨厌的策略会在人群中漂移,因为使用针锋相对策略的人群可以通过非报复性的好策略进行渗透,这反过来使他们容易成为讨厌策略的猎物。理查德·道金斯 Richard Dawkins指出,在这里,没有静态的混合策略会形成一个稳定的平衡,系统将始终在边界之间振荡。这种策略最终在比赛中获得了前三名的成绩,或者是接近垫底的成绩。<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of [[minmaxing]]). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book ''[[The Selfish Gene]]'', pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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这种策略利用了这样一个事实,即在这场特殊的比赛中允许多个参赛项目,并且团队的表现由得分最高的项目来衡量(这意味着使用自我牺牲的项目是一种分数最大化的形式)。在一个只能控制一个玩家的比赛中,针锋相对当然是一个更好的策略。由于这一新规则的存在,与阿克塞尔罗德的具有深远影响的竞赛相比,这种竞赛在分析单个主体策略时也就没有什么理论意义。然而,它为在分析多主体框架下,特别是在存在干扰的情况下,如何实现协作策略提供了基础。事实上,早在这场新规则锦标赛开始之前,道金斯就在他的《自私的基因》一书中指出,如果允许多次参赛,这种策略就有可能获胜,但他说,如果提交这种策略的话,阿克塞尔罗德很可能不会允许。因为它依赖于规避囚徒困境的规则,即两个参与者之间不允许交流,南安普顿的项目可以说在开场的“十步舞”中就是这样做以认识对方的; 这只是强调了交流在改变游戏平衡方面的价值。<br />
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===Stochastic iterated prisoner's dilemma===<br />
随机重复囚徒困境<br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities".<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref> In an encounter between player ''X'' and player ''Y'', ''X'' 's strategy is specified by a set of probabilities ''P'' of cooperating with ''Y''. ''P'' is a function of the outcomes of their previous encounters or some subset thereof. If ''P'' is a function of only their most recent ''n'' encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that ''X'' will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which ''X'' cooperated and ''Y'' defected, then <math>P_{cd}</math> is the probability that ''X'' will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as ''P''={1,0,1,0}, in which ''X'' responds as ''Y'' did in the previous encounter. Another is the [[win–stay, lose–switch]] strategy written as ''P''={1,0,0,1}, in which ''X'' responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<ref name="Press2012"/><br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player X and player Y, X 's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which X cooperated and Y defected, then <math>P_{cd}</math> is the probability that X will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as P={1,0,1,0}, in which X responds as Y did in the previous encounter. Another is the win–stay, lose–switch strategy written as P={1,0,0,1}, in which X responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<br />
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在随机重复<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>博弈中,策略由“合作概率”来确定。<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref>在玩家''X''和玩家''Y''之间的遭遇中,''X''‘s的策略由一组与''Y''合作的概率''P''确定,''P''是他们之前遭遇的结果的函数,或者是其中的一些子集。如果''P''只是它们最近遇到次数 ''n''的函数,那么它被称为“记忆-n”策略。我们可以由四个联合概率指定一个记忆-1策略: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>,其中<math>P_{ab}</math>是在当前遭遇中基于先前联合的概率。如果每个概率都是1或0,这种策略称为确定性策略。确定性策略的一个例子是针锋相对策略,写成 p {1,0,1,0} ,其中 x 的反应和 y 在前一次遭遇中的反应一样。另一种是胜-保持-败-转换策略,它被写成 p {1,0,0,1} ,在这种策略中,如果 x 获得胜利(即:cc 或 dc),x会做出与上一次遭遇一样的反应 ,但如果失败,x会改变策略(即cd 或 dd)。研究表明,对于任何一种记忆-n 策略,存在一个相应的记忆-1策略,这个策略给出相同的统计结果,因此只需要考虑记忆-1策略。<ref name="Press2012"/><br />
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If we define ''P'' as the above 4-element strategy vector of ''X'' and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of ''Y'', a transition matrix ''M'' may be defined for ''X'' whose ''ij'' th entry is the probability that the outcome of a particular encounter between ''X'' and ''Y'' will be ''j'' given that the previous encounter was ''i'', where ''i'' and ''j'' are one of the four outcome indices: ''cc'', ''cd'', ''dc'', or ''dd''. For example, from ''X'' 's point of view, the probability that the outcome of the present encounter is ''cd'' given that the previous encounter was ''cd'' is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for ''Q'' are from ''Y'' 's point of view: a ''cd'' outcome for ''X'' is a ''dc'' outcome for ''Y''.) Under these definitions, the iterated prisoner's dilemma qualifies as a [[stochastic process]] and ''M'' is a [[stochastic matrix]], allowing all of the theory of stochastic processes to be applied.<ref name="Press2012"/><br />
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If we define P as the above 4-element strategy vector of X and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of Y, a transition matrix M may be defined for X whose ij th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X 's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for Q are from Y 's point of view: a cd outcome for X is a dc outcome for Y.) Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.<br />
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如果我们将''P''定义为''X''的上述4元策略向量,并将<math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math>定义为''Y''的4元策略向量,则对于''X''可以定义一个转移矩阵''M'',其第ij项是''X''和''Y''之间特定相遇的结果为j的概率,给定i,其中i和j是cc、cd、dc或dd 四个结果索引中的一个。例如,从''X''的角度来看,如果给定''cd'',那么这次的结果是''cd''的概率等于<math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>。(''Q''的指标是 从''Y''的角度: ''X''的''cd''结果是''Y''的''dc''结果)在这些定义下,重复的囚徒困境被定义为一个随机过程,''M''是一个随机矩阵,允许应用所有的随机过程理论。<ref name="Press2012"/><br />
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One result of stochastic theory is that there exists a stationary vector ''v'' for the matrix ''M'' such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that ''v'' is normalized so that the sum of its four components is unity. The ''ij'' th entry in <math>M^n</math> will give the probability that the outcome of an encounter between ''X'' and ''Y'' will be ''j'' given that the encounter ''n'' steps previous is ''i''. In the limit as ''n'' approaches infinity, ''M'' will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing ''j'' which will be independent of ''i''. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that ''v'' is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to ''v''. Thus the stationary vector specifies the equilibrium outcome probabilities for ''X''. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From ''X'' 's point of view), the equilibrium payoffs for ''X'' and ''Y'' can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.<br />
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One result of stochastic theory is that there exists a stationary vector v for the matrix M such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij th entry in <math>M^n</math> will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j which will be independent of i. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to v. Thus the stationary vector specifies the equilibrium outcome probabilities for X. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From X 's point of view), the equilibrium payoffs for X and Y can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies P and Q to be compared for their long term payoffs.<br />
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随机理论的一个结果是,矩阵''M''存在一个平稳向量''v''使得<math>v\cdot M=v</math>成立。一般地,我们可以指定''v''是标准化的,因此它的4个组成部分之和为1。the equilibrium payoffs for and can now be specified as and, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.第''ij''项<math>M^n</math>给出了''X''和''Y''相遇的结果的概率为''j'',给定前面相遇''n''步的概率是''i''。当''n''趋于无穷时,''M''收敛于一个具有固定值的矩阵,并且''j''趋向一个长期概率,与''i''独立。换句话说, <math>M^\infty</math>的行将是相同的,从而给出了重复囚徒困境的长期均衡结果概率,而不需要明确地计算大量的相互作用。可以看出,''v''是<math>M^n</math>特别是<math>M^\infty</math>, 的平稳向量,因此<math>M^\infty</math>的每一行都等于''v''。因此平稳向量指定了''X''的均衡结果概率。定义<math>S_x=\{R,S,T,P\}</math>和<math>S_y=\{R,T,S,P\}</math>作为{cc,cd,dc,dd}结果的短期收益向量(从''X''的角度来看) ,现在可以将''X''和''Y''的均衡收益指定为<math>s_x=v\cdot S_x</math>和<math>s_y=v\cdot S_y</math>,使得''P''、''Q''两种策略的长期收益可以比较。<br />
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====Zero-determinant strategies====<br />
<font color="#ff8000">零决定策略 Zero-determinant strategies</font><br />
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[[File:IPD Venn.svg|right|thumb|upright=2.5|The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram]]. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and [[weak selection]]. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and weak selection. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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<font color="#ff8000">维恩图 Venn diagram</font>中讨论了<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma</font>(IPD)中零决定策略(ZD)、合作策略和背叛策略之间的关系。合作策略总是与其他合作策略相互配合,而背叛策略总是与其他背叛策略相抵触。这两种策略都包都含在强选择下稳健的策略子集,这意味着当它们驻留在一个种群中时,没有选择其他的记忆-1策略来入侵此策略。只有合作策略包含在始终稳健的策略子集,意味着无论选择强项还是弱项,都不会选择其他任何记忆-1策略来入侵和替换此策略。零决定策略和良好的合作策略之间的交集是一组宽松的零决定策略。勒索策略是零决定策略和非稳健背叛策略的交集。针锋相对是合作、背叛和零决定策略的交集。<br />
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In 2012, [[William H. Press]] and [[Freeman Dyson]] published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies.<ref name="Press2012"/> The long term payoffs for encounters between ''X'' and ''Y'' can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector ''v''. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in ''f'', it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where ''U''={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector v. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in f, it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where U={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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2012年,威廉·H·普莱斯 William H. Press和弗里曼·戴森 Freeman Dyson针对随机重复囚徒困境提出了一类新的策略,称为“零决定”策略。<ref name="Press2012"/>''X''和''Y''之间的长期收益可以表示为一个矩阵的决定因素,它是两个策略和短期收益向量的函数: <math>s_x=D(P,Q,S_x)</math>和<math>s_y=D(P,Q,S_y)</math>,不涉及平稳向量''v''。 由于行列式函数<math>s_y=D(P,Q,f)</math>在''f''中是线性的,因此可以推出<math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math>(其中''U''={1,1,1,1})。任何策略的<math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math>被定义为零决定策略,长期收益服从关系式<math>\alpha s_x+\beta s_y+\gamma=0</math>。<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of [[ultimatum game]]. Specifically, ''X'' is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of ''Y'' 's strategy, offering an opportunity for ''X'' to "extort" player ''Y'' (and vice versa). (It turns out that if ''X'' tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.<ref name="Press2012"/>)<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of Y 's strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.)<br />
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针锋相对是一种零决定策略,在不获得超越其他玩家优势的意义下是“公平”的。然而,零决定策略空间还包含这样的策略:在两个玩家的情况下,可以允许一个玩家单方面设置另一个玩家的分数,或者强迫进化的玩家获得比他自己的分数低一些的收益。被勒索的玩家可能会背叛,但会因此获得较低的回报并且受到伤害。因此,勒索的解决方案将重复囚徒困境转化为一种<font color="#ff8000">最后通牒博弈 ultimatum game </font>。具体来说,''X''能够选择一种策略,对于这种策略,<math>D(P,Q,\beta S_y+\gamma U)=0</math>单方面地将<math>s_y</math>设置为一个特定值范围内的特定值,与''Y''的策略无关,为''X''提供了“勒索”玩家''Y''的机会(反之亦然)。(事实证明,如果''X''试图将<math>s_x</math>设置为一个特定的值,那么可能的范围要小得多,只包括完全合作或完全叛变。<ref name="Press2012"/>)<br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not [[evolutionarily stable strategy|evolutionarily stable]]. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<br />
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重复囚徒困境的一个扩展是进化的随机重复囚徒困境,其中允许特定策略的相对丰度改变,更成功的策略相对增加。这个过程可以通过让不太成功的玩家模仿更成功的策略,或者通过从游戏中淘汰不太成功的玩家,同时让更成功的玩家成倍增加。研究表明,不公平的零决定策略不是进化稳定策略。关键的直觉告诉我们,进化稳定策略不仅要能够入侵另一个群体(这是勒索零决定策略可以做到的) ,而且还要在同类型的其他玩家面前表现良好(勒索零决定策略玩家表现不佳,因为他们减少了彼此的盈余)。<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and [[win–stay, lose–switch]] agents.<ref name=Hilbe2013 /><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.<br />
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理论和模拟证实,超过一个临界种群规模,零决定勒索在与更多合作策略的进化竞争中会失败,因此,种群越大,种群的平均收益就越大。此外,在某些情况下,勒索者甚至可能通过帮助打破统一的背叛者与使用“赢-保持-输”策略的转换玩家之间的对峙而促进合作。<ref name=Hilbe2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies ''is'' both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the [[Prisoner's dilemma#Special case: Donation game|donation game]] by Alexander Stewart and Joshua Plotkin in 2013.<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref> Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013)<ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<ref name=Stewart2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013) to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<br />
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虽然勒索零决定策略在人口众多的情况下并不稳定,但另一种宽松的零决定策略既稳定又稳健。事实上,当人口不算太少的时候,这些策略可以取代任何其他零决定策略,甚至在一系列针对重复囚徒困境的广泛通用策略(包括“获胜-保持-输”的转换策略)中表现良好。亚历山大·斯图尔特 Alexander Stewart和约书亚·普洛特金 Joshua Plotkin在2013年的捐赠博弈中证明了这一点。<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref>宽松的策略会与其他合作的玩家合作,面对背叛,慷慨的玩家比他的对手失去更多的效用。宽松策略是零决定策略和所谓的“好”策略的交集,阿金(2013) <ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.将这两种策略定义为玩家对过去的相互合作作出回应,并在至少获得合作预期收益的情况下平均分配预期收益的策略。在好的策略中,当总体不太小时,宽松(零决定)子集表现良好。如果总体很少,背叛策略往往占主导地位。<ref name=Stewart2013 /><br />
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===Continuous iterated prisoner's dilemma===<br />
<font color="#ff8000">连续重复囚徒困境 Continuous iterated prisoner's dilemma </font> <br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref> found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from [[Assortative mating|assorting]] with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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关于重复囚徒困境的研究大多集中在离散情况下,在这种情况下,参与者要么合作,要么背叛,因为这个模型分析起来比较简单。然而,一些研究人员已经研究了连续重复囚徒困境模型,在这个模型中,玩家能够对另一个玩家做出可变的贡献。乐 Le和博伊德 Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref>发现,在这种情况下,合作比离散重复的囚徒困境更难发展。这个结果的基本直觉很简单: 在一个持续的囚徒困境中,如果一个人群开始处于非合作均衡状态,那么与非合作者相比,合作程度稍高的玩家不会从相互配合中获益。相比之下,在离散的囚徒困境中,相对于非合作者,针锋相对的合作者在非合作均衡中相互配合会获得巨大的回报。由于自然界可以提供更多的机会来进行各种各样的合作,而不是严格地将合作或背叛分为两类,因此连续的囚徒困境可以帮助解释为什么现实生活中针锋相对的合作的例子在自然界中极其罕见。(例如,哈默斯坦 Hammerstein <ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)。<br />
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even though tit for tat seems robust in theoretical models.<br />
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even though tit for tat seems robust in theoretical models.<br />
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尽管在理论模型中,针锋相对策略似乎是稳健的。<br />
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===Emergence of stable strategies===<br />
<font color="#ff8000">稳定策略的出现 Emergence of stable strategies </font> <br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref> Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies. Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<br />
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玩家似乎不能协调相互合作,因此常常陷入劣等而稳定的背叛策略。这样,重复回合可以促进稳定策略的发展。<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref>重复回合往往产生新颖的策略,这对复杂的社会互动有影响。其中一个策略就是“赢-保持-输”的转变。这个策略比一个简单的针锋相对策略要好&nbsp;–也就是说,如果你能逃脱作弊的惩罚,就重复这个行为,如果你被抓住了,就改变策略。<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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这种针锋相对策略的唯一问题是它们很容易出现信号错误。当一个人因报复而作弊,而另一个人将其单纯解释为欺骗时,就会出现问题。结果,第二个人现在作弊,然后在接下来的连锁反应中开始了反复交替的作弊模式。<br />
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==Real-life examples==<br />
现实生活的例子<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the [[social science]]s such as [[economics]], [[politics]], and [[sociology]], as well as to the biological sciences such as [[ethology]] and [[evolutionary biology]]. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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囚犯的环境似乎是人为的,但实际上,在人类交往以及自然界的交互中有许多具有相同收益矩阵的例子。因此,囚徒困境是经济学、政治学、社会学等社会科学以及动物行为学、进化生物学等生物学研究的热点问题。许多自然过程都被抽象为生物进行无休止的囚徒困境博弈的模型。囚徒困境这种广泛的适用性让博弈变得非常重要。<br />
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===Environmental studies===<br />
环境研究<br />
In [[environmental studies]], the PD is evident in crises such as global [[climate change|climate-change]]. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb [[Carbon dioxide|{{Co2}}]] emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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In environmental studies, the PD is evident in crises such as global climate-change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide| emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<br />
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在环境研究中,囚徒困境在诸如全球气候变化等危机中显而易见。有人认为,所有国家都将从稳定的气候中受益,但是每一个国家通常都在限制二氧化碳排放方面犹豫不决。人们错误地认为,如果所有国家的行为都改变,任何一个国家保持目前的行为所带来的直接好处都会大于所谓的最终好处,这就解释了2007年气候变化方面的僵局。<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<br />
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气候变化政治与囚徒困境之间的一个重要区别是不确定性; 污染对气候变化的影响程度和速度尚不清楚。因此,政府面临的困境不同于囚徒困境,因为合作的回报是未知的。这种差异表明,各国之间的合作远远少于真正的重复囚徒困境中的合作,因此避免可能发生的气候灾难的可能性远远小于使用真正的重复囚徒困境博弈论情景分析<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of [[Michael Porter]]'s hypothesis, in which government regulation of competing firms is substantial.<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.<br />
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欧桑 Osang和南迪 Nandy (2003)提供了一个理论解释,并根据迈克尔·波特 Michael Porter的假设,即政府对竞争企业的监管是实质性的,证明了监管驱动的双赢局面。<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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===Animals===<br />
动物<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, [[guppy|guppies]] inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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许多动物的合作行为可以理解为囚徒困境的一个例子。通常动物会建立长期的伙伴关系,这种关系可以更具体地模拟为重复囚徒困境。例如,孔雀鱼成群结队地合作监察捕食者,它们被认为是在惩罚不合作的监察者。<br />
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[[Vampire bats]] are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<br />
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吸血蝙蝠是从事相互的食物交换的群居动物。应用囚徒困境收益可以帮助解释这种行为: <ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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* C/C: "Reward: I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much."<br />
* 合作/合作:"回报:我在不幸运的晚上得到了能让我果腹的血,那在幸运的晚上我也应该分出点血,那不会花费多少。"<br />
* D/C: "Temptation: You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night."<br />
* 背叛/合作:"诱惑:你在我的不幸的夜里救了我,但在我的幸运夜我不会给你血,那样我会活的更好。"<br />
* C/D: "Sucker's Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death."<br />
* 合作/叛变:"可怜者的回报:在我的幸运夜我救了你的命,但在我的不幸夜里你没有救我,我有饿死的风险。"<br />
* D/D: "Punishment: I don't have to pay the slight costs of feeding you on my good nights. But I run a real risk of starving on my poor nights."<br />
* 叛变/叛变:"惩罚:我在我的幸运夜里不必付出代价来救你,但我在我的不幸夜里有挨饿的风险。"<br />
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===Psychology===<br />
心理学<br />
In [[addiction]] research / [[behavioral economics]], [[George Ainslie (psychologist)|George Ainslie]] points out<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref> that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, ''defecting'' means ''relapsing'', and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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In addiction research / behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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在成瘾研究/行为经济学中,乔治·安斯利 George Ainslie指出<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref>,可以将成瘾视为成瘾者现在和未来自我之间的跨期囚徒困境问题。在这种情况下,背叛意味着复发,很容易看出,目前和未来都没有背叛是迄今为止最好的结果。如果一个人今天戒了,但在将来又复吸,这是最糟糕的结果&nbsp;–从某种意义上来说,今天戒瘾所包含的纪律和自我牺牲已经被“浪费”了,因为未来的复吸意味着瘾君子又回到了他开始的地方,他将被迫重新开始(这相当令人沮丧,也使得重新开始更加困难)。今天和明天复发是一个稍微“好一点”的结果,因为尽管瘾君子仍然上瘾,但他们没有努力去尝试停止。最后一种情况是,现在与成瘾斗争的任何人都会熟悉现在的成瘾行为,而在明天放弃。这里的问题是(和其他囚徒困境问题一样),背叛“今天”有一个明显的好处,但明天这个人将面临同样的囚徒困境问题,同样明显的好处是背叛,最终导致一连串无休止的背叛。<br />
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[[John Gottman]] in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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John Gottman in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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约翰·高特曼 John Gottman在他的研究《信任的科学》中将良好的关系定义为伙伴知道不进入(背叛,背叛)牢房中或者至少不要陷入这样的动态循环关系中。<br />
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===Economics===<br />
经济学<br />
The prisoner's dilemma has been called the ''[[Escherichia coli|E. coli]]'' of social psychology, and it has been used widely to research various topics such as [[Oligopoly|oligopolistic]] competition and collective action to produce a collective good.<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref> <br />
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The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good. <br />
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囚徒困境被称为社会心理学中的“大肠杆菌”,它被广泛用于研究寡头垄断竞争和集体行动来产生集体利益等问题。<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When [[cigarette advertising]] was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. <ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref> This analysis is likely to be pertinent in many other business situations involving advertising. <ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.<br />
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广告有时被认为是囚徒困境的一个真实例子。当香烟广告在美国是合法的时候,相互竞争的香烟制造商必须决定在广告上花多少钱。公司A的广告效果部分取决于公司B的广告效果。同样,公司B的广告带来的利润也受到公司A的广告影响。如果公司A和公司B都选择在给定的时间段内做广告,那么一家公司的广告就会抵消另一方的广告,倘若收入保持不变,费用就会因广告成本而增加。两家公司都将从广告减少中获益。然而,如果B公司选择不做广告,A公司就可以通过广告获得巨大的利益。尽管如此,一家公司的最佳广告数量仍取决于另一家公司的广告投放量。由于最佳策略取决于其他公司的选择,因此这里没有占主导地位的策略,这使得它与囚徒困境略有不同。但结果是相似的,如果两家公司的广告都少于均衡状态,他们的处境会更好。有时合作行为确实会在商业环境中出现。例如,香烟制造商支持立法禁止香烟广告,因为这将降低成本并增加整个行业的利润。<ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref>这种分析可能适用于许多其他涉及广告的商业情况。<ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref> <br />
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Without enforceable agreements, members of a [[cartel]] are also involved in a (multi-player) prisoner's dilemma.<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. [[Anti-trust]] authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for [[consumer]]s.<br />
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Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.<br />
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没有可强制执行的协议,卡特尔 cartel的成员国也会陷入(多玩家)囚徒困境。<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> “合作”通常意味着将价格保持在预先商定的最低水平。“背叛”意味着低于最低价格水平销售,并立即从其他卡特尔成员那里获得业务(和利润)。反垄断机构希望潜在的卡特尔成员相互背叛,确保消费者获得尽可能低的价格。<br />
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===Sport===<br />
运动<br />
[[Doping in sport]] has been cited as an example of a prisoner's dilemma.<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Doping in sport has been cited as an example of a prisoner's dilemma.<br />
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体育运动中的兴奋剂被认为是囚徒困境的一个例子。<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<ref name="wired" /><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<br />
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两名参赛运动员可以选择使用非法或危险药物来提高成绩。如果两个运动员都没有服用这种药物,那么他们都不会获得优势。如果只有一个人这样做,那么这个运动员就比他们的竞争对手获得了明显的优势,但由于法律或服用药物的医疗风险,这种优势会减少。然而,如果两名运动员都服用了这种药物,那么好处就被抵消了,只剩下风险,这使得他们的处境比没有服用兴奋剂的情况更加糟糕。<ref name="wired" /><br />
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===International politics===<br />
国际政治<br />
In [[international politics|international political theory]], the Prisoner's Dilemma is often used to demonstrate the coherence of [[strategic realism]], which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given [[anarchy (international relations)|international anarchy]]. A classic example is an arms race like the [[Cold War]] and similar conflicts.<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref> During the Cold War the opposing alliances of [[NATO]] and the [[Warsaw Pact]] both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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In international political theory, the Prisoner's Dilemma is often used to demonstrate the coherence of strategic realism, which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given international anarchy. A classic example is an arms race like the Cold War and similar conflicts. During the Cold War the opposing alliances of NATO and the Warsaw Pact both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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在国际政治理论中,囚徒困境经常被用来证明战略现实主义的一致性,这种战略现实主义认为,在国际关系中,由于国际无政府状态,所有国家(无论其国内政策或公开宣称的意识形态如何)都会为了自身的理性利益来行动。一个典型的例子是类似冷战和类似冲突的军备竞赛。<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref>在冷战期间,北约和华约组织的对立联盟都可以选择武装或解除武装。从双方的观点来看,解除武装而对手继续武装可能会导致军事劣势和被歼灭。相反,如果选择武装而对手已经解除了武装,那么就会获得优势。如果双方都选择武装自己,那么任何一方都承担不起攻击对方的代价,但是双方都为发展和维持核武库付出了高昂的代价。如果双方都选择裁军,战争就可以避免,也不会有任何代价。<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a [[War of attrition (game)|war of attrition]] for the next thirty years until the Soviet Union could not withstand the economic cost.<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref> The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a war of attrition for the next thirty years until the Soviet Union could not withstand the economic cost. The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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虽然最好的结果是双方解除武装,但是双方的理性选择是武装起来,事实也的确如此。在接下来的三十年里,双方都在军事研究和武器装备的消耗战上投入了大量的资源,直到苏联无法承受经济损失。<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref>同样的逻辑也适用于任何类似的情况,无论是主权国家之间的经济竞争还是技术竞争。<br />
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===Multiplayer dilemmas===<br />
<font color="#ff8000">多玩家困境 Multiplayer dilemmas</font><br />
Many real-life dilemmas involve multiple players.<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref> Although metaphorical, [[Garrett Hardin|Hardin's]] [[tragedy of the commons]] may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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许多现实生活中的困境牵涉到多个参与者。<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref>尽管具有隐喻性,但哈丁的<font color="#ff8000">公地悲剧 tragedy of the commons</font>可以看作是囚徒困境多个参与者的一个例子: 每个村民做出选择是为了个人利益还是克制。对于一致(甚至频繁)叛变的集体回报是非常低的(代表了对“公共资源”的破坏)。大多数人可能会遇到的公地困境是在一个共用的房子里洗碗。通过不洗碗,个人可以节省时间,但如果每个居民都选择这种行为,那么集体的代价是任何人都没有干净的盘子。<br />
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The commons are not always exploited: [[William Poundstone]], in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to [[Excludability|take a paper without paying]] (''defecting'') but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by [[Elinor Ostrom]], winner of the 2009 [[Nobel Memorial Prize in Economic Sciences]], hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<br />
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公共资源并不总是被利用: 威廉·庞德斯通 William Poundstone在一本关于囚徒困境的书(见下文参考文献)中描述了新西兰的一种情况,信箱没有上锁。人们可以不付钱就拿报纸(背叛) ,但很少有人这样做,他们觉得如果他们不付钱,那么其他人也不会付钱,这会摧毁整个系统。2009年诺贝尔经济学奖获得者埃莉诺·奥斯特罗姆 Elinor Ostrom随后的研究认为公地悲剧过于简单化,其负面结果会受到外部影响。在没有复杂压力的情况下,团体之间为了共同利益进行沟通和管理,执行社会规范以保护资源并为团体实现最大利益,这是实现囚徒困境最佳结果的一个例子。<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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==Related games==<br />
相关博弈<br />
===Closed-bag exchange===<br />
<font color="#ff8000">封闭袋子交换 Closed-bag exchange </font><br />
[[File:Prisoner's Dilemma briefcase exchange (colorized).svg|thumb|The prisoner's dilemma as a briefcase exchange]]<br />
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The prisoner's dilemma as a briefcase exchange<br />
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囚徒困境是一个公文包式的交换<br />
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[[Douglas Hofstadter]]<ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref> once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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Douglas Hofstadter once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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侯世达 Douglas Hofstadter <ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref>曾经指出,人们通常会发现诸如囚徒困境的问题,比如,当它以一个简单囚徒困境博弈的形式,或者以权衡的方式表现出来时,会更容易理解。他使用的几个例子之一是“封闭袋子交换” :<br />
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{{quote|Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.}}<br />
两人相遇并交换包裹,事先知道一个包里装着钱,一个装着订单。任一玩家都可选择尊重交易,放入事先约定的东西;也可以选择背叛,交换空的公文包。<br />
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Defection always gives a game-theoretically preferable outcome.<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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Defection always gives a game-theoretically preferable outcome.<br />
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背叛总是会带来一个理论上更可取的结果。<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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===''Friend or Foe?''===<br />
朋友还是敌人?<br />
''[[Friend or Foe? (TV series)|Friend or Foe?]]'' is a game show that aired from 2002 to 2005 on the [[Game Show Network]] in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, ''Friend or Foe'' has a rewards model between prisoner's dilemma and the [[Chicken (game)|game of Chicken]].<br />
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Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.<br />
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朋友还是敌人?是一个竞赛节目,从2002年至2005年在美国的Game show Network播出。这是囚徒困境博弈在真人身上测试的一个例子,只是在人为的环境中。在游戏节目中,有三对选手参加比赛。当一对被淘汰时,他们会玩一个类似囚徒困境的游戏来决定奖金如何分配。如果他们都合作(朋友) ,他们分享奖金50-50。如果一方合作而另一方背叛(敌人) ,那么叛变者将得到所有的奖金,而合作者将一无所获。如果双方都背叛,那么双方都将一无所有。请注意,奖励矩阵与上面给出的标准矩阵略有不同,因为“双方都背叛”和“合作而对方背叛”情况下的奖励是相同的。与标准囚徒困境中的严格均衡相比,这使得“两个都背叛”情况成为一个弱均衡。如果一个参赛者知道他们的对手将投票给“敌人” ,那么他们自己的选择不会影响他们自己的奖金。从特定意义上讲,“朋友还是敌人”节目在囚徒困境和“胆小鬼”博弈之间有一个奖励模型。<br />
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The rewards matrix is<br />
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The rewards matrix is<br />
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奖励矩阵是<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Friend"<br />(cooperate)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Foe"<br />(defect)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"Friend"<br />(cooperate)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"Foe"<br />(defect)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"朋友"<br />(合作)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"敌人"<br />(背叛)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"朋友"<br />(合作)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
<br />
! scope="row" | {{color|#009|"敌人"<br />(背叛)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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This payoff matrix has also been used on the [[United Kingdom|British]] [[television]] programmes ''Trust Me'', ''[[Shafted]]'', ''[[The Bank Job (TV series)|The Bank Job]]'' and ''[[Golden Balls]]'', and on the [[United States|American]] shows ''[[Bachelor Pad]]'' and ''[[Take It All (game show)|Take It All]]''. Game data from the ''[[Golden Balls]]'' series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
<br />
This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls, and on the American shows Bachelor Pad and Take It All. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<br />
<br />
英国电视节目《相信我》、《阴影》、《银行工作》和《黄金球》以及美国电视节目《单身公寓》和《全部拿走》也采用了这种奖励矩阵。一个经济学家团队分析了“金球奖”系列的游戏数据,他们发现,现实生活中,合作对于金额而言“惊人地高” ,但在游戏的背景下,相对较低。<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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<br />
===Iterated snowdrift===<br />
<font color="#ff8000">重复雪堆 Iterated snowdrift </font><br />
{{main|snowdrift game}}<br />
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Researchers from the [[University of Lausanne]] and the [[University of Edinburgh]] have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a [[chicken game]], it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a [[snowdrift]], each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
<br />
Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
<br />
来自洛桑大学和爱丁堡大学的研究人员认为,“重复雪堆游戏”可能更能反映现实世界的社会状况。虽然这个模型实际上是一个胆小鬼博弈。在这个模型中,由于背叛可以降低被剥削的风险,个体总是从合作选择中获益。这个雪堆游戏可以设想两个司机被困在雪堆的两侧,每个司机都可以选择铲雪清理道路,或者留在自己的车里。一个玩家的最高回报来自于让对手清除所有的积雪,但是仍然可以从对手的工作中得到回报。<br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<br />
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这可能更好地反映了现实世界的情景,研究人员举了两位科学家合作完成一份报告的例子,如果另一位科学家更加努力地工作,这两位科学家都会受益。“但当你的合作者不做任何工作时,你自己完成所有的工作可能会更好。你最终还是会完成一个项目。” <ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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{|<br />
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|-<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ Example snowdrift payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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|-<br />
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! Cooperates<br />
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| 200, 200 || 100, 300<br />
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|-<br />
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! Defects<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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||<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ Example PD payouts (A, B)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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|-<br />
<br />
! Cooperates<br />
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| 200, 200 || -100, 300<br />
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|-<br />
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! Defects<br />
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| 300, -100 || 0, 0<br />
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|}<br />
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{|<br />
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|-<br />
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|<br />
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{| class="wikitable" style="text-align: center;"<br />
<br />
|+ 重复雪堆的支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
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|-<br />
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! 合作<br />
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| 200, 200 || 100, 300<br />
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|-<br />
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! 背叛<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ 囚徒困境支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
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|-<br />
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! 合作<br />
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| 200, 200 || -100, 300<br />
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|-<br />
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! 背叛<br />
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| 300, -100 || 0, 0<br />
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|}<br />
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===Coordination games===<br />
<font color="#ff8000">协调博弈 Coordination games</font><br />
{{main|coordination games}}<br />
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In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local [[left- and right-hand traffic]] convention helps to co-ordinate their actions.<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.<br />
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在协调博弈中,参与者必须协调自己的策略以获得一个好的结果。一个例子是两辆车在暴风雪中突然相遇,每辆车必须选择是左转还是右转。如果两辆车都向左转弯,或者都向右转弯,那么两辆车就不会相撞。当地的左右向交通惯例有助于协调他们的行动。<br />
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Symmetrical co-ordination games include [[Stag hunt]] and [[Bach or Stravinsky]].<br />
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Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.<br />
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对称的协调游戏包括猎鹿 Stag hunt和巴赫 Bach或斯特拉文斯基 Stravinsky。<br />
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===Asymmetric prisoner's dilemmas===<br />
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<font color="#ff8000">不对称的囚徒困境 Asymmetric prisoner's dilemmas</font><br />
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A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an [[alibi]], whence the term "alibi game".<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
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A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, whence the term "alibi game".<br />
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一个更一般的博弈集是不对称的。就像在囚徒困境中一样,最好的结果是合作,而背叛是有动机的。与对称的囚徒困境不同的是一个玩家比另一个玩家有更多的损失或收获。这样的博弈被描述为囚徒困境,其中一个囚徒有不在场证明,这就是术语“不在场证明游戏”的由来。<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<br />
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在实验中,在重复博弈中获得不均等收益的参与者可能会寻求利润最大化,但是前提是两个玩家都必须获得均等的收益。这可能会导致一个稳定的均衡策略,即弱势参与者在每隔X场博弈中都会背叛,而另一个参与者总是保持合作。这种行为可能取决于实验围绕公平的社会规范。<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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==Software==<br />
软件<br />
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
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已经有一些可以用来运行囚徒困境模拟和比赛的软件包,其中一些有可用的源代码。<br />
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* The source code for the [[The Evolution of Cooperation|second tournament]] run by Robert Axelrod (written by Axelrod and many contributors in [[Fortran]]) is available [http://www-personal.umich.edu/~axe/research/Software/CC/CC2.html online]<br />
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* [https://web.archive.org/web/19991010053242/http://www.lifl.fr/IPD/ipd.frame.html Prison], a library written in [[Java (programming language)|Java]], last updated in 1998<br />
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* [https://github.com/Axelrod-Python/Axelrod Axelrod-Python], written in [[Python (programming language)|Python]]<br />
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* [http://selborne.nl/ipd/ play the Iterative Prisoner's Dilemma in the browser], play against strategies or let strategies play against other strategies<br />
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==In fiction==<br />
在小说中<br />
[[Hannu Rajaniemi]] set the opening scene of his ''[[The Quantum Thief]]'' trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in [[mathematical physics]]&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, ''[[The Fractal Prince]]'' and ''[[The Causal Angel]]'', published in 2012 and 2014, respectively.<br />
<br />
Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in mathematical physics&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.<br />
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汉努·拉贾尼埃米 Hannu Rajaniemi将他的《量子窃贼》三部曲的开场场景设置在一个“囚徒困境”中。该系列的主题被描述为“双重宇宙的不足” ,最终的对手是一个叫做全面背叛者的角色。作为一个处理这个问题的艺术家,拉贾尼埃米尤其有趣,因为他是剑桥大学培养的数学家,拥有数学物理学博士学位——物质和信息的可互换性是这本书的一个主要特征,它发生在<font color="#ff8000">后奇点post-singularity</font>的未来。该系列的第一本书于2010年出版,其续集《分形王子》和《因果天使》分别于2012年和2014年出版。<br />
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A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game ''[[Zero Escape: Virtue's Last Reward]]'' and a minor part in its 2016 sequel ''[[Zero Escape: Zero Time Dilemma]]''.<br />
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A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.<br />
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一个(重复)囚徒困境博弈的模型是2012年电子游戏《零度逃脱: 美德的最后奖励》的重点,也是2016年续集《零度逃脱: 极限脱出刻之困境》的一个次要部分。<br />
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In ''The Mysterious Benedict Society and the Prisoner's Dilemma'' by [[Trenton Lee Stewart]], the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
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In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
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在特伦顿·李·斯图尔特 Trenton Lee Stewart的《神秘的本尼迪克特社会和囚徒困境》中,主要角色从玩一个版本的游戏开始,然后一起逃离“监狱”。后来他们变成了真正的囚犯,再次越狱。<br />
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In ''[[The Adventure Zone]]: Balance'' during ''The Suffering Game'' subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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在冒险区: 苦难游戏的平衡中,玩家角色在他们在两个领域的时间内两次呈现出囚徒困境,一次是合作,一次是背叛。<br />
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In the 8th novel from the author James S. A. Corey [[Tiamat's Wrath]] . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. {{cn|date=April 2020}}<br />
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In the 8th novel from the author James S. A. Corey Tiamat's Wrath . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. <br />
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在作者詹姆斯·S·A·科里·提亚玛特 James S. A. Corey Tiamat的《愤怒》中的第八部小说中,温斯顿•杜阿尔特 Winston Duarte向他14岁的女儿特蕾莎 Teresa解释了她面临的囚徒困境,来训练她的战略思维能力。<br />
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==See also==<br />
请参阅<br />
{{div col|colwidth=18em}}<br />
<br />
* [[Abilene paradox]]<br />
<font color="#ff8000"> 阿背伦悖论</font><br />
* [[Centipede game]]<br />
<font color="#ff8000"> 蜈蚣博弈</font><br />
* [[Christmas truce]]<br />
<font color="#ff8000"> 圣诞休战</font><br />
* [[Folk theorem (game theory)]]<br />
<font color="#ff8000"> 无名氏定理(博弈论)/font><br />
* [[Free-rider problem]]<br />
<font color="#ff8000"> 搭便车问题</font><br />
* [[Hobbesian trap]]<br />
]<font color="#ff8000"> 霍布斯主义陷阱</font><br />
* [[Innocent prisoner's dilemma]]<br />
<font color="#ff8000"> 无辜囚徒困局</font><br />
* [[Liar Game]]<br />
<font color="#ff8000">说谎者博弈</font><br />
* [[Optional prisoner's dilemma]]<br />
<font color="#ff8000"> 可选择囚徒困境</font><br />
* [[Robert H. Frank#Prisoner's dilemma and cooperation|Prisoner's dilemma and cooperation]]<br />
罗伯特·H·弗兰克囚徒的困境和合作|<font color="#ff8000"> 囚徒困境</font>和合作<br />
* [[Public goods game]]<br />
<font color="#ff8000"> 公共商品博弈</font><br />
* [[Gift-exchange game]]<br />
<font color="#ff8000"> 互利博弈</font><br />
* [[Reciprocal altruism]]<br />
<font color="#ff8000"> 相互利他行为</font><br />
* [[Social preferences]]<br />
<font color="#ff8000"> 社会偏好</font><br />
* [[Swift trust theory]]<br />
<font color="#ff8000"> 快速信任理论</font><br />
* [[Unscrupulous diner's dilemma]]<br />
]<font color="#ff8000"> 无道德食客困境</font><br />
{{div col end}}<br />
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==References==<br />
==参考==<br />
{{notelist}}<br />
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{{reflist|colwidth=30em}}<br />
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<br />
<br />
==Further reading==<br />
==拓展阅读==<br />
{{refbegin|30em}}<br />
<br />
* [[S.M. Amadae|Amadae, S.]] (2016). 'Prisoner's Dilemma,' ''Prisoners of Reason.'' [[Cambridge University Press]], NY, pp.&nbsp;24–61.<br />
<br />
* {{cite book |first1=Robert |last1=Aumann |authorlink=Robert Aumann |chapter=Acceptable points in general cooperative ''n''-person games |editor1-first=R. D. |editor1-last=Luce |editor2-first=A. W. |editor2-last=Tucker |title=Contributions to the Theory 23 of Games IV |series=Annals of Mathematics Study |volume=40 |pages=287–324 |publisher=Princeton University Press |location=Princeton NJ |year=1959 |mr=0104521}}<br />
<br />
* [[Robert Axelrod|Axelrod, R.]] (1984). ''[[The Evolution of Cooperation]]''. {{isbn|0-465-02121-2}}<br />
<br />
* [[Cristina Bicchieri|Bicchieri, Cristina]] (1993). Rationality and Coordination. [[Cambridge University Press]].<br />
<br />
* {{cite journal |first1=David M. |last1=Chess |date=December 1988 |title=Simulating the evolution of behavior: the iterated prisoners' dilemma problem |url=http://www.complex-systems.com/pdf/02-6-4.pdf |journal=Complex Systems |volume=2 |issue=6 |pages=663–70}}<br />
<br />
* [[Melvin Dresher|Dresher, M.]] (1961). ''The Mathematics of Games of Strategy: Theory and Applications'' [[Prentice-Hall]], Englewood Cliffs, NJ.<br />
<br />
* Greif, A. (2006). ''Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.'' Cambridge University Press, [[Cambridge]], UK.<br />
<br />
* [[Anatol Rapoport|Rapoport, Anatol]] and Albert M. Chammah (1965). ''Prisoner's Dilemma''. [[University of Michigan Press]].<br />
<br />
{{refend}}<br />
<br />
<br />
<br />
==External links==<br />
外部链接<br />
*{{Commonscat-inline}}<br />
<br />
* [http://plato.stanford.edu/entries/prisoner-dilemma/ Prisoner's Dilemma (''Stanford Encyclopedia of Philosophy'')]<br />
<br />
* [http://www.msri.org/ext/larryg/pages/15.htm The Bowerbird's Dilemma] The Prisoner's Dilemma in ornithology&nbsp;– mathematical cartoon by Larry Gonick.<br />
<br />
* [https://www.youtube.com/watch?v=_1SEXTVsxjk The Prisoner's Dilemma] The Prisoner's Dilemma with Lego minifigures.<br />
<br />
* {{cite encyclopedia |last1=Dixit |first1=Avinash |authorlink1=Avinash Dixit |last2= Nalebuff |first2=Barry |authorlink2=Barry Nalebuff |editor=[[David R. Henderson]]|encyclopedia=[[Concise Encyclopedia of Economics]] |title=Prisoner's Dilemma |url=http://www.econlib.org/library/Enc/PrisonersDilemma.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}<br />
<br />
* [http://gametheory101.com/The_Prisoner_s_Dilemma.html Game Theory 101: Prisoner's Dilemma]<br />
<br />
* [https://www.youtube.com/watch?v=I71mjZefg8g Dawkins: Nice Guys Finish First]<br />
<br />
* [https://axelrod.readthedocs.io/en/stable/ Axelrod] Iterated Prisoner's Dilemma [[Python (programming language)|Python]] library<br />
<br />
* [http://gametheorygames.nl/index.html Play the Iterated Prisoner's Dilemma on gametheorygames.nl]<br />
<br />
* [https://web.archive.org/web/20141011014608/http://demo.otree.org/demo/Prisoner%27s+Dilemma/ Play Prisoner's Dilemma on ''oTree''] (N/A 11-5-17)<br />
<br />
* Nicky Case's [https://web.archive.org/web/20181229222135/https://ncase.me/trust/ Evolution of Trust], an example of the donation game<br />
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* [http://iterated-prisoners-dilemma.info Iterated Prisoner's Dilemma online game] by Wayne Davis<br />
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{{Decision theory paradoxes}}<br />
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{{Game theory}}<br />
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{{Authority control}}<br />
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[[Category:Non-cooperative games]]<br />
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Category:Non-cooperative games<br />
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类别: 非合作性游戏<br />
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[[Category:Thought experiments]]<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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[[Category:Dilemmas]]<br />
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Category:Dilemmas<br />
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类别: 困境<br />
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[[Category:Environmental studies]]<br />
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Category:Environmental studies<br />
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类别: 环境研究<br />
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[[Category:Social psychology]]<br />
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Category:Social psychology<br />
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类别: 社会心理学<br />
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[[Category:Moral psychology]]<br />
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Category:Moral psychology<br />
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范畴: 道德心理学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Prisoner's dilemma]]. Its edit history can be viewed at [[囚徒困境/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%9B%9A%E5%BE%92%E5%9B%B0%E5%A2%83&diff=21302囚徒困境2021-01-25T11:47:16Z<p>Vicky:/* Strategy for the iterated prisoner's dilemma */</p>
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<div>此词条由Henry初步翻译。已由Smile审校。<br />
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{{other uses}}<br />
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{{short description|Canonical example of a game analyzed in game theory}}<br />
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{| class="wikitable floatright"<br />
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|+ Prisoner's dilemma payoff matrix<br />
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! {{diagonal split header|A|B}}<br />
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! B stays<br />silent<br />
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! B<br />betrays<br />
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|-<br />
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! A stays<br />silent <br />
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| {{diagonal split header|-1|-1|transparent}}<br />
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| {{diagonal split header|-3|0|transparent}}<br />
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|-<br />
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! A<br />betrays<br />
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| {{diagonal split header|0|-3|transparent}}<br />
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| {{diagonal split header|-2|-2|transparent}}<br />
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{| class="wikitable floatright"<br />
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|+ <font color="#ff8000"> 囚徒困境支付矩阵 Prisoner's dilemma payoff matrix</font><br />
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! {{diagonal split header|A|B}}<br />
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! B 保持<br />缄默<br />
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! B<br />背叛<br />
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! A 保持<br />缄默 <br />
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| {{diagonal split header|-1|-1|transparent}}<br />
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| {{diagonal split header|-3|0|transparent}}<br />
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|-<br />
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! A<br />背叛<br />
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The '''prisoner's dilemma''' is a standard example of a game analyzed in [[game theory]] that shows why two completely [[Rationality#Economics|rational]] individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by [[Merrill Flood]] and [[Melvin Dresher]] while working at [[RAND Corporation|RAND]] in 1950. [[Albert W. Tucker]] formalized the game with prison sentence rewards and named it "prisoner's dilemma",<ref>Poundstone, 1992</ref> presenting it as follows:<br />
<br />
The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", prensenting it as follows:<br />
<br />
<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>是<font color="#ff8000"> 博弈论game theory</font>分析博弈的一个代表性例子,它揭示了为什么两个完全理性的个体可能不会合作,即使这样做符合他们的最大利益。它最初是由梅里尔·弗勒德 Merrill Flood和 梅文·加舍尔 Melvin Dresher于1950年在兰德公司工作时构建的。阿尔伯特.W.塔克 Albert W. Tucker将这种博弈以监禁刑罚奖励的方式正式化,并将其命名为囚徒困境,具体阐述如下:<br />
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<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
* If A and B each betray the other, each of them serves two years in prison<br />
* If A betrays B but B remains silent, A will be set free and B will serve three years in prison<br />
* If A remains silent but B betrays A, A will serve three years in prison and B will be set free<br />
* If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).}}<br />
<br />
{{一个犯罪团伙的两名成员被捕入狱。每个囚犯都被单独监禁,与他人无法沟通。检察官缺乏足够的证据来对这两个人定罪,但有足够的证据以较低的罪名定罪。同时,检察官向每个犯人提供了一个交易。每个囚犯都有机会出卖对方,证明对方犯下的罪行,或者他们可以合作,保持沉默。可能的结果有:<br />
<br />
*如果A和B都背叛了对方,他们都会在监狱服刑两年。<br />
*如果A背叛了B但B保持沉默,A会被无罪释放而B会服刑三年。<br />
*如果A保持沉默但B背叛了A,A会服刑三年而B会无罪释放。<br />
*如果A和B都保持沉默,他们就只用服刑一年(以较低的罪名)。}}<br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref> In reality, humans display a [[systemic bias]] towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action.<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref> This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref> The prisoner's dilemma became the focus of extensive experimental research.<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other. In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action. This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome. The prisoner's dilemma became the focus of extensive experimental research. <br />
<br />
这意味着,囚犯除了监禁刑罚之外,没有机会奖励或惩罚他们的同伴,他们的决定也不会影响他们未来的声誉。因为背叛一个同伴比与他们合作能得到更大的回报,所以所有纯粹理性的、自私自利的囚犯都会背叛对方,这意味着,对于两个纯粹理性的囚犯来说,唯一可能的结果就是他们相互背叛。<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref>实际上,尽管“理性的”自利行为的简单模型已经预测到了这一点,但人类在这种和类似的博弈中仍然表现出对合作行为的<font color="#ff8000">系统性偏差 systemic bias </font>。<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref>自从在兰德公司首次进行这项测试以来,人们就已经知道了这种对合作的偏见; 参与测试的秘书们相互信任,为了最好的共同的目标而努力。<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref>囚徒困境成为大量实验研究的焦点。<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
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An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by [[backward induction]]) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<br />
<br />
一个扩展的<font color="#ff8000">重复iterated</font>版本的博弈由此衍生出来。在这个版本中,经典博弈会在在同一组囚犯之间重复进行,他们不断有机会为了之前的决定对其他囚犯进行惩罚。如果参与者知道博弈的次数,那么(通过<font color="#ff8000">逆向归纳法 backward induction </font>)两个经典的理性的玩家就会因为和在单次博弈中相同的原因反复背叛对方。在无限次或未知次数的博弈中,没有固定的最优策略,因而,举办囚徒困境竞赛来竞争和检验这种情况下的算法。<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
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The prisoner's dilemma game can be used as a model for many [[#Real-life examples|real world situations]] involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activitie <br />
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囚徒困境博弈可以作为许多现实中涉及合作行为的模型。在非正式用法中,“囚徒困境”一词可适用于不严格符合经典或重复博弈的形式标准的情况: 例如,两个实体可以从合作中获得巨大利益或者会因为合作失败而遭受损失,但发现协调他们的活动很困难或者代价昂贵(并非是不可能的)。<br />
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==Strategy for the prisoner's dilemma==<br />
囚徒困境的策略<br />
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Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
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Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
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两名囚犯被分开关押在各自的房间里,不能相互交流。<br />
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The normal game is shown below:<br />
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The normal game is shown below:<br />
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正常的博弈如下:<br />
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{| class="wikitable"<br />
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{| class="wikitable"<br />
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{ | class“ wikitable”<br />
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|-<br />
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|-<br />
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|-<br />
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! {{diagonal split header|<br />Prisoner A|Prisoner B}} !! Prisoner B stays silent<br>(''cooperates'') !! Prisoner B betrays<br>(''defects'')<br />
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! !! Prisoner B stays silent<br>(cooperates) !! Prisoner B betrays<br>(defects)<br />
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! {{diagonal split header|<br />犯人A|犯人B}}!!犯人B保持沉默<br>(''合作'') !! 犯人B背叛<br>(''背叛'')<br />
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|-<br />
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|-<br />
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|-<br />
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! Prisoner A stays silent<br>(''cooperates'')<br />
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! Prisoner A stays silent<br>(cooperates)<br />
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!犯人 a 保持沉默<br>(''合作'')<br />
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| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
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| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
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|每人服刑1年||囚犯 A: 3年<br />囚犯 B: 无罪释放<br />
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|-<br />
<br />
|-<br />
<br />
|-<br />
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! Prisoner A betrays<br>(''defects'')<br />
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! Prisoner A betrays<br>(defects)<br />
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!犯人A背叛<br>(''背叛'')<br />
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| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
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| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
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|囚犯 A: 获释<br />囚犯 B: 3年||每人服刑2年<br />
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|}<br />
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|}<br />
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|}<br />
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It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by [[Dilemma#Use in logic|dilemma]]: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by dilemma: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
假设两个囚犯都了解博弈的本质,对彼此不忠诚,且在博弈之外没有机会得到报复或奖励。那么不管对方怎么决定,每个犯人背叛对方都会得到更高的奖励(“叛变”)。推理涉及一个进退两难的论点:B 要么合作,要么叛变。如果B合作,A 应该叛变,因为得到释放总比服刑1年好。如果 B叛变,A也应该叛变,因为服刑2年总比服刑3年好。所以不管怎样,A都应该叛变。并行推理表明B应该选择叛变。<br />
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Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a [[dominant strategy]]. Mutual defection is the only strong [[Nash equilibrium]] in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
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Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a dominant strategy. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
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因为不管对方的选择如何,背叛总是比合作带来更好的回报,所以这是一个<font color="#ff8000">占优策略 dominant strategy</font>。相互背叛是博弈中唯一的强<font color="#ff8000">纳什均衡点 dominant strategy </font>(即每个参与者单方面的改变策略只能使自己的情况变糟)。因此,困境在于,虽然相互合作比相互背叛产生更好的结果,但它却不是理性的结果,因为从自我利益的角度来看,合作的选择是非理性的。<br />
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<br />
==Generalized form==<br />
<font color="#ff8000">广泛形态 Generalized form </font><br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
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传统囚徒困境的结构可以从其最初的囚徒环境中概括出来。假设两个玩家用红色和蓝色表示,并且每个玩家选择“合作”或“背叛”。<br />
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If both players cooperate, they both receive the reward ''R'' for cooperating. If both players defect, they both receive the punishment payoff ''P''. If Blue defects while Red cooperates, then Blue receives the temptation payoff ''T'', while Red receives the "sucker's" payoff, ''S''. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff ''S'', while Red receives the temptation payoff ''T''.<br />
<br />
If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the tem punishment payoffptation payoff T.<br />
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如果两个玩家合作,他们都会因为合作而获得奖励''R''。如果两个参与人都叛变,他们都会受到惩罚''P''。 如果蓝方叛变而红方合作,那么蓝方得到诱惑回报''T'',而红方受到“上当受骗者”损失''S''。同样地,如果蓝方合作而红方叛变,那么蓝方得到上当受骗者的损失''S'',而红方得到诱惑支付''T''。<br />
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<br />
This can be expressed in [[Normal-form game|normal form]]:<br />
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This can be expressed in normal form:<br />
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这可以用标准形式的博弈来表示:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
| + <font color="#ff8000">正则 PD 支付矩阵 Canonical PD payoff matrix </font> <br />
<br />
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
! {{diagonal split header|{{color|#009|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
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and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
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要成为强意义下的囚徒困境博弈,收益必须满足以下条件:<br />
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<br />
<br />
:{{tmath|T > R > P > S}}<br />
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The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents.<br />
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The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents.<br />
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回报关系{{tmath|R > P}}意味着相互合作优于相互背叛,然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。<br />
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<br />
===Special case: donation game===<br />
特例:<font color="#ff8000">捐赠博弈 donation game </font><br />
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The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus<br />
<br />
The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus<br />
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捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式,在这种博弈中,合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b'',而叛变意味着什么也不提供。收益矩阵如下:<br />
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<br />
{| class="wikitable" style="text-align:center"<br />
<br />
! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
! {{diagonal split header|{{navy (color)|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section).<br />
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Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section).<br />
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请注意{{tmath|2R>T+S}}(即{{tmath|2(b-c)>b-c}})这使得捐赠博弈成为一个重复博弈(见下一节)。<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything.<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.<br />
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捐赠博弈可能适用于市场。假设种植者X 种橘子,种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b'',“b”比橙子的边际效用''c''高,因为X有橙子剩余而没有苹果。同样地,对于苹果种植者Y来说,橙子的边际效用是''b'',而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子,并且每个人都完成了交易,那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货,那么这个违约者将得到''b''的收益,而合作者将失去''c''的收益。 如果两者都违约,那么谁也不会得到或失去任何东西。<br />
<br />
==The iterated prisoner's dilemma==<br />
<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma </font> {{more citations needed section|date=November 2012}}<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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如果两个参与者连续进行多次囚徒困境博弈,他们记住对手先前的行动并相应地改变策略,这种博弈被称为重复囚徒困境。<br />
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In addition to the general form above, the iterative version also requires that {{tmath|2R > T + S}}, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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In addition to the general form above, the iterative version also requires that , to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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除了上面的一般形式之外,重复版本还要求{{tmath|2R > T + S}},防止交替合作和背叛比相互合作有更大的回报。<br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "[[Peace war game|peace-war game]]".<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
<br />
The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "peace-war game".<br />
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重复囚徒困境博弈是人类合作与信任的理论基础。假设博弈可以为两个需要信任的人之间的交易建模,那么群体中的合作行为也可以由多个参与者重复的博弈模型来建模。因此,这些年来,它吸引了许多学者。1975年,葛夫曼 Grofman和普尔 Pool估计专门撰写有关该领域的学术文章超过2000篇。重复囚徒困境也被称为“和平-战争博弈”。<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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If the game is played exactly ''N'' times and both players know this, then it is optimal to defect in all rounds. The only possible [[Nash equilibrium]] is to always defect. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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If the game is played exactly N times and both players know this, then it is optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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如果这个游戏正好玩了N次,并且两个玩家都知道这一点,那么在所有回合中最佳的策略就是叛变。唯一可能的纳什均衡点就是永远叛变。证明是通过归纳法证出来的: 不妨假设一个人在最后一回合叛变,因为对手之后没有机会反击。因此,双方都会在最后一个回合叛变。所以玩家同样也会在倒数第二回合时叛变,因为无论采取什么策略,对手都会在倒数第一回合叛变,依此类推。如果博弈次数未知但次数有限的情况也同样如此。<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The [[superrational]] strategy in the iterated prisoner's dilemma with fixed ''N'' is to cooperate against a superrational opponent, and in the limit of large ''N'', experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
<br />
Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoner's dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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与标准的囚徒困境不同,在重复囚徒困境中,叛变策略是严重违反直觉的,以至于不能很好地预测人类玩家的行为。然而,在标准的经济理论中,这是唯一正确的答案。具有固定次数 N的重复囚徒困境中的<font color="#ff8000">超理性 superrational</font>策略是与超理性对手进行合作,在N很大的限制下,实验结果的策略与超理性结果的策略一致,而不是博弈论的理性结果。<br />
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For [[cooperation]] to emerge between game theoretic rational players, the total number of rounds ''N'' must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by [[Robert Aumann]] in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
<br />
For cooperation to emerge between game theoretic rational players, the total number of rounds N must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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为了使合作在博弈论的理性参与者之间出现,参与者必须不知道回合总数N。在这种情况下,“总是叛变”可能不再是一个严格占优策略,而只是一个纳什均衡。罗伯特·奥曼 Robert Aumann在1959年的一篇论文中表明,理性参与者在无限多次的博弈中通过反复互动可以维持合作的结果。<br />
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<br />
According to a 2019 experimental study in the ''American Economic Review'' which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, [[Tit for tat|tit-for-tat]], and [[Grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
<br />
According to a 2019 experimental study in the American Economic Review which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, tit-for-tat, and Grim trigger. Which strategy the subjects chose depended on the parameters of the game.<br />
<br />
根据《美国经济评论》于2019年进行的一项实验研究,该实验中通过完美的监控测试了现实中被用在重复囚徒困境情况下的策略,监测选择的策略总是背叛,针锋相对的和 <font color="#ff8000"> 冷酷触发策略 Grim trigger</font>。受试者选择的策略取决于博弈的参数。<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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<br />
<br />
===Strategy for the iterated prisoner's dilemma===<br />
重复囚徒困境下的策略<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by [[Robert Axelrod]] in his book ''[[The Evolution of Cooperation]]'' (1984). In it he reports on a tournament he organized of the ''N'' step prisoner's dilemma (with ''N'' fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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Interest in the iterated prisoner's dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In it he reports on a tournament he organized of the N step prisoner's dilemma (with N fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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罗伯特·阿克塞尔罗德 Robert Axelrod在他的著作《合作的进化》(1984)中激起了人们对重复囚徒困境(IPD)的兴趣。在这篇文章中,他报道了自己组织的固定N次囚徒困境的比赛,参与者必须一次又一次地选择他们的共同策略,并且要记住他们之前的遭遇。阿克塞尔罗德邀请世界各地的学术界同仁设计计算机策略来参加IPD锦标赛。输入的程序在算法复杂性、最初敌意、宽恕能力等方面有很大差异。<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more [[altruism|altruistic]] strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by [[natural selection]].<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.<br />
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阿克塞尔罗德发现,当这些遭遇长时间在许多玩家身上重复发生时,每个玩家都有不同的策略,从长远来看,贪婪策略往往表现得非常糟糕,而更加利他的策略表现得更好,这完全是根据自身利益来判断的。他利用这一结果揭示了通过自然选择,从最初纯粹自私行为向利他行为进化的可能机制。<br />
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The winning [[deterministic algorithm|deterministic]] strategy was tit for tat, which [[Anatol Rapoport]] developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of [[BASIC]], and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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The winning deterministic strategy was tit for tat, which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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最终获胜的决定性策略是针锋相对策略,这是阿纳托尔·拉波波特 Anatol Rapoport开发并参加比赛的策略。这是所有参赛程序中最简单的一个,只有四行 BASIC 语言,并且赢得了比赛。策略很简单,就是在游戏的第一次重复中进行合作; 在此之后,玩家将执行做他的对手在前一步中所做的事情。根据具体情况,一个稍微好一点的策略可以是“带着宽恕之心针锋相对”。当对手叛变时,在下一次博弈中,玩家有时还是会合作,但概率很小(大约1-5%)。这允许博弈偶尔能从陷入叛变循环中恢复过来。确切的概率取决于对手的安排。<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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通过分析得分最高的战略,阿克塞尔罗德阐述了战略成功的几个必要条件。<br />
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; Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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;友好:最重要的条件是策略必须是好的,也就是说,它不会在对手之前叛变(这有时被称为“乐观”算法)。几乎所有得分最高的策略都是友好的; 因此,一个纯粹的自私策略不会为了纯粹自身的利益而“欺骗”对手。<br />
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; Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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;报复:然而,阿克塞尔罗德认为,成功的战略决不能是盲目的乐观主义。它有时必须进行报复。非报复策略的一个例子就是永远合作。这是一个非常糟糕的选择,因为“肮脏”的策略会无情地利用这些玩家。<br />
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; Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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;宽容: 成功的策略也必须是宽容的。虽然玩家会报复,但如果对手不继续叛变,他们将再次回到合作的状态。这阻止了长时间的报复和反报复,最大限度地提高积分。<br />
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; Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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;不嫉妒: 最后一个品质是不嫉妒,不强求比对手得分更多。<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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对于一次性的囚徒困境博弈,最优(点数最大化)策略就是简单的叛变; 正如上面所说,无论对手的构成如何,这都是正确的。然而,在重复囚徒困境博弈中,最优策略取决于可能的对手的策略,以及他们对叛变和合作的反应。例如,考虑一个群体,其中每个人每次都会叛变,只有一个人遵循针锋相对的策略。那个人就会由于第一回合的失利而处于轻微的不利地位。在这样一个群体中,个体的最佳策略是每次都叛变。在一定比例的总是选择背叛的玩家和其余组成选择针锋相对策略的玩家的人群中,个人的最佳策略取决于这一比例和博弈的次数。<br />
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In the strategy called Pavlov, [[win-stay, lose-switch]], faced with a failure to cooperate, the player switches strategy the next turn.<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref> In certain circumstances,{{specify|date=November 2012}} Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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In the strategy called Pavlov, win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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在所谓的<font color="#ff8000">巴甫洛夫策略 Pavlov strategy</font>中,<font color="#ff8000">去输存赢 win-stay, lose-switch</font>,面对一次合作失败,玩家将在下一次变换策略。<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref>在某些情况下,{{specify|date=November 2012}}巴甫洛夫通过使用类似策略给与合作者优惠待遇打败了其他所有策略。<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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得出最佳策略通常有两种方法:<br />
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* [[Bayesian Nash equilibrium]]: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit for tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.{{efn|1=For example see the 2003 study<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref> for discussion of the concept and whether it can apply in real [[economic]] or strategic situations.}}<br />
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<font color="#ff8000">贝叶斯纳什均衡 Bayesian Nash equilibrium</font>:如果可以确定对立策略的统计分布(例如,50%针锋相对,50%总是合作),那么,可以通过分析得出最佳的反策略{{efn|1=例如2003年的研究<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref>讨论这一概念以及它是否可以应用于实际经济或战略情况。}}<br />
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* [[Monte Carlo method|Monte Carlo]] simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a [[genetic algorithm]] for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit for tat players (see for instance Chess 1988),{{Clarify|date=August 2016}} but no analytic proof exists that this will always occur.<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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<font color="#ff8000">蒙特卡洛方法 Monte Carlo method </font>已经对种群进行了模拟,分数低的个体死亡,分数高的个体繁殖(<font color="#ff8000">遗传算法 genetic algorithm </font>用于寻找一个最佳策略)。最终群体中的算法组合通常取决于初始总体的组合。引入突变(繁殖过程中的随机变异)可以减少对初始种群的依赖性。使用这种系统进行经验性实验往往会为针锋相对的玩家带来麻烦(见Chess 1988),{{Clarify|date=August 2016}},但是没有分析证据表明这种情况会一直发生。<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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Although tit for tat is considered to be the most [[robust]] basic strategy, a team from [[Southampton University]] in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start.<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref> Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show [[University of Southampton]]'s strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between [[computer program|software strategies]] (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian [[Evolutionarily stable strategy|ESS]] simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. [[Richard Dawkins]] showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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Although tit for tat is considered to be the most robust basic strategy, a team from Southampton University in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between software strategies (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian ESS simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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尽管针锋相对被认为是最有力的基本策略,来自英格兰南安普敦大学的一个团队在20周年的重复囚徒困境竞赛中提出了一个新策略,这个策略被证明比针锋相对更为成功。这种策略依赖于程序之间的串通,以获得单个程序的最高分数。这所大学提交了60个程序,这些程序的设计目的是在比赛开始时通过一系列的5到10个动作来互相认识。<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref>一旦认识建立,一个程序总是合作,另一个程序总是叛变,保证叛变者得到最多的分数。如果这个程序意识到它正在和一个非南安普顿的球员比赛,它会不断地叛变,试图最小化与之竞争的程序的得分。因此,2004年囚徒困境锦标赛的结果显示了南安普敦大学战略位居前三名,尽管它比冷酷战略赢得更少,输的更多。(在囚徒困境锦标赛中,比赛的目的不是“赢”比赛——这一点频繁叛变很容易实现)。此外,即使没有软件策略之间的暗中串通(南安普顿队利用了这一点) ,针锋相对并不总是任何特定锦标赛的绝对赢家; 更准确地说,它是在一系列锦标赛中的长期结果超过了它的竞争对手。(在任何一个事件中,一个给定的策略可以比针锋相对稍微更好地适应竞争,但是针锋相对更稳健)。这同样适用于带有宽恕变量的针锋相对,和其他最佳策略: 在任何特定的一天,他们可能不会“赢得”一个特定的混合反战略。另一种方法是使用达尔文 Darwinian的<font color="#ff8000"> ESS模拟 ESS simulation</font>。在这样的模拟中,针锋相对几乎总是占主导地位,尽管讨厌的策略会在人群中漂移,因为使用针锋相对策略的人群可以通过非报复性的好策略进行渗透,这反过来使他们容易成为讨厌策略的猎物。理查德·道金斯 Richard Dawkins指出,在这里,没有静态的混合策略会形成一个稳定的平衡,系统将始终在边界之间振荡。这种策略最终在比赛中获得了前三名的成绩,或者是接近垫底的成绩。<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of [[minmaxing]]). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book ''[[The Selfish Gene]]'', pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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这种策略利用了这样一个事实,即在这场特殊的比赛中允许多个参赛项目,并且团队的表现由得分最高的项目来衡量(这意味着使用自我牺牲的项目是一种分数最大化的形式)。在一个只能控制一个玩家的比赛中,针锋相对当然是一个更好的策略。由于这一新规则的存在,与阿克塞尔罗德的具有深远影响的竞赛相比,这种竞赛在分析单个主体策略时也就没有什么理论意义。然而,它为在分析多主体框架下,特别是在存在干扰的情况下,如何实现协作策略提供了基础。事实上,早在这场新规则锦标赛开始之前,道金斯就在他的《自私的基因》一书中指出,如果允许多次参赛,这种策略就有可能获胜,但他说,如果提交这种策略的话,阿克塞尔罗德很可能不会允许。因为它依赖于规避囚徒困境的规则,即两个参与者之间不允许交流,南安普顿的项目可以说在开场的“十步舞”中就是这样做以认识对方的; 这只是强调了交流在改变游戏平衡方面的价值。<br />
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===Stochastic iterated prisoner's dilemma===<br />
随机的重复囚徒困境<br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities".<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref> In an encounter between player ''X'' and player ''Y'', ''X'' 's strategy is specified by a set of probabilities ''P'' of cooperating with ''Y''. ''P'' is a function of the outcomes of their previous encounters or some subset thereof. If ''P'' is a function of only their most recent ''n'' encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that ''X'' will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which ''X'' cooperated and ''Y'' defected, then <math>P_{cd}</math> is the probability that ''X'' will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as ''P''={1,0,1,0}, in which ''X'' responds as ''Y'' did in the previous encounter. Another is the [[win–stay, lose–switch]] strategy written as ''P''={1,0,0,1}, in which ''X'' responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<ref name="Press2012"/><br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player X and player Y, X 's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which X cooperated and Y defected, then <math>P_{cd}</math> is the probability that X will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as P={1,0,1,0}, in which X responds as Y did in the previous encounter. Another is the win–stay, lose–switch strategy written as P={1,0,0,1}, in which X responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<br />
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在随机重复<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>博弈中,策略由“合作概率”来确定。<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref>在玩家''X''和玩家''Y''之间的遭遇中,''X''‘s的策略由一组与''Y''合作的概率''P''确定,''P''是他们之前遭遇的结果的函数,或者是其中的一些子集。如果''P''只是它们最近遇到次数 ''n''的函数,那么它被称为“记忆-n”策略。我们可以由四个联合概率指定一个记忆-1策略: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>,其中<math>P_{ab}</math>是在当前遭遇中基于先前联合的概率。如果每个概率都是1或0,这种策略称为确定性策略。确定性策略的一个例子是针锋相对策略,写成 p {1,0,1,0} ,其中 x 的反应和 y 在前一次遭遇中的反应一样。另一种是胜-保持-败-转换策略,它被写成 p {1,0,0,1} ,在这种策略中,如果 x 获得胜利(即:cc 或 dc),x会做出与上一次遭遇一样的反应 ,但如果失败,x会改变策略(即cd 或 dd)。研究表明,对于任何一种记忆-n 策略,存在一个相应的记忆-1策略,这个策略给出相同的统计结果,因此只需要考虑记忆-1策略。<ref name="Press2012"/><br />
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If we define ''P'' as the above 4-element strategy vector of ''X'' and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of ''Y'', a transition matrix ''M'' may be defined for ''X'' whose ''ij'' th entry is the probability that the outcome of a particular encounter between ''X'' and ''Y'' will be ''j'' given that the previous encounter was ''i'', where ''i'' and ''j'' are one of the four outcome indices: ''cc'', ''cd'', ''dc'', or ''dd''. For example, from ''X'' 's point of view, the probability that the outcome of the present encounter is ''cd'' given that the previous encounter was ''cd'' is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for ''Q'' are from ''Y'' 's point of view: a ''cd'' outcome for ''X'' is a ''dc'' outcome for ''Y''.) Under these definitions, the iterated prisoner's dilemma qualifies as a [[stochastic process]] and ''M'' is a [[stochastic matrix]], allowing all of the theory of stochastic processes to be applied.<ref name="Press2012"/><br />
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If we define P as the above 4-element strategy vector of X and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of Y, a transition matrix M may be defined for X whose ij th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X 's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for Q are from Y 's point of view: a cd outcome for X is a dc outcome for Y.) Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.<br />
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如果我们将''P''定义为''X''的上述4元策略向量,并将<math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math>定义为''Y''的4元策略向量,则对于''X''可以定义一个转移矩阵''M'',其第ij项是''X''和''Y''之间特定相遇的结果为j的概率,给定i,其中i和j是cc、cd、dc或dd 四个结果索引中的一个。例如,从''X''的角度来看,如果给定''cd'',那么这次的结果是''cd''的概率等于<math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>。(''Q''的指标是 从''Y''的角度: ''X''的''cd''结果是''Y''的''dc''结果)在这些定义下,重复的囚徒困境被定义为一个随机过程,''M''是一个随机矩阵,允许应用所有的随机过程理论。<ref name="Press2012"/><br />
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One result of stochastic theory is that there exists a stationary vector ''v'' for the matrix ''M'' such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that ''v'' is normalized so that the sum of its four components is unity. The ''ij'' th entry in <math>M^n</math> will give the probability that the outcome of an encounter between ''X'' and ''Y'' will be ''j'' given that the encounter ''n'' steps previous is ''i''. In the limit as ''n'' approaches infinity, ''M'' will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing ''j'' which will be independent of ''i''. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that ''v'' is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to ''v''. Thus the stationary vector specifies the equilibrium outcome probabilities for ''X''. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From ''X'' 's point of view), the equilibrium payoffs for ''X'' and ''Y'' can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.<br />
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One result of stochastic theory is that there exists a stationary vector v for the matrix M such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij th entry in <math>M^n</math> will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j which will be independent of i. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to v. Thus the stationary vector specifies the equilibrium outcome probabilities for X. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From X 's point of view), the equilibrium payoffs for X and Y can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies P and Q to be compared for their long term payoffs.<br />
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随机理论的一个结果是,矩阵''M''存在一个平稳向量''v''使得<math>v\cdot M=v</math>成立。一般地,我们可以指定''v''是标准化的,因此它的4个组成部分之和为1。the equilibrium payoffs for and can now be specified as and, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.第''ij''项<math>M^n</math>给出了''X''和''Y''相遇的结果的概率为''j'',给定前面相遇''n''步的概率是''i''。当''n''趋于无穷时,''M''收敛于一个具有固定值的矩阵,并且''j''趋向一个长期概率,与''i''独立。换句话说, <math>M^\infty</math>的行将是相同的,从而给出了重复囚徒困境的长期均衡结果概率,而不需要明确地计算大量的相互作用。可以看出,''v''是<math>M^n</math>特别是<math>M^\infty</math>, 的平稳向量,因此<math>M^\infty</math>的每一行都等于''v''。因此平稳向量指定了''X''的均衡结果概率。定义<math>S_x=\{R,S,T,P\}</math>和<math>S_y=\{R,T,S,P\}</math>作为{cc,cd,dc,dd}结果的短期收益向量(从''X''的角度来看) ,现在可以将''X''和''Y''的均衡收益指定为<math>s_x=v\cdot S_x</math>和<math>s_y=v\cdot S_y</math>,使得''P''、''Q''两种策略的长期收益可以比较。<br />
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====Zero-determinant strategies====<br />
<font color="#ff8000">零决定策略 Zero-determinant strategies</font><br />
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[[File:IPD Venn.svg|right|thumb|upright=2.5|The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram]]. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and [[weak selection]]. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and weak selection. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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<font color="#ff8000">维恩图 Venn diagram</font>中讨论了<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma</font>(IPD)中零决定策略(ZD)、合作策略和背叛策略之间的关系。合作策略总是与其他合作策略相互配合,而背叛策略总是与其他背叛策略相抵触。这两种策略都包都含在强选择下稳健的策略子集,这意味着当它们驻留在一个种群中时,没有选择其他的记忆-1策略来入侵此策略。只有合作策略包含在始终稳健的策略子集,意味着无论选择强项还是弱项,都不会选择其他任何记忆-1策略来入侵和替换此策略。零决定策略和良好的合作策略之间的交集是一组宽松的零决定策略。勒索策略是零决定策略和非稳健背叛策略的交集。针锋相对是合作、背叛和零决定策略的交集。<br />
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In 2012, [[William H. Press]] and [[Freeman Dyson]] published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies.<ref name="Press2012"/> The long term payoffs for encounters between ''X'' and ''Y'' can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector ''v''. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in ''f'', it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where ''U''={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector v. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in f, it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where U={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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2012年,威廉·H·普莱斯 William H. Press和弗里曼·戴森 Freeman Dyson针对随机重复囚徒困境提出了一类新的策略,称为“零决定”策略。<ref name="Press2012"/>''X''和''Y''之间的长期收益可以表示为一个矩阵的决定因素,它是两个策略和短期收益向量的函数: <math>s_x=D(P,Q,S_x)</math>和<math>s_y=D(P,Q,S_y)</math>,不涉及平稳向量''v''。 由于行列式函数<math>s_y=D(P,Q,f)</math>在''f''中是线性的,因此可以推出<math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math>(其中''U''={1,1,1,1})。任何策略的<math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math>被定义为零决定策略,长期收益服从关系式<math>\alpha s_x+\beta s_y+\gamma=0</math>。<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of [[ultimatum game]]. Specifically, ''X'' is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of ''Y'' 's strategy, offering an opportunity for ''X'' to "extort" player ''Y'' (and vice versa). (It turns out that if ''X'' tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.<ref name="Press2012"/>)<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of Y 's strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.)<br />
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针锋相对是一种零决定策略,在不获得超越其他玩家优势的意义下是“公平”的。然而,零决定策略空间还包含这样的策略:在两个玩家的情况下,可以允许一个玩家单方面设置另一个玩家的分数,或者强迫进化的玩家获得比他自己的分数低一些的收益。被勒索的玩家可能会背叛,但会因此获得较低的回报并且受到伤害。因此,勒索的解决方案将重复囚徒困境转化为一种<font color="#ff8000">最后通牒博弈 ultimatum game </font>。具体来说,''X''能够选择一种策略,对于这种策略,<math>D(P,Q,\beta S_y+\gamma U)=0</math>单方面地将<math>s_y</math>设置为一个特定值范围内的特定值,与''Y''的策略无关,为''X''提供了“勒索”玩家''Y''的机会(反之亦然)。(事实证明,如果''X''试图将<math>s_x</math>设置为一个特定的值,那么可能的范围要小得多,只包括完全合作或完全叛变。<ref name="Press2012"/>)<br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not [[evolutionarily stable strategy|evolutionarily stable]]. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<br />
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重复囚徒困境的一个扩展是进化的随机重复囚徒困境,其中允许特定策略的相对丰度改变,更成功的策略相对增加。这个过程可以通过让不太成功的玩家模仿更成功的策略,或者通过从游戏中淘汰不太成功的玩家,同时让更成功的玩家成倍增加。研究表明,不公平的零决定策略不是进化稳定策略。关键的直觉告诉我们,进化稳定策略不仅要能够入侵另一个群体(这是勒索零决定策略可以做到的) ,而且还要在同类型的其他玩家面前表现良好(勒索零决定策略玩家表现不佳,因为他们减少了彼此的盈余)。<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and [[win–stay, lose–switch]] agents.<ref name=Hilbe2013 /><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.<br />
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理论和模拟证实,超过一个临界种群规模,零决定勒索在与更多合作策略的进化竞争中会失败,因此,种群越大,种群的平均收益就越大。此外,在某些情况下,勒索者甚至可能通过帮助打破统一的背叛者与使用“赢-保持-输”策略的转换玩家之间的对峙而促进合作。<ref name=Hilbe2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies ''is'' both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the [[Prisoner's dilemma#Special case: Donation game|donation game]] by Alexander Stewart and Joshua Plotkin in 2013.<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref> Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013)<ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<ref name=Stewart2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013) to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<br />
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虽然勒索零决定策略在人口众多的情况下并不稳定,但另一种宽松的零决定策略既稳定又稳健。事实上,当人口不算太少的时候,这些策略可以取代任何其他零决定策略,甚至在一系列针对重复囚徒困境的广泛通用策略(包括“获胜-保持-输”的转换策略)中表现良好。亚历山大·斯图尔特 Alexander Stewart和约书亚·普洛特金 Joshua Plotkin在2013年的捐赠博弈中证明了这一点。<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref>宽松的策略会与其他合作的玩家合作,面对背叛,慷慨的玩家比他的对手失去更多的效用。宽松策略是零决定策略和所谓的“好”策略的交集,阿金(2013) <ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.将这两种策略定义为玩家对过去的相互合作作出回应,并在至少获得合作预期收益的情况下平均分配预期收益的策略。在好的策略中,当总体不太小时,宽松(零决定)子集表现良好。如果总体很少,背叛策略往往占主导地位。<ref name=Stewart2013 /><br />
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===Continuous iterated prisoner's dilemma===<br />
<font color="#ff8000">连续重复囚徒困境 Continuous iterated prisoner's dilemma </font> <br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref> found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from [[Assortative mating|assorting]] with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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关于重复囚徒困境的研究大多集中在离散情况下,在这种情况下,参与者要么合作,要么背叛,因为这个模型分析起来比较简单。然而,一些研究人员已经研究了连续重复囚徒困境模型,在这个模型中,玩家能够对另一个玩家做出可变的贡献。乐 Le和博伊德 Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref>发现,在这种情况下,合作比离散重复的囚徒困境更难发展。这个结果的基本直觉很简单: 在一个持续的囚徒困境中,如果一个人群开始处于非合作均衡状态,那么与非合作者相比,合作程度稍高的玩家不会从相互配合中获益。相比之下,在离散的囚徒困境中,相对于非合作者,针锋相对的合作者在非合作均衡中相互配合会获得巨大的回报。由于自然界可以提供更多的机会来进行各种各样的合作,而不是严格地将合作或背叛分为两类,因此连续的囚徒困境可以帮助解释为什么现实生活中针锋相对的合作的例子在自然界中极其罕见。(例如,哈默斯坦 Hammerstein <ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)。<br />
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even though tit for tat seems robust in theoretical models.<br />
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even though tit for tat seems robust in theoretical models.<br />
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尽管在理论模型中,针锋相对策略似乎是稳健的。<br />
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===Emergence of stable strategies===<br />
<font color="#ff8000">稳定策略的出现 Emergence of stable strategies </font> <br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref> Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies. Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<br />
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玩家似乎不能协调相互合作,因此常常陷入劣等而稳定的背叛策略。这样,重复回合可以促进稳定策略的发展。<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref>重复回合往往产生新颖的策略,这对复杂的社会互动有影响。其中一个策略就是“赢-保持-输”的转变。这个策略比一个简单的针锋相对策略要好&nbsp;–也就是说,如果你能逃脱作弊的惩罚,就重复这个行为,如果你被抓住了,就改变策略。<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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这种针锋相对策略的唯一问题是它们很容易出现信号错误。当一个人因报复而作弊,而另一个人将其单纯解释为欺骗时,就会出现问题。结果,第二个人现在作弊,然后在接下来的连锁反应中开始了反复交替的作弊模式。<br />
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==Real-life examples==<br />
现实生活的例子<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the [[social science]]s such as [[economics]], [[politics]], and [[sociology]], as well as to the biological sciences such as [[ethology]] and [[evolutionary biology]]. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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囚犯的环境似乎是人为的,但实际上,在人类交往以及自然界的交互中有许多具有相同收益矩阵的例子。因此,囚徒困境是经济学、政治学、社会学等社会科学以及动物行为学、进化生物学等生物学研究的热点问题。许多自然过程都被抽象为生物进行无休止的囚徒困境博弈的模型。囚徒困境这种广泛的适用性让博弈变得非常重要。<br />
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===Environmental studies===<br />
环境研究<br />
In [[environmental studies]], the PD is evident in crises such as global [[climate change|climate-change]]. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb [[Carbon dioxide|{{Co2}}]] emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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In environmental studies, the PD is evident in crises such as global climate-change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide| emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<br />
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在环境研究中,囚徒困境在诸如全球气候变化等危机中显而易见。有人认为,所有国家都将从稳定的气候中受益,但是每一个国家通常都在限制二氧化碳排放方面犹豫不决。人们错误地认为,如果所有国家的行为都改变,任何一个国家保持目前的行为所带来的直接好处都会大于所谓的最终好处,这就解释了2007年气候变化方面的僵局。<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<br />
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气候变化政治与囚徒困境之间的一个重要区别是不确定性; 污染对气候变化的影响程度和速度尚不清楚。因此,政府面临的困境不同于囚徒困境,因为合作的回报是未知的。这种差异表明,各国之间的合作远远少于真正的重复囚徒困境中的合作,因此避免可能发生的气候灾难的可能性远远小于使用真正的重复囚徒困境博弈论情景分析<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of [[Michael Porter]]'s hypothesis, in which government regulation of competing firms is substantial.<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.<br />
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欧桑 Osang和南迪 Nandy (2003)提供了一个理论解释,并根据迈克尔·波特 Michael Porter的假设,即政府对竞争企业的监管是实质性的,证明了监管驱动的双赢局面。<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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===Animals===<br />
动物<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, [[guppy|guppies]] inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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许多动物的合作行为可以理解为囚徒困境的一个例子。通常动物会建立长期的伙伴关系,这种关系可以更具体地模拟为重复囚徒困境。例如,孔雀鱼成群结队地合作监察捕食者,它们被认为是在惩罚不合作的监察者。<br />
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[[Vampire bats]] are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<br />
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吸血蝙蝠是从事相互的食物交换的群居动物。应用囚徒困境收益可以帮助解释这种行为: <ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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* C/C: "Reward: I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much."<br />
* 合作/合作:"回报:我在不幸运的晚上得到了能让我果腹的血,那在幸运的晚上我也应该分出点血,那不会花费多少。"<br />
* D/C: "Temptation: You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night."<br />
* 背叛/合作:"诱惑:你在我的不幸的夜里救了我,但在我的幸运夜我不会给你血,那样我会活的更好。"<br />
* C/D: "Sucker's Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death."<br />
* 合作/叛变:"可怜者的回报:在我的幸运夜我救了你的命,但在我的不幸夜里你没有救我,我有饿死的风险。"<br />
* D/D: "Punishment: I don't have to pay the slight costs of feeding you on my good nights. But I run a real risk of starving on my poor nights."<br />
* 叛变/叛变:"惩罚:我在我的幸运夜里不必付出代价来救你,但我在我的不幸夜里有挨饿的风险。"<br />
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===Psychology===<br />
心理学<br />
In [[addiction]] research / [[behavioral economics]], [[George Ainslie (psychologist)|George Ainslie]] points out<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref> that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, ''defecting'' means ''relapsing'', and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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In addiction research / behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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在成瘾研究/行为经济学中,乔治·安斯利 George Ainslie指出<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref>,可以将成瘾视为成瘾者现在和未来自我之间的跨期囚徒困境问题。在这种情况下,背叛意味着复发,很容易看出,目前和未来都没有背叛是迄今为止最好的结果。如果一个人今天戒了,但在将来又复吸,这是最糟糕的结果&nbsp;–从某种意义上来说,今天戒瘾所包含的纪律和自我牺牲已经被“浪费”了,因为未来的复吸意味着瘾君子又回到了他开始的地方,他将被迫重新开始(这相当令人沮丧,也使得重新开始更加困难)。今天和明天复发是一个稍微“好一点”的结果,因为尽管瘾君子仍然上瘾,但他们没有努力去尝试停止。最后一种情况是,现在与成瘾斗争的任何人都会熟悉现在的成瘾行为,而在明天放弃。这里的问题是(和其他囚徒困境问题一样),背叛“今天”有一个明显的好处,但明天这个人将面临同样的囚徒困境问题,同样明显的好处是背叛,最终导致一连串无休止的背叛。<br />
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[[John Gottman]] in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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John Gottman in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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约翰·高特曼 John Gottman在他的研究《信任的科学》中将良好的关系定义为伙伴知道不进入(背叛,背叛)牢房中或者至少不要陷入这样的动态循环关系中。<br />
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===Economics===<br />
经济学<br />
The prisoner's dilemma has been called the ''[[Escherichia coli|E. coli]]'' of social psychology, and it has been used widely to research various topics such as [[Oligopoly|oligopolistic]] competition and collective action to produce a collective good.<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref> <br />
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The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good. <br />
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囚徒困境被称为社会心理学中的“大肠杆菌”,它被广泛用于研究寡头垄断竞争和集体行动来产生集体利益等问题。<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When [[cigarette advertising]] was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. <ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref> This analysis is likely to be pertinent in many other business situations involving advertising. <ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.<br />
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广告有时被认为是囚徒困境的一个真实例子。当香烟广告在美国是合法的时候,相互竞争的香烟制造商必须决定在广告上花多少钱。公司A的广告效果部分取决于公司B的广告效果。同样,公司B的广告带来的利润也受到公司A的广告影响。如果公司A和公司B都选择在给定的时间段内做广告,那么一家公司的广告就会抵消另一方的广告,倘若收入保持不变,费用就会因广告成本而增加。两家公司都将从广告减少中获益。然而,如果B公司选择不做广告,A公司就可以通过广告获得巨大的利益。尽管如此,一家公司的最佳广告数量仍取决于另一家公司的广告投放量。由于最佳策略取决于其他公司的选择,因此这里没有占主导地位的策略,这使得它与囚徒困境略有不同。但结果是相似的,如果两家公司的广告都少于均衡状态,他们的处境会更好。有时合作行为确实会在商业环境中出现。例如,香烟制造商支持立法禁止香烟广告,因为这将降低成本并增加整个行业的利润。<ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref>这种分析可能适用于许多其他涉及广告的商业情况。<ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref> <br />
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Without enforceable agreements, members of a [[cartel]] are also involved in a (multi-player) prisoner's dilemma.<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. [[Anti-trust]] authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for [[consumer]]s.<br />
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Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.<br />
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没有可强制执行的协议,卡特尔 cartel的成员国也会陷入(多玩家)囚徒困境。<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> “合作”通常意味着将价格保持在预先商定的最低水平。“背叛”意味着低于最低价格水平销售,并立即从其他卡特尔成员那里获得业务(和利润)。反垄断机构希望潜在的卡特尔成员相互背叛,确保消费者获得尽可能低的价格。<br />
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===Sport===<br />
运动<br />
[[Doping in sport]] has been cited as an example of a prisoner's dilemma.<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Doping in sport has been cited as an example of a prisoner's dilemma.<br />
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体育运动中的兴奋剂被认为是囚徒困境的一个例子。<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<ref name="wired" /><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<br />
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两名参赛运动员可以选择使用非法或危险药物来提高成绩。如果两个运动员都没有服用这种药物,那么他们都不会获得优势。如果只有一个人这样做,那么这个运动员就比他们的竞争对手获得了明显的优势,但由于法律或服用药物的医疗风险,这种优势会减少。然而,如果两名运动员都服用了这种药物,那么好处就被抵消了,只剩下风险,这使得他们的处境比没有服用兴奋剂的情况更加糟糕。<ref name="wired" /><br />
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===International politics===<br />
国际政治<br />
In [[international politics|international political theory]], the Prisoner's Dilemma is often used to demonstrate the coherence of [[strategic realism]], which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given [[anarchy (international relations)|international anarchy]]. A classic example is an arms race like the [[Cold War]] and similar conflicts.<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref> During the Cold War the opposing alliances of [[NATO]] and the [[Warsaw Pact]] both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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In international political theory, the Prisoner's Dilemma is often used to demonstrate the coherence of strategic realism, which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given international anarchy. A classic example is an arms race like the Cold War and similar conflicts. During the Cold War the opposing alliances of NATO and the Warsaw Pact both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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在国际政治理论中,囚徒困境经常被用来证明战略现实主义的一致性,这种战略现实主义认为,在国际关系中,由于国际无政府状态,所有国家(无论其国内政策或公开宣称的意识形态如何)都会为了自身的理性利益来行动。一个典型的例子是类似冷战和类似冲突的军备竞赛。<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref>在冷战期间,北约和华约组织的对立联盟都可以选择武装或解除武装。从双方的观点来看,解除武装而对手继续武装可能会导致军事劣势和被歼灭。相反,如果选择武装而对手已经解除了武装,那么就会获得优势。如果双方都选择武装自己,那么任何一方都承担不起攻击对方的代价,但是双方都为发展和维持核武库付出了高昂的代价。如果双方都选择裁军,战争就可以避免,也不会有任何代价。<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a [[War of attrition (game)|war of attrition]] for the next thirty years until the Soviet Union could not withstand the economic cost.<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref> The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a war of attrition for the next thirty years until the Soviet Union could not withstand the economic cost. The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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虽然最好的结果是双方解除武装,但是双方的理性选择是武装起来,事实也的确如此。在接下来的三十年里,双方都在军事研究和武器装备的消耗战上投入了大量的资源,直到苏联无法承受经济损失。<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref>同样的逻辑也适用于任何类似的情况,无论是主权国家之间的经济竞争还是技术竞争。<br />
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===Multiplayer dilemmas===<br />
<font color="#ff8000">多玩家困境 Multiplayer dilemmas</font><br />
Many real-life dilemmas involve multiple players.<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref> Although metaphorical, [[Garrett Hardin|Hardin's]] [[tragedy of the commons]] may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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许多现实生活中的困境牵涉到多个参与者。<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref>尽管具有隐喻性,但哈丁的<font color="#ff8000">公地悲剧 tragedy of the commons</font>可以看作是囚徒困境多个参与者的一个例子: 每个村民做出选择是为了个人利益还是克制。对于一致(甚至频繁)叛变的集体回报是非常低的(代表了对“公共资源”的破坏)。大多数人可能会遇到的公地困境是在一个共用的房子里洗碗。通过不洗碗,个人可以节省时间,但如果每个居民都选择这种行为,那么集体的代价是任何人都没有干净的盘子。<br />
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The commons are not always exploited: [[William Poundstone]], in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to [[Excludability|take a paper without paying]] (''defecting'') but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by [[Elinor Ostrom]], winner of the 2009 [[Nobel Memorial Prize in Economic Sciences]], hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<br />
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公共资源并不总是被利用: 威廉·庞德斯通 William Poundstone在一本关于囚徒困境的书(见下文参考文献)中描述了新西兰的一种情况,信箱没有上锁。人们可以不付钱就拿报纸(背叛) ,但很少有人这样做,他们觉得如果他们不付钱,那么其他人也不会付钱,这会摧毁整个系统。2009年诺贝尔经济学奖获得者埃莉诺·奥斯特罗姆 Elinor Ostrom随后的研究认为公地悲剧过于简单化,其负面结果会受到外部影响。在没有复杂压力的情况下,团体之间为了共同利益进行沟通和管理,执行社会规范以保护资源并为团体实现最大利益,这是实现囚徒困境最佳结果的一个例子。<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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==Related games==<br />
相关博弈<br />
===Closed-bag exchange===<br />
<font color="#ff8000">封闭袋子交换 Closed-bag exchange </font><br />
[[File:Prisoner's Dilemma briefcase exchange (colorized).svg|thumb|The prisoner's dilemma as a briefcase exchange]]<br />
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The prisoner's dilemma as a briefcase exchange<br />
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囚徒困境是一个公文包式的交换<br />
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[[Douglas Hofstadter]]<ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref> once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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Douglas Hofstadter once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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侯世达 Douglas Hofstadter <ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref>曾经指出,人们通常会发现诸如囚徒困境的问题,比如,当它以一个简单囚徒困境博弈的形式,或者以权衡的方式表现出来时,会更容易理解。他使用的几个例子之一是“封闭袋子交换” :<br />
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{{quote|Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.}}<br />
两人相遇并交换包裹,事先知道一个包里装着钱,一个装着订单。任一玩家都可选择尊重交易,放入事先约定的东西;也可以选择背叛,交换空的公文包。<br />
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Defection always gives a game-theoretically preferable outcome.<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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Defection always gives a game-theoretically preferable outcome.<br />
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背叛总是会带来一个理论上更可取的结果。<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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===''Friend or Foe?''===<br />
朋友还是敌人?<br />
''[[Friend or Foe? (TV series)|Friend or Foe?]]'' is a game show that aired from 2002 to 2005 on the [[Game Show Network]] in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, ''Friend or Foe'' has a rewards model between prisoner's dilemma and the [[Chicken (game)|game of Chicken]].<br />
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Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.<br />
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朋友还是敌人?是一个竞赛节目,从2002年至2005年在美国的Game show Network播出。这是囚徒困境博弈在真人身上测试的一个例子,只是在人为的环境中。在游戏节目中,有三对选手参加比赛。当一对被淘汰时,他们会玩一个类似囚徒困境的游戏来决定奖金如何分配。如果他们都合作(朋友) ,他们分享奖金50-50。如果一方合作而另一方背叛(敌人) ,那么叛变者将得到所有的奖金,而合作者将一无所获。如果双方都背叛,那么双方都将一无所有。请注意,奖励矩阵与上面给出的标准矩阵略有不同,因为“双方都背叛”和“合作而对方背叛”情况下的奖励是相同的。与标准囚徒困境中的严格均衡相比,这使得“两个都背叛”情况成为一个弱均衡。如果一个参赛者知道他们的对手将投票给“敌人” ,那么他们自己的选择不会影响他们自己的奖金。从特定意义上讲,“朋友还是敌人”节目在囚徒困境和“胆小鬼”博弈之间有一个奖励模型。<br />
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The rewards matrix is<br />
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The rewards matrix is<br />
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奖励矩阵是<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Friend"<br />(cooperate)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Foe"<br />(defect)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"Friend"<br />(cooperate)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"Foe"<br />(defect)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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{| class="wikitable"<br />
<br />
! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"朋友"<br />(合作)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"敌人"<br />(背叛)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"朋友"<br />(合作)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"敌人"<br />(背叛)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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This payoff matrix has also been used on the [[United Kingdom|British]] [[television]] programmes ''Trust Me'', ''[[Shafted]]'', ''[[The Bank Job (TV series)|The Bank Job]]'' and ''[[Golden Balls]]'', and on the [[United States|American]] shows ''[[Bachelor Pad]]'' and ''[[Take It All (game show)|Take It All]]''. Game data from the ''[[Golden Balls]]'' series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls, and on the American shows Bachelor Pad and Take It All. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<br />
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英国电视节目《相信我》、《阴影》、《银行工作》和《黄金球》以及美国电视节目《单身公寓》和《全部拿走》也采用了这种奖励矩阵。一个经济学家团队分析了“金球奖”系列的游戏数据,他们发现,现实生活中,合作对于金额而言“惊人地高” ,但在游戏的背景下,相对较低。<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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===Iterated snowdrift===<br />
<font color="#ff8000">重复雪堆 Iterated snowdrift </font><br />
{{main|snowdrift game}}<br />
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Researchers from the [[University of Lausanne]] and the [[University of Edinburgh]] have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a [[chicken game]], it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a [[snowdrift]], each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
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Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
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来自洛桑大学和爱丁堡大学的研究人员认为,“重复雪堆游戏”可能更能反映现实世界的社会状况。虽然这个模型实际上是一个胆小鬼博弈。在这个模型中,由于背叛可以降低被剥削的风险,个体总是从合作选择中获益。这个雪堆游戏可以设想两个司机被困在雪堆的两侧,每个司机都可以选择铲雪清理道路,或者留在自己的车里。一个玩家的最高回报来自于让对手清除所有的积雪,但是仍然可以从对手的工作中得到回报。<br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<br />
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这可能更好地反映了现实世界的情景,研究人员举了两位科学家合作完成一份报告的例子,如果另一位科学家更加努力地工作,这两位科学家都会受益。“但当你的合作者不做任何工作时,你自己完成所有的工作可能会更好。你最终还是会完成一个项目。” <ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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{|<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ Example snowdrift payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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! Cooperates<br />
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| 200, 200 || 100, 300<br />
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|-<br />
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! Defects<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
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|+ Example PD payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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|-<br />
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! Cooperates<br />
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| 200, 200 || -100, 300<br />
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|-<br />
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! Defects<br />
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| 300, -100 || 0, 0<br />
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|}<br />
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{|<br />
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|-<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ 重复雪堆的支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
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|-<br />
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! 合作<br />
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| 200, 200 || 100, 300<br />
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|-<br />
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! 背叛<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
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|+ 囚徒困境支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
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|-<br />
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! 合作<br />
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| 200, 200 || -100, 300<br />
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|-<br />
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! 背叛<br />
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| 300, -100 || 0, 0<br />
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|}<br />
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===Coordination games===<br />
<font color="#ff8000">协调博弈 Coordination games</font><br />
{{main|coordination games}}<br />
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In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local [[left- and right-hand traffic]] convention helps to co-ordinate their actions.<br />
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In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.<br />
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在协调博弈中,参与者必须协调自己的策略以获得一个好的结果。一个例子是两辆车在暴风雪中突然相遇,每辆车必须选择是左转还是右转。如果两辆车都向左转弯,或者都向右转弯,那么两辆车就不会相撞。当地的左右向交通惯例有助于协调他们的行动。<br />
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Symmetrical co-ordination games include [[Stag hunt]] and [[Bach or Stravinsky]].<br />
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Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.<br />
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对称的协调游戏包括猎鹿 Stag hunt和巴赫 Bach或斯特拉文斯基 Stravinsky。<br />
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===Asymmetric prisoner's dilemmas===<br />
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<font color="#ff8000">不对称的囚徒困境 Asymmetric prisoner's dilemmas</font><br />
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A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an [[alibi]], whence the term "alibi game".<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
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A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, whence the term "alibi game".<br />
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一个更一般的博弈集是不对称的。就像在囚徒困境中一样,最好的结果是合作,而背叛是有动机的。与对称的囚徒困境不同的是一个玩家比另一个玩家有更多的损失或收获。这样的博弈被描述为囚徒困境,其中一个囚徒有不在场证明,这就是术语“不在场证明游戏”的由来。<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<br />
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在实验中,在重复博弈中获得不均等收益的参与者可能会寻求利润最大化,但是前提是两个玩家都必须获得均等的收益。这可能会导致一个稳定的均衡策略,即弱势参与者在每隔X场博弈中都会背叛,而另一个参与者总是保持合作。这种行为可能取决于实验围绕公平的社会规范。<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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==Software==<br />
软件<br />
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
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已经有一些可以用来运行囚徒困境模拟和比赛的软件包,其中一些有可用的源代码。<br />
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* The source code for the [[The Evolution of Cooperation|second tournament]] run by Robert Axelrod (written by Axelrod and many contributors in [[Fortran]]) is available [http://www-personal.umich.edu/~axe/research/Software/CC/CC2.html online]<br />
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* [https://web.archive.org/web/19991010053242/http://www.lifl.fr/IPD/ipd.frame.html Prison], a library written in [[Java (programming language)|Java]], last updated in 1998<br />
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* [https://github.com/Axelrod-Python/Axelrod Axelrod-Python], written in [[Python (programming language)|Python]]<br />
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* [http://selborne.nl/ipd/ play the Iterative Prisoner's Dilemma in the browser], play against strategies or let strategies play against other strategies<br />
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==In fiction==<br />
在小说中<br />
[[Hannu Rajaniemi]] set the opening scene of his ''[[The Quantum Thief]]'' trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in [[mathematical physics]]&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, ''[[The Fractal Prince]]'' and ''[[The Causal Angel]]'', published in 2012 and 2014, respectively.<br />
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Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in mathematical physics&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.<br />
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汉努·拉贾尼埃米 Hannu Rajaniemi将他的《量子窃贼》三部曲的开场场景设置在一个“囚徒困境”中。该系列的主题被描述为“双重宇宙的不足” ,最终的对手是一个叫做全面背叛者的角色。作为一个处理这个问题的艺术家,拉贾尼埃米尤其有趣,因为他是剑桥大学培养的数学家,拥有数学物理学博士学位——物质和信息的可互换性是这本书的一个主要特征,它发生在<font color="#ff8000">后奇点post-singularity</font>的未来。该系列的第一本书于2010年出版,其续集《分形王子》和《因果天使》分别于2012年和2014年出版。<br />
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A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game ''[[Zero Escape: Virtue's Last Reward]]'' and a minor part in its 2016 sequel ''[[Zero Escape: Zero Time Dilemma]]''.<br />
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A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.<br />
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一个(重复)囚徒困境博弈的模型是2012年电子游戏《零度逃脱: 美德的最后奖励》的重点,也是2016年续集《零度逃脱: 极限脱出刻之困境》的一个次要部分。<br />
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In ''The Mysterious Benedict Society and the Prisoner's Dilemma'' by [[Trenton Lee Stewart]], the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
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In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
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在特伦顿·李·斯图尔特 Trenton Lee Stewart的《神秘的本尼迪克特社会和囚徒困境》中,主要角色从玩一个版本的游戏开始,然后一起逃离“监狱”。后来他们变成了真正的囚犯,再次越狱。<br />
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In ''[[The Adventure Zone]]: Balance'' during ''The Suffering Game'' subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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在冒险区: 苦难游戏的平衡中,玩家角色在他们在两个领域的时间内两次呈现出囚徒困境,一次是合作,一次是背叛。<br />
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In the 8th novel from the author James S. A. Corey [[Tiamat's Wrath]] . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. {{cn|date=April 2020}}<br />
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In the 8th novel from the author James S. A. Corey Tiamat's Wrath . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. <br />
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在作者詹姆斯·S·A·科里·提亚玛特 James S. A. Corey Tiamat的《愤怒》中的第八部小说中,温斯顿•杜阿尔特 Winston Duarte向他14岁的女儿特蕾莎 Teresa解释了她面临的囚徒困境,来训练她的战略思维能力。<br />
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==See also==<br />
请参阅<br />
{{div col|colwidth=18em}}<br />
<br />
* [[Abilene paradox]]<br />
<font color="#ff8000"> 阿背伦悖论</font><br />
* [[Centipede game]]<br />
<font color="#ff8000"> 蜈蚣博弈</font><br />
* [[Christmas truce]]<br />
<font color="#ff8000"> 圣诞休战</font><br />
* [[Folk theorem (game theory)]]<br />
<font color="#ff8000"> 无名氏定理(博弈论)/font><br />
* [[Free-rider problem]]<br />
<font color="#ff8000"> 搭便车问题</font><br />
* [[Hobbesian trap]]<br />
]<font color="#ff8000"> 霍布斯主义陷阱</font><br />
* [[Innocent prisoner's dilemma]]<br />
<font color="#ff8000"> 无辜囚徒困局</font><br />
* [[Liar Game]]<br />
<font color="#ff8000">说谎者博弈</font><br />
* [[Optional prisoner's dilemma]]<br />
<font color="#ff8000"> 可选择囚徒困境</font><br />
* [[Robert H. Frank#Prisoner's dilemma and cooperation|Prisoner's dilemma and cooperation]]<br />
罗伯特·H·弗兰克囚徒的困境和合作|<font color="#ff8000"> 囚徒困境</font>和合作<br />
* [[Public goods game]]<br />
<font color="#ff8000"> 公共商品博弈</font><br />
* [[Gift-exchange game]]<br />
<font color="#ff8000"> 互利博弈</font><br />
* [[Reciprocal altruism]]<br />
<font color="#ff8000"> 相互利他行为</font><br />
* [[Social preferences]]<br />
<font color="#ff8000"> 社会偏好</font><br />
* [[Swift trust theory]]<br />
<font color="#ff8000"> 快速信任理论</font><br />
* [[Unscrupulous diner's dilemma]]<br />
]<font color="#ff8000"> 无道德食客困境</font><br />
{{div col end}}<br />
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==References==<br />
==参考==<br />
{{notelist}}<br />
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==Further reading==<br />
==拓展阅读==<br />
{{refbegin|30em}}<br />
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* [[S.M. Amadae|Amadae, S.]] (2016). 'Prisoner's Dilemma,' ''Prisoners of Reason.'' [[Cambridge University Press]], NY, pp.&nbsp;24–61.<br />
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* {{cite book |first1=Robert |last1=Aumann |authorlink=Robert Aumann |chapter=Acceptable points in general cooperative ''n''-person games |editor1-first=R. D. |editor1-last=Luce |editor2-first=A. W. |editor2-last=Tucker |title=Contributions to the Theory 23 of Games IV |series=Annals of Mathematics Study |volume=40 |pages=287–324 |publisher=Princeton University Press |location=Princeton NJ |year=1959 |mr=0104521}}<br />
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* [[Robert Axelrod|Axelrod, R.]] (1984). ''[[The Evolution of Cooperation]]''. {{isbn|0-465-02121-2}}<br />
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* [[Cristina Bicchieri|Bicchieri, Cristina]] (1993). Rationality and Coordination. [[Cambridge University Press]].<br />
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* {{cite journal |first1=David M. |last1=Chess |date=December 1988 |title=Simulating the evolution of behavior: the iterated prisoners' dilemma problem |url=http://www.complex-systems.com/pdf/02-6-4.pdf |journal=Complex Systems |volume=2 |issue=6 |pages=663–70}}<br />
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* [[Melvin Dresher|Dresher, M.]] (1961). ''The Mathematics of Games of Strategy: Theory and Applications'' [[Prentice-Hall]], Englewood Cliffs, NJ.<br />
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* Greif, A. (2006). ''Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.'' Cambridge University Press, [[Cambridge]], UK.<br />
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* [[Anatol Rapoport|Rapoport, Anatol]] and Albert M. Chammah (1965). ''Prisoner's Dilemma''. [[University of Michigan Press]].<br />
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{{refend}}<br />
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==External links==<br />
外部链接<br />
*{{Commonscat-inline}}<br />
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* [http://plato.stanford.edu/entries/prisoner-dilemma/ Prisoner's Dilemma (''Stanford Encyclopedia of Philosophy'')]<br />
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* [http://www.msri.org/ext/larryg/pages/15.htm The Bowerbird's Dilemma] The Prisoner's Dilemma in ornithology&nbsp;– mathematical cartoon by Larry Gonick.<br />
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* [https://www.youtube.com/watch?v=_1SEXTVsxjk The Prisoner's Dilemma] The Prisoner's Dilemma with Lego minifigures.<br />
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* {{cite encyclopedia |last1=Dixit |first1=Avinash |authorlink1=Avinash Dixit |last2= Nalebuff |first2=Barry |authorlink2=Barry Nalebuff |editor=[[David R. Henderson]]|encyclopedia=[[Concise Encyclopedia of Economics]] |title=Prisoner's Dilemma |url=http://www.econlib.org/library/Enc/PrisonersDilemma.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}<br />
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* [http://gametheory101.com/The_Prisoner_s_Dilemma.html Game Theory 101: Prisoner's Dilemma]<br />
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* [https://www.youtube.com/watch?v=I71mjZefg8g Dawkins: Nice Guys Finish First]<br />
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* [https://axelrod.readthedocs.io/en/stable/ Axelrod] Iterated Prisoner's Dilemma [[Python (programming language)|Python]] library<br />
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* [http://gametheorygames.nl/index.html Play the Iterated Prisoner's Dilemma on gametheorygames.nl]<br />
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* [https://web.archive.org/web/20141011014608/http://demo.otree.org/demo/Prisoner%27s+Dilemma/ Play Prisoner's Dilemma on ''oTree''] (N/A 11-5-17)<br />
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* Nicky Case's [https://web.archive.org/web/20181229222135/https://ncase.me/trust/ Evolution of Trust], an example of the donation game<br />
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* [http://iterated-prisoners-dilemma.info Iterated Prisoner's Dilemma online game] by Wayne Davis<br />
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{{Decision theory paradoxes}}<br />
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{{Game theory}}<br />
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{{Authority control}}<br />
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[[Category:Non-cooperative games]]<br />
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Category:Non-cooperative games<br />
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类别: 非合作性游戏<br />
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[[Category:Thought experiments]]<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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[[Category:Dilemmas]]<br />
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Category:Dilemmas<br />
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类别: 困境<br />
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[[Category:Environmental studies]]<br />
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Category:Environmental studies<br />
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类别: 环境研究<br />
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[[Category:Social psychology]]<br />
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Category:Social psychology<br />
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类别: 社会心理学<br />
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[[Category:Moral psychology]]<br />
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Category:Moral psychology<br />
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范畴: 道德心理学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Prisoner's dilemma]]. Its edit history can be viewed at [[囚徒困境/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%9B%9A%E5%BE%92%E5%9B%B0%E5%A2%83&diff=21301囚徒困境2021-01-25T11:42:17Z<p>Vicky:</p>
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<div>此词条由Henry初步翻译。已由Smile审校。<br />
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{{other uses}}<br />
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{{short description|Canonical example of a game analyzed in game theory}}<br />
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{| class="wikitable floatright"<br />
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The '''prisoner's dilemma''' is a standard example of a game analyzed in [[game theory]] that shows why two completely [[Rationality#Economics|rational]] individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by [[Merrill Flood]] and [[Melvin Dresher]] while working at [[RAND Corporation|RAND]] in 1950. [[Albert W. Tucker]] formalized the game with prison sentence rewards and named it "prisoner's dilemma",<ref>Poundstone, 1992</ref> presenting it as follows:<br />
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The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", prensenting it as follows:<br />
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<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>是<font color="#ff8000"> 博弈论game theory</font>分析博弈的一个代表性例子,它揭示了为什么两个完全理性的个体可能不会合作,即使这样做符合他们的最大利益。它最初是由梅里尔·弗勒德 Merrill Flood和 梅文·加舍尔 Melvin Dresher于1950年在兰德公司工作时构建的。阿尔伯特.W.塔克 Albert W. Tucker将这种博弈以监禁刑罚奖励的方式正式化,并将其命名为囚徒困境,具体阐述如下:<br />
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{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
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{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
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* If A and B each betray the other, each of them serves two years in prison<br />
* If A betrays B but B remains silent, A will be set free and B will serve three years in prison<br />
* If A remains silent but B betrays A, A will serve three years in prison and B will be set free<br />
* If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).}}<br />
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{{一个犯罪团伙的两名成员被捕入狱。每个囚犯都被单独监禁,与他人无法沟通。检察官缺乏足够的证据来对这两个人定罪,但有足够的证据以较低的罪名定罪。同时,检察官向每个犯人提供了一个交易。每个囚犯都有机会出卖对方,证明对方犯下的罪行,或者他们可以合作,保持沉默。可能的结果有:<br />
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*如果A和B都背叛了对方,他们都会在监狱服刑两年。<br />
*如果A背叛了B但B保持沉默,A会被无罪释放而B会服刑三年。<br />
*如果A保持沉默但B背叛了A,A会服刑三年而B会无罪释放。<br />
*如果A和B都保持沉默,他们就只用服刑一年(以较低的罪名)。}}<br />
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It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref> In reality, humans display a [[systemic bias]] towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action.<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref> This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref> The prisoner's dilemma became the focus of extensive experimental research.<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
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It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other. In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action. This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome. The prisoner's dilemma became the focus of extensive experimental research. <br />
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这意味着,囚犯除了监禁刑罚之外,没有机会奖励或惩罚他们的同伴,他们的决定也不会影响他们未来的声誉。因为背叛一个同伴比与他们合作能得到更大的回报,所以所有纯粹理性的、自私自利的囚犯都会背叛对方,这意味着,对于两个纯粹理性的囚犯来说,唯一可能的结果就是他们相互背叛。<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref>实际上,尽管“理性的”自利行为的简单模型已经预测到了这一点,但人类在这种和类似的博弈中仍然表现出对合作行为的<font color="#ff8000">系统性偏差 systemic bias </font>。<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref>自从在兰德公司首次进行这项测试以来,人们就已经知道了这种对合作的偏见; 参与测试的秘书们相互信任,为了最好的共同的目标而努力。<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref>囚徒困境成为大量实验研究的焦点。<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
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<br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by [[backward induction]]) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<br />
<br />
一个扩展的<font color="#ff8000">重复iterated</font>版本的博弈由此衍生出来。在这个版本中,经典博弈会在在同一组囚犯之间重复进行,他们不断有机会为了之前的决定对其他囚犯进行惩罚。如果参与者知道博弈的次数,那么(通过<font color="#ff8000">逆向归纳法 backward induction </font>)两个经典的理性的玩家就会因为和在单次博弈中相同的原因反复背叛对方。在无限次或未知次数的博弈中,没有固定的最优策略,因而,举办囚徒困境竞赛来竞争和检验这种情况下的算法。<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
<br />
<br />
The prisoner's dilemma game can be used as a model for many [[#Real-life examples|real world situations]] involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activitie <br />
<br />
囚徒困境博弈可以作为许多现实中涉及合作行为的模型。在非正式用法中,“囚徒困境”一词可适用于不严格符合经典或重复博弈的形式标准的情况: 例如,两个实体可以从合作中获得巨大利益或者会因为合作失败而遭受损失,但发现协调他们的活动很困难或者代价昂贵(并非是不可能的)。<br />
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<br />
<br />
==Strategy for the prisoner's dilemma==<br />
囚徒困境的策略<br />
<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
两名囚犯被分开关押在各自的房间里,不能相互交流。<br />
<br />
The normal game is shown below:<br />
<br />
The normal game is shown below:<br />
<br />
正常的博弈如下:<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class“ wikitable”<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! {{diagonal split header|<br />Prisoner A|Prisoner B}} !! Prisoner B stays silent<br>(''cooperates'') !! Prisoner B betrays<br>(''defects'')<br />
<br />
! !! Prisoner B stays silent<br>(cooperates) !! Prisoner B betrays<br>(defects)<br />
<br />
! {{diagonal split header|<br />犯人A|犯人B}}!!犯人B保持沉默<br>(''合作'') !! 犯人B背叛<br>(''背叛'')<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A stays silent<br>(''cooperates'')<br />
<br />
! Prisoner A stays silent<br>(cooperates)<br />
<br />
!犯人 a 保持沉默<br>(''合作'')<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
|每人服刑1年||囚犯 A: 3年<br />囚犯 B: 无罪释放<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A betrays<br>(''defects'')<br />
<br />
! Prisoner A betrays<br>(defects)<br />
<br />
!犯人A背叛<br>(''背叛'')<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
|囚犯 A: 获释<br />囚犯 B: 3年||每人服刑2年<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by [[Dilemma#Use in logic|dilemma]]: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by dilemma: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
假设两个囚犯都了解博弈的本质,对彼此不忠诚,且在博弈之外没有机会得到报复或奖励。那么不管对方怎么决定,每个犯人背叛对方都会得到更高的奖励(“叛变”)。推理涉及一个进退两难的论点:B 要么合作,要么叛变。如果B合作,A 应该叛变,因为得到释放总比服刑1年好。如果 B叛变,A也应该叛变,因为服刑2年总比服刑3年好。所以不管怎样,A都应该叛变。并行推理表明B应该选择叛变。<br />
<br />
<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a [[dominant strategy]]. Mutual defection is the only strong [[Nash equilibrium]] in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a dominant strategy. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
因为不管对方的选择如何,背叛总是比合作带来更好的回报,所以这是一个<font color="#ff8000">占优策略 dominant strategy</font>。相互背叛是博弈中唯一的强<font color="#ff8000">纳什均衡点 dominant strategy </font>(即每个参与者单方面的改变策略只能使自己的情况变糟)。因此,困境在于,虽然相互合作比相互背叛产生更好的结果,但它却不是理性的结果,因为从自我利益的角度来看,合作的选择是非理性的。<br />
<br />
<br />
<br />
==Generalized form==<br />
<font color="#ff8000">广泛形态 Generalized form </font><br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
传统囚徒困境的结构可以从其最初的囚徒环境中概括出来。假设两个玩家用红色和蓝色表示,并且每个玩家选择“合作”或“背叛”。<br />
<br />
<br />
<br />
If both players cooperate, they both receive the reward ''R'' for cooperating. If both players defect, they both receive the punishment payoff ''P''. If Blue defects while Red cooperates, then Blue receives the temptation payoff ''T'', while Red receives the "sucker's" payoff, ''S''. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff ''S'', while Red receives the temptation payoff ''T''.<br />
<br />
If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the tem punishment payoffptation payoff T.<br />
<br />
如果两个玩家合作,他们都会因为合作而获得奖励''R''。如果两个参与人都叛变,他们都会受到惩罚''P''。 如果蓝方叛变而红方合作,那么蓝方得到诱惑回报''T'',而红方受到“上当受骗者”损失''S''。同样地,如果蓝方合作而红方叛变,那么蓝方得到上当受骗者的损失''S'',而红方得到诱惑支付''T''。<br />
<br />
<br />
<br />
This can be expressed in [[Normal-form game|normal form]]:<br />
<br />
This can be expressed in normal form:<br />
<br />
这可以用标准形式的博弈来表示:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
| + <font color="#ff8000">正则 PD 支付矩阵 Canonical PD payoff matrix </font> <br />
<br />
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
! {{diagonal split header|{{color|#009|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
要成为强意义下的囚徒困境博弈,收益必须满足以下条件:<br />
<br />
<br />
<br />
:{{tmath|T > R > P > S}}<br />
<br />
<br />
<br />
The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents.<br />
<br />
The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents.<br />
<br />
回报关系{{tmath|R > P}}意味着相互合作优于相互背叛,然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。<br />
<br />
<br />
<br />
===Special case: donation game===<br />
特例:<font color="#ff8000">捐赠博弈 donation game </font><br />
<br />
The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus<br />
<br />
The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus<br />
<br />
捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式,在这种博弈中,合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b'',而叛变意味着什么也不提供。收益矩阵如下:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
! {{diagonal split header|{{navy (color)|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section).<br />
<br />
Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section).<br />
<br />
请注意{{tmath|2R>T+S}}(即{{tmath|2(b-c)>b-c}})这使得捐赠博弈成为一个重复博弈(见下一节)。<br />
<br />
<br />
The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything.<br />
<br />
The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.<br />
<br />
捐赠博弈可能适用于市场。假设种植者X 种橘子,种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b'',“b”比橙子的边际效用''c''高,因为X有橙子剩余而没有苹果。同样地,对于苹果种植者Y来说,橙子的边际效用是''b'',而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子,并且每个人都完成了交易,那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货,那么这个违约者将得到''b''的收益,而合作者将失去''c''的收益。 如果两者都违约,那么谁也不会得到或失去任何东西。<br />
<br />
==The iterated prisoner's dilemma==<br />
<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma </font> {{more citations needed section|date=November 2012}}<br />
<br />
If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
<br />
If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
<br />
如果两个参与者连续进行多次囚徒困境博弈,他们记住对手先前的行动并相应地改变策略,这种博弈被称为重复囚徒困境。<br />
<br />
<br />
<br />
In addition to the general form above, the iterative version also requires that {{tmath|2R > T + S}}, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
<br />
In addition to the general form above, the iterative version also requires that , to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
<br />
除了上面的一般形式之外,重复版本还要求{{tmath|2R > T + S}},防止交替合作和背叛比相互合作有更大的回报。<br />
<br />
<br />
<br />
The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "[[Peace war game|peace-war game]]".<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
<br />
The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "peace-war game".<br />
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重复囚徒困境博弈是人类合作与信任的理论基础。假设博弈可以为两个需要信任的人之间的交易建模,那么群体中的合作行为也可以由多个参与者重复的博弈模型来建模。因此,这些年来,它吸引了许多学者。1975年,葛夫曼 Grofman和普尔 Pool估计专门撰写有关该领域的学术文章超过2000篇。重复囚徒困境也被称为“和平-战争博弈”。<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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If the game is played exactly ''N'' times and both players know this, then it is optimal to defect in all rounds. The only possible [[Nash equilibrium]] is to always defect. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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If the game is played exactly N times and both players know this, then it is optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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如果这个游戏正好玩了N次,并且两个玩家都知道这一点,那么在所有回合中最佳的策略就是叛变。唯一可能的纳什均衡点就是永远叛变。证明是通过归纳法证出来的: 不妨假设一个人在最后一回合叛变,因为对手之后没有机会反击。因此,双方都会在最后一个回合叛变。所以玩家同样也会在倒数第二回合时叛变,因为无论采取什么策略,对手都会在倒数第一回合叛变,依此类推。如果博弈次数未知但次数有限的情况也同样如此。<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The [[superrational]] strategy in the iterated prisoner's dilemma with fixed ''N'' is to cooperate against a superrational opponent, and in the limit of large ''N'', experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoner's dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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与标准的囚徒困境不同,在重复囚徒困境中,叛变策略是严重违反直觉的,以至于不能很好地预测人类玩家的行为。然而,在标准的经济理论中,这是唯一正确的答案。具有固定次数 N的重复囚徒困境中的<font color="#ff8000">超理性 superrational</font>策略是与超理性对手进行合作,在N很大的限制下,实验结果的策略与超理性结果的策略一致,而不是博弈论的理性结果。<br />
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For [[cooperation]] to emerge between game theoretic rational players, the total number of rounds ''N'' must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by [[Robert Aumann]] in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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For cooperation to emerge between game theoretic rational players, the total number of rounds N must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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为了使合作在博弈论的理性参与者之间出现,参与者必须不知道回合总数N。在这种情况下,“总是叛变”可能不再是一个严格占优策略,而只是一个纳什均衡。罗伯特·奥曼 Robert Aumann在1959年的一篇论文中表明,理性参与者在无限多次的博弈中通过反复互动可以维持合作的结果。<br />
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According to a 2019 experimental study in the ''American Economic Review'' which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, [[Tit for tat|tit-for-tat]], and [[Grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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According to a 2019 experimental study in the American Economic Review which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, tit-for-tat, and Grim trigger. Which strategy the subjects chose depended on the parameters of the game.<br />
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根据《美国经济评论》于2019年进行的一项实验研究,该实验中通过完美的监控测试了现实中被用在重复囚徒困境情况下的策略,监测选择的策略总是背叛,针锋相对的和 <font color="#ff8000"> 冷酷触发策略 Grim trigger</font>。受试者选择的策略取决于博弈的参数。<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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===Strategy for the iterated prisoner's dilemma===<br />
重复囚徒困境下的策略<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by [[Robert Axelrod]] in his book ''[[The Evolution of Cooperation]]'' (1984). In it he reports on a tournament he organized of the ''N'' step prisoner's dilemma (with ''N'' fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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Interest in the iterated prisoner's dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In it he reports on a tournament he organized of the N step prisoner's dilemma (with N fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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罗伯特·阿克塞尔罗德 Robert Axelrod在他的著作《合作的进化》(1984)中激起了人们对重复囚徒困境(IPD)的兴趣。在这篇文章中,他报道了自己组织的固定N次囚徒困境的比赛,参与者必须一次又一次地选择他们的共同策略,并且要记住他们之前的遭遇。阿克塞尔罗德邀请世界各地的学术界同仁设计计算机策略来参加IPD锦标赛。输入的程序在算法复杂性、最初敌意、宽恕能力等方面有很大差异。<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more [[altruism|altruistic]] strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by [[natural selection]].<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.<br />
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阿克塞尔罗德发现,当这些遭遇长时间在许多玩家身上重复发生时,每个玩家都有不同的策略,从长远来看,贪婪策略往往表现得非常糟糕,而更加利他的策略表现得更好,这完全是根据自身利益来判断的。他利用这一结果揭示了通过自然选择,从最初纯粹自私行为向利他行为进化的可能机制。<br />
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The winning [[deterministic algorithm|deterministic]] strategy was tit for tat, which [[Anatol Rapoport]] developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of [[BASIC]], and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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The winning deterministic strategy was tit for tat, which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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最终获胜的决定性策略是针锋相对策略,这是阿纳托尔·拉波波特 Anatol Rapoport开发并参加比赛的策略。这是所有参赛程序中最简单的一个,只有四行 BASIC 语言,并且赢得了比赛。策略很简单,就是在游戏的第一次重复中进行合作; 在此之后,玩家将执行做他的对手在前一步中所做的事情。根据具体情况,一个稍微好一点的策略可以是“带着宽恕之心针锋相对”。当对手叛变时,在下一次博弈中,玩家有时还是会合作,但概率很小(大约1-5%)。这允许博弈偶尔能从陷入叛变循环中恢复过来。确切的概率取决于对手的安排。<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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通过分析得分最高的战略,阿克塞尔罗德阐述了战略成功的几个必要条件。<br />
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; Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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;友好:最重要的条件是策略必须是好的,也就是说,它不会在对手之前叛变(这有时被称为“乐观”算法)。几乎所有得分最高的策略都是友好的; 因此,一个纯粹的自私策略不会为了纯粹自身的利益而“欺骗”对手。<br />
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; Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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;报复:然而,阿克塞尔罗德认为,成功的战略决不能是盲目的乐观主义。它有时必须进行报复。非报复策略的一个例子就是永远合作。这是一个非常糟糕的选择,因为“肮脏”的策略会无情地利用这些玩家。<br />
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; Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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;宽容: 成功的策略也必须是宽容的。虽然玩家会报复,但如果对手不继续叛变,他们将再次回到合作的状态。这阻止了长时间的报复和反报复,最大限度地提高积分。<br />
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; Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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;不嫉妒: 最后一个品质是不嫉妒,不强求比对手得分更多。<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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对于一次性的囚徒困境博弈,最优(点数最大化)策略就是简单的叛变; 正如上面所说,无论对手的构成如何,这都是正确的。然而,在重复囚徒困境博弈中,最优策略取决于可能的对手的策略,以及他们对叛变和合作的反应。例如,考虑一个群体,其中每个人每次都会叛变,只有一个人遵循针锋相对的策略。那个人就会由于第一回合的失利而处于轻微的不利地位。在这样一个群体中,个体的最佳策略是每次都叛变。在一定比例的总是选择背叛的玩家和其余组成选择针锋相对策略的玩家的人群中,个人的最佳策略取决于这一比例和博弈的次数。<br />
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In the strategy called Pavlov, [[win-stay, lose-switch]], faced with a failure to cooperate, the player switches strategy the next turn.<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref> In certain circumstances,{{specify|date=November 2012}} Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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In the strategy called Pavlov, win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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在所谓的<font color="#ff8000">巴甫洛夫策略 Pavlov strategy</font>中,赢-保持,输-变换,面对一次合作失败,玩家将在下一次变换策略。<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref>在某些情况下,{{specify|date=November 2012}}巴甫洛夫通过使用类似策略给与合作者优惠待遇打败了其他所有策略。<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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得出最佳策略通常有两种方法:<br />
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* [[Bayesian Nash equilibrium]]: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit for tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.{{efn|1=For example see the 2003 study<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref> for discussion of the concept and whether it can apply in real [[economic]] or strategic situations.}}<br />
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<font color="#ff8000">贝叶斯纳什均衡 Bayesian Nash equilibrium</font>:如果可以确定对立策略的统计分布(例如,50%针锋相对,50%总是合作),那么,可以通过分析得出最佳的反策略{{efn|1=例如2003年的研究<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref>讨论这一概念以及它是否可以应用于实际经济或战略情况。}}<br />
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* [[Monte Carlo method|Monte Carlo]] simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a [[genetic algorithm]] for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit for tat players (see for instance Chess 1988),{{Clarify|date=August 2016}} but no analytic proof exists that this will always occur.<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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<font color="#ff8000">蒙特卡洛方法 Monte Carlo method </font>已经对种群进行了模拟,分数低的个体死亡,分数高的个体繁殖(<font color="#ff8000">遗传算法 genetic algorithm </font>用于寻找一个最佳策略)。最终群体中的算法组合通常取决于初始总体的组合。引入突变(繁殖过程中的随机变异)可以减少对初始种群的依赖性。使用这种系统进行经验性实验往往会为针锋相对的玩家带来麻烦(见Chess 1988),{{Clarify|date=August 2016}},但是没有分析证据表明这种情况会一直发生。<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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Although tit for tat is considered to be the most [[robust]] basic strategy, a team from [[Southampton University]] in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start.<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref> Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show [[University of Southampton]]'s strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between [[computer program|software strategies]] (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian [[Evolutionarily stable strategy|ESS]] simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. [[Richard Dawkins]] showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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Although tit for tat is considered to be the most robust basic strategy, a team from Southampton University in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between software strategies (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian ESS simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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尽管针锋相对被认为是最有力的基本策略,来自英格兰南安普敦大学的一个团队在20周年的重复囚徒困境竞赛中提出了一个新策略,这个策略被证明比针锋相对更为成功。这种策略依赖于程序之间的串通,以获得单个程序的最高分数。这所大学提交了60个程序,这些程序的设计目的是在比赛开始时通过一系列的5到10个动作来互相认识。<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref>一旦认识建立,一个程序总是合作,另一个程序总是叛变,保证叛变者得到最多的分数。如果这个程序意识到它正在和一个非南安普顿的球员比赛,它会不断地叛变,试图最小化与之竞争的程序的得分。因此,2004年囚徒困境锦标赛的结果显示了南安普敦大学战略位居前三名,尽管它比冷酷战略赢得更少,输的更多。(在囚徒困境锦标赛中,比赛的目的不是“赢”比赛——这一点频繁叛变很容易实现)。此外,即使没有软件策略之间的暗中串通(南安普顿队利用了这一点) ,针锋相对并不总是任何特定锦标赛的绝对赢家; 更准确地说,它是在一系列锦标赛中的长期结果超过了它的竞争对手。(在任何一个事件中,一个给定的策略可以比针锋相对稍微更好地适应竞争,但是针锋相对更稳健)。这同样适用于带有宽恕变量的针锋相对,和其他最佳策略: 在任何特定的一天,他们可能不会“赢得”一个特定的混合反战略。另一种方法是使用达尔文 Darwinian的<font color="#ff8000"> ESS模拟 ESS simulation</font>。在这样的模拟中,针锋相对几乎总是占主导地位,尽管讨厌的策略会在人群中漂移,因为使用针锋相对策略的人群可以通过非报复性的好策略进行渗透,这反过来使他们容易成为讨厌策略的猎物。理查德·道金斯 Richard Dawkins指出,在这里,没有静态的混合策略会形成一个稳定的平衡,系统将始终在边界之间振荡。这种策略最终在比赛中获得了前三名的成绩,或者是接近垫底的成绩。<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of [[minmaxing]]). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book ''[[The Selfish Gene]]'', pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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这种策略利用了这样一个事实,即在这场特殊的比赛中允许多个参赛项目,并且团队的表现由得分最高的项目来衡量(这意味着使用自我牺牲的项目是一种分数最大化的形式)。在一个只能控制一个玩家的比赛中,针锋相对当然是一个更好的策略。由于这一新规则的存在,与阿克塞尔罗德的具有深远影响的竞赛相比,这种竞赛在分析单个主体策略时也就没有什么理论意义。然而,它为在分析多主体框架下,特别是在存在干扰的情况下,如何实现协作策略提供了基础。事实上,早在这场新规则锦标赛开始之前,道金斯就在他的《自私的基因》一书中指出,如果允许多次参赛,这种策略就有可能获胜,但他说,如果提交这种策略的话,阿克塞尔罗德很可能不会允许。因为它依赖于规避囚徒困境的规则,即两个参与者之间不允许交流,南安普顿的项目可以说在开场的“十步舞”中就是这样做以认识对方的; 这只是强调了交流在改变游戏平衡方面的价值。<br />
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===Stochastic iterated prisoner's dilemma===<br />
随机的重复囚徒困境<br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities".<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref> In an encounter between player ''X'' and player ''Y'', ''X'' 's strategy is specified by a set of probabilities ''P'' of cooperating with ''Y''. ''P'' is a function of the outcomes of their previous encounters or some subset thereof. If ''P'' is a function of only their most recent ''n'' encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that ''X'' will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which ''X'' cooperated and ''Y'' defected, then <math>P_{cd}</math> is the probability that ''X'' will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as ''P''={1,0,1,0}, in which ''X'' responds as ''Y'' did in the previous encounter. Another is the [[win–stay, lose–switch]] strategy written as ''P''={1,0,0,1}, in which ''X'' responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<ref name="Press2012"/><br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player X and player Y, X 's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which X cooperated and Y defected, then <math>P_{cd}</math> is the probability that X will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as P={1,0,1,0}, in which X responds as Y did in the previous encounter. Another is the win–stay, lose–switch strategy written as P={1,0,0,1}, in which X responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<br />
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在随机重复<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>博弈中,策略由“合作概率”来确定。<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref>在玩家''X''和玩家''Y''之间的遭遇中,''X''‘s的策略由一组与''Y''合作的概率''P''确定,''P''是他们之前遭遇的结果的函数,或者是其中的一些子集。如果''P''只是它们最近遇到次数 ''n''的函数,那么它被称为“记忆-n”策略。我们可以由四个联合概率指定一个记忆-1策略: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>,其中<math>P_{ab}</math>是在当前遭遇中基于先前联合的概率。如果每个概率都是1或0,这种策略称为确定性策略。确定性策略的一个例子是针锋相对策略,写成 p {1,0,1,0} ,其中 x 的反应和 y 在前一次遭遇中的反应一样。另一种是胜-保持-败-转换策略,它被写成 p {1,0,0,1} ,在这种策略中,如果 x 获得胜利(即:cc 或 dc),x会做出与上一次遭遇一样的反应 ,但如果失败,x会改变策略(即cd 或 dd)。研究表明,对于任何一种记忆-n 策略,存在一个相应的记忆-1策略,这个策略给出相同的统计结果,因此只需要考虑记忆-1策略。<ref name="Press2012"/><br />
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If we define ''P'' as the above 4-element strategy vector of ''X'' and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of ''Y'', a transition matrix ''M'' may be defined for ''X'' whose ''ij'' th entry is the probability that the outcome of a particular encounter between ''X'' and ''Y'' will be ''j'' given that the previous encounter was ''i'', where ''i'' and ''j'' are one of the four outcome indices: ''cc'', ''cd'', ''dc'', or ''dd''. For example, from ''X'' 's point of view, the probability that the outcome of the present encounter is ''cd'' given that the previous encounter was ''cd'' is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for ''Q'' are from ''Y'' 's point of view: a ''cd'' outcome for ''X'' is a ''dc'' outcome for ''Y''.) Under these definitions, the iterated prisoner's dilemma qualifies as a [[stochastic process]] and ''M'' is a [[stochastic matrix]], allowing all of the theory of stochastic processes to be applied.<ref name="Press2012"/><br />
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If we define P as the above 4-element strategy vector of X and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of Y, a transition matrix M may be defined for X whose ij th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X 's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for Q are from Y 's point of view: a cd outcome for X is a dc outcome for Y.) Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.<br />
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如果我们将''P''定义为''X''的上述4元策略向量,并将<math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math>定义为''Y''的4元策略向量,则对于''X''可以定义一个转移矩阵''M'',其第ij项是''X''和''Y''之间特定相遇的结果为j的概率,给定i,其中i和j是cc、cd、dc或dd 四个结果索引中的一个。例如,从''X''的角度来看,如果给定''cd'',那么这次的结果是''cd''的概率等于<math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>。(''Q''的指标是 从''Y''的角度: ''X''的''cd''结果是''Y''的''dc''结果)在这些定义下,重复的囚徒困境被定义为一个随机过程,''M''是一个随机矩阵,允许应用所有的随机过程理论。<ref name="Press2012"/><br />
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One result of stochastic theory is that there exists a stationary vector ''v'' for the matrix ''M'' such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that ''v'' is normalized so that the sum of its four components is unity. The ''ij'' th entry in <math>M^n</math> will give the probability that the outcome of an encounter between ''X'' and ''Y'' will be ''j'' given that the encounter ''n'' steps previous is ''i''. In the limit as ''n'' approaches infinity, ''M'' will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing ''j'' which will be independent of ''i''. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that ''v'' is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to ''v''. Thus the stationary vector specifies the equilibrium outcome probabilities for ''X''. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From ''X'' 's point of view), the equilibrium payoffs for ''X'' and ''Y'' can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.<br />
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One result of stochastic theory is that there exists a stationary vector v for the matrix M such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij th entry in <math>M^n</math> will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j which will be independent of i. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to v. Thus the stationary vector specifies the equilibrium outcome probabilities for X. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From X 's point of view), the equilibrium payoffs for X and Y can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies P and Q to be compared for their long term payoffs.<br />
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随机理论的一个结果是,矩阵''M''存在一个平稳向量''v''使得<math>v\cdot M=v</math>成立。一般地,我们可以指定''v''是标准化的,因此它的4个组成部分之和为1。the equilibrium payoffs for and can now be specified as and, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.第''ij''项<math>M^n</math>给出了''X''和''Y''相遇的结果的概率为''j'',给定前面相遇''n''步的概率是''i''。当''n''趋于无穷时,''M''收敛于一个具有固定值的矩阵,并且''j''趋向一个长期概率,与''i''独立。换句话说, <math>M^\infty</math>的行将是相同的,从而给出了重复囚徒困境的长期均衡结果概率,而不需要明确地计算大量的相互作用。可以看出,''v''是<math>M^n</math>特别是<math>M^\infty</math>, 的平稳向量,因此<math>M^\infty</math>的每一行都等于''v''。因此平稳向量指定了''X''的均衡结果概率。定义<math>S_x=\{R,S,T,P\}</math>和<math>S_y=\{R,T,S,P\}</math>作为{cc,cd,dc,dd}结果的短期收益向量(从''X''的角度来看) ,现在可以将''X''和''Y''的均衡收益指定为<math>s_x=v\cdot S_x</math>和<math>s_y=v\cdot S_y</math>,使得''P''、''Q''两种策略的长期收益可以比较。<br />
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====Zero-determinant strategies====<br />
<font color="#ff8000">零决定策略 Zero-determinant strategies</font><br />
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[[File:IPD Venn.svg|right|thumb|upright=2.5|The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram]]. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and [[weak selection]]. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and weak selection. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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<font color="#ff8000">维恩图 Venn diagram</font>中讨论了<font color="#ff8000">重复囚徒困境 iterated prisoner's dilemma</font>(IPD)中零决定策略(ZD)、合作策略和背叛策略之间的关系。合作策略总是与其他合作策略相互配合,而背叛策略总是与其他背叛策略相抵触。这两种策略都包都含在强选择下稳健的策略子集,这意味着当它们驻留在一个种群中时,没有选择其他的记忆-1策略来入侵此策略。只有合作策略包含在始终稳健的策略子集,意味着无论选择强项还是弱项,都不会选择其他任何记忆-1策略来入侵和替换此策略。零决定策略和良好的合作策略之间的交集是一组宽松的零决定策略。勒索策略是零决定策略和非稳健背叛策略的交集。针锋相对是合作、背叛和零决定策略的交集。<br />
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In 2012, [[William H. Press]] and [[Freeman Dyson]] published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies.<ref name="Press2012"/> The long term payoffs for encounters between ''X'' and ''Y'' can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector ''v''. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in ''f'', it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where ''U''={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector v. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in f, it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where U={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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2012年,威廉·H·普莱斯 William H. Press和弗里曼·戴森 Freeman Dyson针对随机重复囚徒困境提出了一类新的策略,称为“零决定”策略。<ref name="Press2012"/>''X''和''Y''之间的长期收益可以表示为一个矩阵的决定因素,它是两个策略和短期收益向量的函数: <math>s_x=D(P,Q,S_x)</math>和<math>s_y=D(P,Q,S_y)</math>,不涉及平稳向量''v''。 由于行列式函数<math>s_y=D(P,Q,f)</math>在''f''中是线性的,因此可以推出<math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math>(其中''U''={1,1,1,1})。任何策略的<math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math>被定义为零决定策略,长期收益服从关系式<math>\alpha s_x+\beta s_y+\gamma=0</math>。<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of [[ultimatum game]]. Specifically, ''X'' is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of ''Y'' 's strategy, offering an opportunity for ''X'' to "extort" player ''Y'' (and vice versa). (It turns out that if ''X'' tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.<ref name="Press2012"/>)<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of Y 's strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.)<br />
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针锋相对是一种零决定策略,在不获得超越其他玩家优势的意义下是“公平”的。然而,零决定策略空间还包含这样的策略:在两个玩家的情况下,可以允许一个玩家单方面设置另一个玩家的分数,或者强迫进化的玩家获得比他自己的分数低一些的收益。被勒索的玩家可能会背叛,但会因此获得较低的回报并且受到伤害。因此,勒索的解决方案将重复囚徒困境转化为一种<font color="#ff8000">最后通牒博弈 ultimatum game </font>。具体来说,''X''能够选择一种策略,对于这种策略,<math>D(P,Q,\beta S_y+\gamma U)=0</math>单方面地将<math>s_y</math>设置为一个特定值范围内的特定值,与''Y''的策略无关,为''X''提供了“勒索”玩家''Y''的机会(反之亦然)。(事实证明,如果''X''试图将<math>s_x</math>设置为一个特定的值,那么可能的范围要小得多,只包括完全合作或完全叛变。<ref name="Press2012"/>)<br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not [[evolutionarily stable strategy|evolutionarily stable]]. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<br />
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重复囚徒困境的一个扩展是进化的随机重复囚徒困境,其中允许特定策略的相对丰度改变,更成功的策略相对增加。这个过程可以通过让不太成功的玩家模仿更成功的策略,或者通过从游戏中淘汰不太成功的玩家,同时让更成功的玩家成倍增加。研究表明,不公平的零决定策略不是进化稳定策略。关键的直觉告诉我们,进化稳定策略不仅要能够入侵另一个群体(这是勒索零决定策略可以做到的) ,而且还要在同类型的其他玩家面前表现良好(勒索零决定策略玩家表现不佳,因为他们减少了彼此的盈余)。<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and [[win–stay, lose–switch]] agents.<ref name=Hilbe2013 /><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.<br />
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理论和模拟证实,超过一个临界种群规模,零决定勒索在与更多合作策略的进化竞争中会失败,因此,种群越大,种群的平均收益就越大。此外,在某些情况下,勒索者甚至可能通过帮助打破统一的背叛者与使用“赢-保持-输”策略的转换玩家之间的对峙而促进合作。<ref name=Hilbe2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies ''is'' both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the [[Prisoner's dilemma#Special case: Donation game|donation game]] by Alexander Stewart and Joshua Plotkin in 2013.<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref> Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013)<ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<ref name=Stewart2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013) to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<br />
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虽然勒索零决定策略在人口众多的情况下并不稳定,但另一种宽松的零决定策略既稳定又稳健。事实上,当人口不算太少的时候,这些策略可以取代任何其他零决定策略,甚至在一系列针对重复囚徒困境的广泛通用策略(包括“获胜-保持-输”的转换策略)中表现良好。亚历山大·斯图尔特 Alexander Stewart和约书亚·普洛特金 Joshua Plotkin在2013年的捐赠博弈中证明了这一点。<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref>宽松的策略会与其他合作的玩家合作,面对背叛,慷慨的玩家比他的对手失去更多的效用。宽松策略是零决定策略和所谓的“好”策略的交集,阿金(2013) <ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.将这两种策略定义为玩家对过去的相互合作作出回应,并在至少获得合作预期收益的情况下平均分配预期收益的策略。在好的策略中,当总体不太小时,宽松(零决定)子集表现良好。如果总体很少,背叛策略往往占主导地位。<ref name=Stewart2013 /><br />
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===Continuous iterated prisoner's dilemma===<br />
<font color="#ff8000">连续重复囚徒困境 Continuous iterated prisoner's dilemma </font> <br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref> found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from [[Assortative mating|assorting]] with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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关于重复囚徒困境的研究大多集中在离散情况下,在这种情况下,参与者要么合作,要么背叛,因为这个模型分析起来比较简单。然而,一些研究人员已经研究了连续重复囚徒困境模型,在这个模型中,玩家能够对另一个玩家做出可变的贡献。乐 Le和博伊德 Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref>发现,在这种情况下,合作比离散重复的囚徒困境更难发展。这个结果的基本直觉很简单: 在一个持续的囚徒困境中,如果一个人群开始处于非合作均衡状态,那么与非合作者相比,合作程度稍高的玩家不会从相互配合中获益。相比之下,在离散的囚徒困境中,相对于非合作者,针锋相对的合作者在非合作均衡中相互配合会获得巨大的回报。由于自然界可以提供更多的机会来进行各种各样的合作,而不是严格地将合作或背叛分为两类,因此连续的囚徒困境可以帮助解释为什么现实生活中针锋相对的合作的例子在自然界中极其罕见。(例如,哈默斯坦 Hammerstein <ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)。<br />
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even though tit for tat seems robust in theoretical models.<br />
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even though tit for tat seems robust in theoretical models.<br />
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尽管在理论模型中,针锋相对策略似乎是稳健的。<br />
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===Emergence of stable strategies===<br />
<font color="#ff8000">稳定策略的出现 Emergence of stable strategies </font> <br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref> Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies. Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<br />
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玩家似乎不能协调相互合作,因此常常陷入劣等而稳定的背叛策略。这样,重复回合可以促进稳定策略的发展。<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref>重复回合往往产生新颖的策略,这对复杂的社会互动有影响。其中一个策略就是“赢-保持-输”的转变。这个策略比一个简单的针锋相对策略要好&nbsp;–也就是说,如果你能逃脱作弊的惩罚,就重复这个行为,如果你被抓住了,就改变策略。<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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这种针锋相对策略的唯一问题是它们很容易出现信号错误。当一个人因报复而作弊,而另一个人将其单纯解释为欺骗时,就会出现问题。结果,第二个人现在作弊,然后在接下来的连锁反应中开始了反复交替的作弊模式。<br />
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==Real-life examples==<br />
现实生活的例子<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the [[social science]]s such as [[economics]], [[politics]], and [[sociology]], as well as to the biological sciences such as [[ethology]] and [[evolutionary biology]]. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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囚犯的环境似乎是人为的,但实际上,在人类交往以及自然界的交互中有许多具有相同收益矩阵的例子。因此,囚徒困境是经济学、政治学、社会学等社会科学以及动物行为学、进化生物学等生物学研究的热点问题。许多自然过程都被抽象为生物进行无休止的囚徒困境博弈的模型。囚徒困境这种广泛的适用性让博弈变得非常重要。<br />
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===Environmental studies===<br />
环境研究<br />
In [[environmental studies]], the PD is evident in crises such as global [[climate change|climate-change]]. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb [[Carbon dioxide|{{Co2}}]] emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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In environmental studies, the PD is evident in crises such as global climate-change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide| emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<br />
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在环境研究中,囚徒困境在诸如全球气候变化等危机中显而易见。有人认为,所有国家都将从稳定的气候中受益,但是每一个国家通常都在限制二氧化碳排放方面犹豫不决。人们错误地认为,如果所有国家的行为都改变,任何一个国家保持目前的行为所带来的直接好处都会大于所谓的最终好处,这就解释了2007年气候变化方面的僵局。<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<br />
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气候变化政治与囚徒困境之间的一个重要区别是不确定性; 污染对气候变化的影响程度和速度尚不清楚。因此,政府面临的困境不同于囚徒困境,因为合作的回报是未知的。这种差异表明,各国之间的合作远远少于真正的重复囚徒困境中的合作,因此避免可能发生的气候灾难的可能性远远小于使用真正的重复囚徒困境博弈论情景分析<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of [[Michael Porter]]'s hypothesis, in which government regulation of competing firms is substantial.<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.<br />
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欧桑 Osang和南迪 Nandy (2003)提供了一个理论解释,并根据迈克尔·波特 Michael Porter的假设,即政府对竞争企业的监管是实质性的,证明了监管驱动的双赢局面。<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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===Animals===<br />
动物<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, [[guppy|guppies]] inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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许多动物的合作行为可以理解为囚徒困境的一个例子。通常动物会建立长期的伙伴关系,这种关系可以更具体地模拟为重复囚徒困境。例如,孔雀鱼成群结队地合作监察捕食者,它们被认为是在惩罚不合作的监察者。<br />
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[[Vampire bats]] are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<br />
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吸血蝙蝠是从事相互的食物交换的群居动物。应用囚徒困境收益可以帮助解释这种行为: <ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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* C/C: "Reward: I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much."<br />
* 合作/合作:"回报:我在不幸运的晚上得到了能让我果腹的血,那在幸运的晚上我也应该分出点血,那不会花费多少。"<br />
* D/C: "Temptation: You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night."<br />
* 背叛/合作:"诱惑:你在我的不幸的夜里救了我,但在我的幸运夜我不会给你血,那样我会活的更好。"<br />
* C/D: "Sucker's Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death."<br />
* 合作/叛变:"可怜者的回报:在我的幸运夜我救了你的命,但在我的不幸夜里你没有救我,我有饿死的风险。"<br />
* D/D: "Punishment: I don't have to pay the slight costs of feeding you on my good nights. But I run a real risk of starving on my poor nights."<br />
* 叛变/叛变:"惩罚:我在我的幸运夜里不必付出代价来救你,但我在我的不幸夜里有挨饿的风险。"<br />
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===Psychology===<br />
心理学<br />
In [[addiction]] research / [[behavioral economics]], [[George Ainslie (psychologist)|George Ainslie]] points out<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref> that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, ''defecting'' means ''relapsing'', and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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In addiction research / behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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在成瘾研究/行为经济学中,乔治·安斯利 George Ainslie指出<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref>,可以将成瘾视为成瘾者现在和未来自我之间的跨期囚徒困境问题。在这种情况下,背叛意味着复发,很容易看出,目前和未来都没有背叛是迄今为止最好的结果。如果一个人今天戒了,但在将来又复吸,这是最糟糕的结果&nbsp;–从某种意义上来说,今天戒瘾所包含的纪律和自我牺牲已经被“浪费”了,因为未来的复吸意味着瘾君子又回到了他开始的地方,他将被迫重新开始(这相当令人沮丧,也使得重新开始更加困难)。今天和明天复发是一个稍微“好一点”的结果,因为尽管瘾君子仍然上瘾,但他们没有努力去尝试停止。最后一种情况是,现在与成瘾斗争的任何人都会熟悉现在的成瘾行为,而在明天放弃。这里的问题是(和其他囚徒困境问题一样),背叛“今天”有一个明显的好处,但明天这个人将面临同样的囚徒困境问题,同样明显的好处是背叛,最终导致一连串无休止的背叛。<br />
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[[John Gottman]] in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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John Gottman in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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约翰·高特曼 John Gottman在他的研究《信任的科学》中将良好的关系定义为伙伴知道不进入(背叛,背叛)牢房中或者至少不要陷入这样的动态循环关系中。<br />
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===Economics===<br />
经济学<br />
The prisoner's dilemma has been called the ''[[Escherichia coli|E. coli]]'' of social psychology, and it has been used widely to research various topics such as [[Oligopoly|oligopolistic]] competition and collective action to produce a collective good.<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref> <br />
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The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good. <br />
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囚徒困境被称为社会心理学中的“大肠杆菌”,它被广泛用于研究寡头垄断竞争和集体行动来产生集体利益等问题。<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When [[cigarette advertising]] was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. <ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref> This analysis is likely to be pertinent in many other business situations involving advertising. <ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.<br />
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广告有时被认为是囚徒困境的一个真实例子。当香烟广告在美国是合法的时候,相互竞争的香烟制造商必须决定在广告上花多少钱。公司A的广告效果部分取决于公司B的广告效果。同样,公司B的广告带来的利润也受到公司A的广告影响。如果公司A和公司B都选择在给定的时间段内做广告,那么一家公司的广告就会抵消另一方的广告,倘若收入保持不变,费用就会因广告成本而增加。两家公司都将从广告减少中获益。然而,如果B公司选择不做广告,A公司就可以通过广告获得巨大的利益。尽管如此,一家公司的最佳广告数量仍取决于另一家公司的广告投放量。由于最佳策略取决于其他公司的选择,因此这里没有占主导地位的策略,这使得它与囚徒困境略有不同。但结果是相似的,如果两家公司的广告都少于均衡状态,他们的处境会更好。有时合作行为确实会在商业环境中出现。例如,香烟制造商支持立法禁止香烟广告,因为这将降低成本并增加整个行业的利润。<ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref>这种分析可能适用于许多其他涉及广告的商业情况。<ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref> <br />
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Without enforceable agreements, members of a [[cartel]] are also involved in a (multi-player) prisoner's dilemma.<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. [[Anti-trust]] authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for [[consumer]]s.<br />
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Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.<br />
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没有可强制执行的协议,卡特尔 cartel的成员国也会陷入(多玩家)囚徒困境。<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> “合作”通常意味着将价格保持在预先商定的最低水平。“背叛”意味着低于最低价格水平销售,并立即从其他卡特尔成员那里获得业务(和利润)。反垄断机构希望潜在的卡特尔成员相互背叛,确保消费者获得尽可能低的价格。<br />
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===Sport===<br />
运动<br />
[[Doping in sport]] has been cited as an example of a prisoner's dilemma.<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Doping in sport has been cited as an example of a prisoner's dilemma.<br />
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体育运动中的兴奋剂被认为是囚徒困境的一个例子。<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<ref name="wired" /><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<br />
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两名参赛运动员可以选择使用非法或危险药物来提高成绩。如果两个运动员都没有服用这种药物,那么他们都不会获得优势。如果只有一个人这样做,那么这个运动员就比他们的竞争对手获得了明显的优势,但由于法律或服用药物的医疗风险,这种优势会减少。然而,如果两名运动员都服用了这种药物,那么好处就被抵消了,只剩下风险,这使得他们的处境比没有服用兴奋剂的情况更加糟糕。<ref name="wired" /><br />
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===International politics===<br />
国际政治<br />
In [[international politics|international political theory]], the Prisoner's Dilemma is often used to demonstrate the coherence of [[strategic realism]], which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given [[anarchy (international relations)|international anarchy]]. A classic example is an arms race like the [[Cold War]] and similar conflicts.<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref> During the Cold War the opposing alliances of [[NATO]] and the [[Warsaw Pact]] both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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In international political theory, the Prisoner's Dilemma is often used to demonstrate the coherence of strategic realism, which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given international anarchy. A classic example is an arms race like the Cold War and similar conflicts. During the Cold War the opposing alliances of NATO and the Warsaw Pact both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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在国际政治理论中,囚徒困境经常被用来证明战略现实主义的一致性,这种战略现实主义认为,在国际关系中,由于国际无政府状态,所有国家(无论其国内政策或公开宣称的意识形态如何)都会为了自身的理性利益来行动。一个典型的例子是类似冷战和类似冲突的军备竞赛。<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref>在冷战期间,北约和华约组织的对立联盟都可以选择武装或解除武装。从双方的观点来看,解除武装而对手继续武装可能会导致军事劣势和被歼灭。相反,如果选择武装而对手已经解除了武装,那么就会获得优势。如果双方都选择武装自己,那么任何一方都承担不起攻击对方的代价,但是双方都为发展和维持核武库付出了高昂的代价。如果双方都选择裁军,战争就可以避免,也不会有任何代价。<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a [[War of attrition (game)|war of attrition]] for the next thirty years until the Soviet Union could not withstand the economic cost.<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref> The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a war of attrition for the next thirty years until the Soviet Union could not withstand the economic cost. The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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虽然最好的结果是双方解除武装,但是双方的理性选择是武装起来,事实也的确如此。在接下来的三十年里,双方都在军事研究和武器装备的消耗战上投入了大量的资源,直到苏联无法承受经济损失。<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref>同样的逻辑也适用于任何类似的情况,无论是主权国家之间的经济竞争还是技术竞争。<br />
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===Multiplayer dilemmas===<br />
<font color="#ff8000">多玩家困境 Multiplayer dilemmas</font><br />
Many real-life dilemmas involve multiple players.<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref> Although metaphorical, [[Garrett Hardin|Hardin's]] [[tragedy of the commons]] may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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许多现实生活中的困境牵涉到多个参与者。<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref>尽管具有隐喻性,但哈丁的<font color="#ff8000">公地悲剧 tragedy of the commons</font>可以看作是囚徒困境多个参与者的一个例子: 每个村民做出选择是为了个人利益还是克制。对于一致(甚至频繁)叛变的集体回报是非常低的(代表了对“公共资源”的破坏)。大多数人可能会遇到的公地困境是在一个共用的房子里洗碗。通过不洗碗,个人可以节省时间,但如果每个居民都选择这种行为,那么集体的代价是任何人都没有干净的盘子。<br />
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The commons are not always exploited: [[William Poundstone]], in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to [[Excludability|take a paper without paying]] (''defecting'') but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by [[Elinor Ostrom]], winner of the 2009 [[Nobel Memorial Prize in Economic Sciences]], hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<br />
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公共资源并不总是被利用: 威廉·庞德斯通 William Poundstone在一本关于囚徒困境的书(见下文参考文献)中描述了新西兰的一种情况,信箱没有上锁。人们可以不付钱就拿报纸(背叛) ,但很少有人这样做,他们觉得如果他们不付钱,那么其他人也不会付钱,这会摧毁整个系统。2009年诺贝尔经济学奖获得者埃莉诺·奥斯特罗姆 Elinor Ostrom随后的研究认为公地悲剧过于简单化,其负面结果会受到外部影响。在没有复杂压力的情况下,团体之间为了共同利益进行沟通和管理,执行社会规范以保护资源并为团体实现最大利益,这是实现囚徒困境最佳结果的一个例子。<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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==Related games==<br />
相关博弈<br />
===Closed-bag exchange===<br />
<font color="#ff8000">封闭袋子交换 Closed-bag exchange </font><br />
[[File:Prisoner's Dilemma briefcase exchange (colorized).svg|thumb|The prisoner's dilemma as a briefcase exchange]]<br />
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The prisoner's dilemma as a briefcase exchange<br />
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囚徒困境是一个公文包式的交换<br />
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[[Douglas Hofstadter]]<ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref> once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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Douglas Hofstadter once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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侯世达 Douglas Hofstadter <ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref>曾经指出,人们通常会发现诸如囚徒困境的问题,比如,当它以一个简单囚徒困境博弈的形式,或者以权衡的方式表现出来时,会更容易理解。他使用的几个例子之一是“封闭袋子交换” :<br />
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{{quote|Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.}}<br />
两人相遇并交换包裹,事先知道一个包里装着钱,一个装着订单。任一玩家都可选择尊重交易,放入事先约定的东西;也可以选择背叛,交换空的公文包。<br />
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Defection always gives a game-theoretically preferable outcome.<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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Defection always gives a game-theoretically preferable outcome.<br />
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背叛总是会带来一个理论上更可取的结果。<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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===''Friend or Foe?''===<br />
朋友还是敌人?<br />
''[[Friend or Foe? (TV series)|Friend or Foe?]]'' is a game show that aired from 2002 to 2005 on the [[Game Show Network]] in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, ''Friend or Foe'' has a rewards model between prisoner's dilemma and the [[Chicken (game)|game of Chicken]].<br />
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Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.<br />
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朋友还是敌人?是一个竞赛节目,从2002年至2005年在美国的Game show Network播出。这是囚徒困境博弈在真人身上测试的一个例子,只是在人为的环境中。在游戏节目中,有三对选手参加比赛。当一对被淘汰时,他们会玩一个类似囚徒困境的游戏来决定奖金如何分配。如果他们都合作(朋友) ,他们分享奖金50-50。如果一方合作而另一方背叛(敌人) ,那么叛变者将得到所有的奖金,而合作者将一无所获。如果双方都背叛,那么双方都将一无所有。请注意,奖励矩阵与上面给出的标准矩阵略有不同,因为“双方都背叛”和“合作而对方背叛”情况下的奖励是相同的。与标准囚徒困境中的严格均衡相比,这使得“两个都背叛”情况成为一个弱均衡。如果一个参赛者知道他们的对手将投票给“敌人” ,那么他们自己的选择不会影响他们自己的奖金。从特定意义上讲,“朋友还是敌人”节目在囚徒困境和“胆小鬼”博弈之间有一个奖励模型。<br />
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The rewards matrix is<br />
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The rewards matrix is<br />
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奖励矩阵是<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Friend"<br />(cooperate)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Foe"<br />(defect)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"Friend"<br />(cooperate)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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! scope="row" | {{color|#009|"Foe"<br />(defect)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"朋友"<br />(合作)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"敌人"<br />(背叛)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"朋友"<br />(合作)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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! scope="row" | {{color|#009|"敌人"<br />(背叛)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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This payoff matrix has also been used on the [[United Kingdom|British]] [[television]] programmes ''Trust Me'', ''[[Shafted]]'', ''[[The Bank Job (TV series)|The Bank Job]]'' and ''[[Golden Balls]]'', and on the [[United States|American]] shows ''[[Bachelor Pad]]'' and ''[[Take It All (game show)|Take It All]]''. Game data from the ''[[Golden Balls]]'' series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls, and on the American shows Bachelor Pad and Take It All. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<br />
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英国电视节目《相信我》、《阴影》、《银行工作》和《黄金球》以及美国电视节目《单身公寓》和《全部拿走》也采用了这种奖励矩阵。一个经济学家团队分析了“金球奖”系列的游戏数据,他们发现,现实生活中,合作对于金额而言“惊人地高” ,但在游戏的背景下,相对较低。<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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===Iterated snowdrift===<br />
<font color="#ff8000">重复雪堆 Iterated snowdrift </font><br />
{{main|snowdrift game}}<br />
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Researchers from the [[University of Lausanne]] and the [[University of Edinburgh]] have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a [[chicken game]], it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a [[snowdrift]], each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
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Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
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来自洛桑大学和爱丁堡大学的研究人员认为,“重复雪堆游戏”可能更能反映现实世界的社会状况。虽然这个模型实际上是一个胆小鬼博弈。在这个模型中,由于背叛可以降低被剥削的风险,个体总是从合作选择中获益。这个雪堆游戏可以设想两个司机被困在雪堆的两侧,每个司机都可以选择铲雪清理道路,或者留在自己的车里。一个玩家的最高回报来自于让对手清除所有的积雪,但是仍然可以从对手的工作中得到回报。<br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<br />
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这可能更好地反映了现实世界的情景,研究人员举了两位科学家合作完成一份报告的例子,如果另一位科学家更加努力地工作,这两位科学家都会受益。“但当你的合作者不做任何工作时,你自己完成所有的工作可能会更好。你最终还是会完成一个项目。” <ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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{|<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ Example snowdrift payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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! Cooperates<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
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|+ Example PD payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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! Cooperates<br />
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! Defects<br />
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{|<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ 重复雪堆的支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
<br />
|-<br />
<br />
! 合作<br />
<br />
| 200, 200 || 100, 300<br />
<br />
|-<br />
<br />
! 背叛<br />
<br />
| 300, 100 || 0, 0<br />
<br />
|}<br />
<br />
||<br />
<br />
{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ 囚徒困境支出示例 (A, B)<br />
<br />
! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
<br />
|-<br />
<br />
! 合作<br />
<br />
| 200, 200 || -100, 300<br />
<br />
|-<br />
<br />
! 背叛<br />
<br />
| 300, -100 || 0, 0<br />
<br />
|}<br />
<br />
<br />
<br />
<br />
===Coordination games===<br />
<font color="#ff8000">协调博弈 Coordination games</font><br />
{{main|coordination games}}<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local [[left- and right-hand traffic]] convention helps to co-ordinate their actions.<br />
<br />
In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.<br />
<br />
在协调博弈中,参与者必须协调自己的策略以获得一个好的结果。一个例子是两辆车在暴风雪中突然相遇,每辆车必须选择是左转还是右转。如果两辆车都向左转弯,或者都向右转弯,那么两辆车就不会相撞。当地的左右向交通惯例有助于协调他们的行动。<br />
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<br />
<br />
Symmetrical co-ordination games include [[Stag hunt]] and [[Bach or Stravinsky]].<br />
<br />
Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.<br />
<br />
对称的协调游戏包括猎鹿 Stag hunt和巴赫 Bach或斯特拉文斯基 Stravinsky。<br />
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<br />
<br />
===Asymmetric prisoner's dilemmas===<br />
<br />
<font color="#ff8000">不对称的囚徒困境 Asymmetric prisoner's dilemmas</font><br />
<br />
A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an [[alibi]], whence the term "alibi game".<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
<br />
A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, whence the term "alibi game".<br />
<br />
一个更一般的博弈集是不对称的。就像在囚徒困境中一样,最好的结果是合作,而背叛是有动机的。与对称的囚徒困境不同的是一个玩家比另一个玩家有更多的损失或收获。这样的博弈被描述为囚徒困境,其中一个囚徒有不在场证明,这就是术语“不在场证明游戏”的由来。<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
<br />
<br />
<br />
In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
<br />
In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<br />
<br />
在实验中,在重复博弈中获得不均等收益的参与者可能会寻求利润最大化,但是前提是两个玩家都必须获得均等的收益。这可能会导致一个稳定的均衡策略,即弱势参与者在每隔X场博弈中都会背叛,而另一个参与者总是保持合作。这种行为可能取决于实验围绕公平的社会规范。<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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<br />
<br />
==Software==<br />
软件<br />
<br />
<br />
Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
<br />
Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
<br />
已经有一些可以用来运行囚徒困境模拟和比赛的软件包,其中一些有可用的源代码。<br />
<br />
* The source code for the [[The Evolution of Cooperation|second tournament]] run by Robert Axelrod (written by Axelrod and many contributors in [[Fortran]]) is available [http://www-personal.umich.edu/~axe/research/Software/CC/CC2.html online]<br />
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* [https://web.archive.org/web/19991010053242/http://www.lifl.fr/IPD/ipd.frame.html Prison], a library written in [[Java (programming language)|Java]], last updated in 1998<br />
<br />
* [https://github.com/Axelrod-Python/Axelrod Axelrod-Python], written in [[Python (programming language)|Python]]<br />
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* [http://selborne.nl/ipd/ play the Iterative Prisoner's Dilemma in the browser], play against strategies or let strategies play against other strategies<br />
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<br />
<br />
==In fiction==<br />
在小说中<br />
[[Hannu Rajaniemi]] set the opening scene of his ''[[The Quantum Thief]]'' trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in [[mathematical physics]]&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, ''[[The Fractal Prince]]'' and ''[[The Causal Angel]]'', published in 2012 and 2014, respectively.<br />
<br />
Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in mathematical physics&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.<br />
<br />
汉努·拉贾尼埃米 Hannu Rajaniemi将他的《量子窃贼》三部曲的开场场景设置在一个“囚徒困境”中。该系列的主题被描述为“双重宇宙的不足” ,最终的对手是一个叫做全面背叛者的角色。作为一个处理这个问题的艺术家,拉贾尼埃米尤其有趣,因为他是剑桥大学培养的数学家,拥有数学物理学博士学位——物质和信息的可互换性是这本书的一个主要特征,它发生在<font color="#ff8000">后奇点post-singularity</font>的未来。该系列的第一本书于2010年出版,其续集《分形王子》和《因果天使》分别于2012年和2014年出版。<br />
<br />
<br />
<br />
A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game ''[[Zero Escape: Virtue's Last Reward]]'' and a minor part in its 2016 sequel ''[[Zero Escape: Zero Time Dilemma]]''.<br />
<br />
A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.<br />
<br />
一个(重复)囚徒困境博弈的模型是2012年电子游戏《零度逃脱: 美德的最后奖励》的重点,也是2016年续集《零度逃脱: 极限脱出刻之困境》的一个次要部分。<br />
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<br />
<br />
In ''The Mysterious Benedict Society and the Prisoner's Dilemma'' by [[Trenton Lee Stewart]], the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
<br />
In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
<br />
在特伦顿·李·斯图尔特 Trenton Lee Stewart的《神秘的本尼迪克特社会和囚徒困境》中,主要角色从玩一个版本的游戏开始,然后一起逃离“监狱”。后来他们变成了真正的囚犯,再次越狱。<br />
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<br />
In ''[[The Adventure Zone]]: Balance'' during ''The Suffering Game'' subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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在冒险区: 苦难游戏的平衡中,玩家角色在他们在两个领域的时间内两次呈现出囚徒困境,一次是合作,一次是背叛。<br />
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<br />
<br />
In the 8th novel from the author James S. A. Corey [[Tiamat's Wrath]] . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. {{cn|date=April 2020}}<br />
<br />
In the 8th novel from the author James S. A. Corey Tiamat's Wrath . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. <br />
<br />
在作者詹姆斯·S·A·科里·提亚玛特 James S. A. Corey Tiamat的《愤怒》中的第八部小说中,温斯顿•杜阿尔特 Winston Duarte向他14岁的女儿特蕾莎 Teresa解释了她面临的囚徒困境,来训练她的战略思维能力。<br />
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<br />
==See also==<br />
请参阅<br />
{{div col|colwidth=18em}}<br />
<br />
* [[Abilene paradox]]<br />
<font color="#ff8000"> 阿背伦悖论</font><br />
* [[Centipede game]]<br />
<font color="#ff8000"> 蜈蚣博弈</font><br />
* [[Christmas truce]]<br />
<font color="#ff8000"> 圣诞休战</font><br />
* [[Folk theorem (game theory)]]<br />
<font color="#ff8000"> 无名氏定理(博弈论)/font><br />
* [[Free-rider problem]]<br />
<font color="#ff8000"> 搭便车问题</font><br />
* [[Hobbesian trap]]<br />
]<font color="#ff8000"> 霍布斯主义陷阱</font><br />
* [[Innocent prisoner's dilemma]]<br />
<font color="#ff8000"> 无辜囚徒困局</font><br />
* [[Liar Game]]<br />
<font color="#ff8000">说谎者博弈</font><br />
* [[Optional prisoner's dilemma]]<br />
<font color="#ff8000"> 可选择囚徒困境</font><br />
* [[Robert H. Frank#Prisoner's dilemma and cooperation|Prisoner's dilemma and cooperation]]<br />
罗伯特·H·弗兰克囚徒的困境和合作|<font color="#ff8000"> 囚徒困境</font>和合作<br />
* [[Public goods game]]<br />
<font color="#ff8000"> 公共商品博弈</font><br />
* [[Gift-exchange game]]<br />
<font color="#ff8000"> 互利博弈</font><br />
* [[Reciprocal altruism]]<br />
<font color="#ff8000"> 相互利他行为</font><br />
* [[Social preferences]]<br />
<font color="#ff8000"> 社会偏好</font><br />
* [[Swift trust theory]]<br />
<font color="#ff8000"> 快速信任理论</font><br />
* [[Unscrupulous diner's dilemma]]<br />
]<font color="#ff8000"> 无道德食客困境</font><br />
{{div col end}}<br />
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==References==<br />
==参考==<br />
{{notelist}}<br />
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{{reflist|colwidth=30em}}<br />
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<br />
<br />
==Further reading==<br />
==拓展阅读==<br />
{{refbegin|30em}}<br />
<br />
* [[S.M. Amadae|Amadae, S.]] (2016). 'Prisoner's Dilemma,' ''Prisoners of Reason.'' [[Cambridge University Press]], NY, pp.&nbsp;24–61.<br />
<br />
* {{cite book |first1=Robert |last1=Aumann |authorlink=Robert Aumann |chapter=Acceptable points in general cooperative ''n''-person games |editor1-first=R. D. |editor1-last=Luce |editor2-first=A. W. |editor2-last=Tucker |title=Contributions to the Theory 23 of Games IV |series=Annals of Mathematics Study |volume=40 |pages=287–324 |publisher=Princeton University Press |location=Princeton NJ |year=1959 |mr=0104521}}<br />
<br />
* [[Robert Axelrod|Axelrod, R.]] (1984). ''[[The Evolution of Cooperation]]''. {{isbn|0-465-02121-2}}<br />
<br />
* [[Cristina Bicchieri|Bicchieri, Cristina]] (1993). Rationality and Coordination. [[Cambridge University Press]].<br />
<br />
* {{cite journal |first1=David M. |last1=Chess |date=December 1988 |title=Simulating the evolution of behavior: the iterated prisoners' dilemma problem |url=http://www.complex-systems.com/pdf/02-6-4.pdf |journal=Complex Systems |volume=2 |issue=6 |pages=663–70}}<br />
<br />
* [[Melvin Dresher|Dresher, M.]] (1961). ''The Mathematics of Games of Strategy: Theory and Applications'' [[Prentice-Hall]], Englewood Cliffs, NJ.<br />
<br />
* Greif, A. (2006). ''Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.'' Cambridge University Press, [[Cambridge]], UK.<br />
<br />
* [[Anatol Rapoport|Rapoport, Anatol]] and Albert M. Chammah (1965). ''Prisoner's Dilemma''. [[University of Michigan Press]].<br />
<br />
{{refend}}<br />
<br />
<br />
<br />
==External links==<br />
外部链接<br />
*{{Commonscat-inline}}<br />
<br />
* [http://plato.stanford.edu/entries/prisoner-dilemma/ Prisoner's Dilemma (''Stanford Encyclopedia of Philosophy'')]<br />
<br />
* [http://www.msri.org/ext/larryg/pages/15.htm The Bowerbird's Dilemma] The Prisoner's Dilemma in ornithology&nbsp;– mathematical cartoon by Larry Gonick.<br />
<br />
* [https://www.youtube.com/watch?v=_1SEXTVsxjk The Prisoner's Dilemma] The Prisoner's Dilemma with Lego minifigures.<br />
<br />
* {{cite encyclopedia |last1=Dixit |first1=Avinash |authorlink1=Avinash Dixit |last2= Nalebuff |first2=Barry |authorlink2=Barry Nalebuff |editor=[[David R. Henderson]]|encyclopedia=[[Concise Encyclopedia of Economics]] |title=Prisoner's Dilemma |url=http://www.econlib.org/library/Enc/PrisonersDilemma.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}<br />
<br />
* [http://gametheory101.com/The_Prisoner_s_Dilemma.html Game Theory 101: Prisoner's Dilemma]<br />
<br />
* [https://www.youtube.com/watch?v=I71mjZefg8g Dawkins: Nice Guys Finish First]<br />
<br />
* [https://axelrod.readthedocs.io/en/stable/ Axelrod] Iterated Prisoner's Dilemma [[Python (programming language)|Python]] library<br />
<br />
* [http://gametheorygames.nl/index.html Play the Iterated Prisoner's Dilemma on gametheorygames.nl]<br />
<br />
* [https://web.archive.org/web/20141011014608/http://demo.otree.org/demo/Prisoner%27s+Dilemma/ Play Prisoner's Dilemma on ''oTree''] (N/A 11-5-17)<br />
<br />
* Nicky Case's [https://web.archive.org/web/20181229222135/https://ncase.me/trust/ Evolution of Trust], an example of the donation game<br />
<br />
* [http://iterated-prisoners-dilemma.info Iterated Prisoner's Dilemma online game] by Wayne Davis<br />
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{{Decision theory paradoxes}}<br />
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{{Game theory}}<br />
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{{Authority control}}<br />
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[[Category:Non-cooperative games]]<br />
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Category:Non-cooperative games<br />
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类别: 非合作性游戏<br />
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[[Category:Thought experiments]]<br />
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Category:Thought experiments<br />
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类别: 思维实验<br />
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[[Category:Dilemmas]]<br />
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Category:Dilemmas<br />
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类别: 困境<br />
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[[Category:Environmental studies]]<br />
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Category:Environmental studies<br />
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类别: 环境研究<br />
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[[Category:Social psychology]]<br />
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Category:Social psychology<br />
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类别: 社会心理学<br />
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[[Category:Moral psychology]]<br />
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Category:Moral psychology<br />
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范畴: 道德心理学<br />
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<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Prisoner's dilemma]]. Its edit history can be viewed at [[囚徒困境/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%9B%9A%E5%BE%92%E5%9B%B0%E5%A2%83&diff=21298囚徒困境2021-01-25T08:32:34Z<p>Vicky:/* Special case: donation game */</p>
<hr />
<div>此词条由Henry初步翻译。已由Smile审校。<br />
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{{other uses}}<br />
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{{short description|Canonical example of a game analyzed in game theory}}<br />
<br />
{| class="wikitable floatright"<br />
<br />
|+ Prisoner's dilemma payoff matrix<br />
<br />
! {{diagonal split header|A|B}}<br />
<br />
! B stays<br />silent<br />
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! B<br />betrays<br />
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|-<br />
<br />
! A stays<br />silent <br />
<br />
| {{diagonal split header|-1|-1|transparent}}<br />
<br />
| {{diagonal split header|-3|0|transparent}}<br />
<br />
|-<br />
<br />
! A<br />betrays<br />
<br />
| {{diagonal split header|0|-3|transparent}}<br />
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| {{diagonal split header|-2|-2|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
{| class="wikitable floatright"<br />
<br />
|+ <font color="#ff8000"> 囚徒困境支付矩阵 Prisoner's dilemma payoff matrix</font><br />
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! {{diagonal split header|A|B}}<br />
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! B 保持<br />缄默<br />
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! B<br />背叛<br />
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|-<br />
<br />
! A 保持<br />缄默 <br />
<br />
| {{diagonal split header|-1|-1|transparent}}<br />
<br />
| {{diagonal split header|-3|0|transparent}}<br />
<br />
|-<br />
<br />
! A<br />背叛<br />
<br />
| {{diagonal split header|0|-3|transparent}}<br />
<br />
| {{diagonal split header|-2|-2|transparent}}<br />
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|}<br />
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<br />
The '''prisoner's dilemma''' is a standard example of a game analyzed in [[game theory]] that shows why two completely [[Rationality#Economics|rational]] individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by [[Merrill Flood]] and [[Melvin Dresher]] while working at [[RAND Corporation|RAND]] in 1950. [[Albert W. Tucker]] formalized the game with prison sentence rewards and named it "prisoner's dilemma",<ref>Poundstone, 1992</ref> presenting it as follows:<br />
<br />
The prisoner's dilemma is a standard example of a game analyzed in game theory that shows why two completely rational individuals might not cooperate, even if it appears that it is in their best interests to do so. It was originally framed by Merrill Flood and Melvin Dresher while working at RAND in 1950. Albert W. Tucker formalized the game with prison sentence rewards and named it "prisoner's dilemma", prensenting it as follows:<br />
<br />
<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>是<font color="#ff8000"> 博弈论game theory</font>分析博弈的一个代表性例子,它揭示了为什么两个完全理性的个体可能不会合作,即使这样做符合他们的最大利益。它最初是由梅里尔·弗勒德 Merrill Flood和 梅文·加舍尔 Melvin Dresher于1950年在兰德公司工作时构建的。阿尔伯特.W.塔克 Albert W. Tucker将这种博弈以监禁刑罚奖励的方式正式化,并将其命名为囚徒困境,具体阐述如下:<br />
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<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
{{quote|Two members of a criminal gang are arrested and imprisoned. Each prisoner is in solitary confinement with no means of communicating with the other. The prosecutors lack sufficient evidence to convict the pair on the principal charge, but they have enough to convict both on a lesser charge. Simultaneously, the prosecutors offer each prisoner a bargain. Each prisoner is given the opportunity either to betray the other by testifying that the other committed the crime, or to cooperate with the other by remaining silent. The possible outcomes are:<br />
<br />
* If A and B each betray the other, each of them serves two years in prison<br />
* If A betrays B but B remains silent, A will be set free and B will serve three years in prison<br />
* If A remains silent but B betrays A, A will serve three years in prison and B will be set free<br />
* If A and B both remain silent, both of them will serve only one year in prison (on the lesser charge).}}<br />
<br />
{{一个犯罪团伙的两名成员被捕入狱。每个囚犯都被单独监禁,与他人无法沟通。检察官缺乏足够的证据来对这两个人定罪,但有足够的证据以较低的罪名定罪。同时,检察官向每个犯人提供了一个交易。每个囚犯都有机会出卖对方,证明对方犯下的罪行,或者他们可以合作,保持沉默。可能的结果有:<br />
<br />
*如果A和B都背叛了对方,他们都会在监狱服刑两年。<br />
*如果A背叛了B但B保持沉默,A会被无罪释放而B会服刑三年。<br />
*如果A保持沉默但B背叛了A,A会服刑三年而B会无罪释放。<br />
*如果A和B都保持沉默,他们就只用服刑一年(以较低的罪名)。}}<br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other.<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref> In reality, humans display a [[systemic bias]] towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action.<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref> This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome.<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref> The prisoner's dilemma became the focus of extensive experimental research.<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
It is implied that the prisoners will have no opportunity to reward or punish their partner other than the prison sentences they get and that their decision will not affect their reputation in the future. Because betraying a partner offers a greater reward than cooperating with them, all purely rational self-interested prisoners will betray the other, meaning the only possible outcome for two purely rational prisoners is for them to betray each other. In reality, humans display a systemic bias towards cooperative behavior in this and similar games despite what is predicted by simple models of "rational" self-interested action. This bias towards cooperation has been known since the test was first conducted at RAND; the secretaries involved trusted each other and worked together for the best common outcome. The prisoner's dilemma became the focus of extensive experimental research. <br />
<br />
这意味着,囚犯除了监禁刑罚之外,没有机会奖励或惩罚他们的同伴,他们的决定也不会影响他们未来的声誉。因为背叛一个同伴比与他们合作能得到更大的回报,所以所有纯粹理性的、自私自利的囚犯都会背叛对方,这意味着,对于两个纯粹理性的囚犯来说,唯一可能的结果就是他们相互背叛。<ref>{{cite web|last=Milovsky|first=Nicholas|title=The Basics of Game Theory and Associated Games|url=https://issuu.com/johnsonnick895/docs/game_theory_paper|accessdate=11 February 2014}}</ref>实际上,尽管“理性的”自利行为的简单模型已经预测到了这一点,但人类在这种和类似的博弈中仍然表现出对合作行为的<font color="#ff8000">系统性偏差 systemic bias </font>。<ref name = Fehr>{{cite journal | last1=Fehr | first1= Ernst | last2=Fischbacher | first2=Urs | date= Oct 23, 2003 | title=The Nature of human altruism |journal=Nature | volume=425 | pages=785–91 | doi=10.1038/nature02043 | url=http://www.iwp.jku.at/born/mpwfst/04/nature02043_f_born.pdf | accessdate=February 27, 2013 | pmid=14574401 | issue=6960|bibcode = 2003Natur.425..785F }}</ref><ref name = Amos>{{cite book | title=Preference, belief, and similarity: selected writings. | publisher=Massachusetts Institute of Technology Press | first1= Amos | last1=Tversky | first2=Eldar | last2=Shafir | url=http://cseweb.ucsd.edu/~gary/PAPER-SUGGESTIONS/Preference,%20Belief,%20and%20Similarity%20Selected%20Writings%20(Bradford%20Books).pdf | year=2004 | isbn=9780262700931 | accessdate=February 27, 2013}}</ref><ref name="Ahn">{{cite journal |last1 = Toh-Kyeong|first1 = Ahn|last2 = Ostrom|first2 = Elinor|last3 = Walker|first3 = James|date = Sep 5, 2002|title = Incorporating Motivational Heterogeneity into Game-Theoretic Models of Collective Action|journal = Public Choice|volume = 117|issue = 3–4|pages = 295–314|doi =10.1023/b:puch.0000003739.54365.fd |url = http://www.indiana.edu/~workshop/seminars/papers/ahnostromwalker_092402.pdf|accessdate = June 27, 2015|hdl = 10535/4697}}</ref><ref name="Hessel">{{cite journal|last1 = Oosterbeek|first1 = Hessel|last2 = Sloof|first2 = Randolph|last3 = Van de Kuilen|first3 = Gus|date = Dec 3, 2003|title = Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis|journal = Experimental Economics|volume = 7|issue = 2|pages = 171–88|doi = 10.1023/B:EXEC.0000026978.14316.74|url = http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|accessdate = February 27, 2013|url-status = dead|archiveurl = https://web.archive.org/web/20130512175243/http://www.econ.nagoya-cu.ac.jp/~yhamagu/ultimatum.pdf|archivedate = May 12, 2013}}</ref>自从在兰德公司首次进行这项测试以来,人们就已经知道了这种对合作的偏见; 参与测试的秘书们相互信任,为了最好的共同的目标而努力。<ref>{{Cite book | url=https://books.google.com/?id=WIhZlB86nJwC&pg=PT96&lpg=PT96&dq=rand+secretaries+prisoner%27s+dilemma#v=onepage |title = Why Most Things Fail|isbn = 9780571266142|last1 = Ormerod|first1 = Paul|date = 2010-12-22}}</ref>囚徒困境成为大量实验研究的焦点。<ref>Deutsch, M. (1958). Trust and suspicion. Journal of Conflict Resolution, 2(4), 265–279. https://doi.org/10.1177/002200275800200401</ref> <ref>Rapoport, A., & Chammah, A. M. (1965). Prisoner’s Dilemma: A study of conflict and cooperation. Ann Arbor, MI: University of Michigan Press.</ref><br />
<br />
<br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by [[backward induction]]) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
An extended "iterated" version of the game also exists. In this version, the classic game is played repeatedly between the same prisoners, who continuously have the opportunity to penalize the other for previous decisions. If the number of times the game will be played is known to the players, then (by backward induction) two classically rational players will betray each other repeatedly, for the same reasons as the single-shot variant. In an infinite or unknown length game there is no fixed optimum strategy, and prisoner's dilemma tournaments have been held to compete and test algorithms for such cases.<br />
<br />
一个扩展的<font color="#ff8000">迭代iterated</font>版本的博弈由此衍生出来。在这个版本中,经典博弈会在在同一组囚犯之间重复进行,他们不断有机会为了之前的决定对其他囚犯进行惩罚。如果参与者知道博弈的次数,那么(通过<font color="#ff8000">逆向归纳法 backward induction </font>)两个经典的理性的玩家就会因为和在单次博弈中相同的原因反复背叛对方。在无限次或未知次数的博弈中,没有固定的最优策略,因而,举办囚徒困境竞赛来竞争和检验这种情况下的算法。<ref>{{cite journal|url = https://egtheory.wordpress.com/2015/03/02/ipd/|title = Short history of iterated prisoner's dilemma tournaments|date = March 2, 2015|access-date = February 8, 2016|journal = Journal of Conflict Resolution|volume = 24|issue = 3|pages = 379–403|last = Kaznatcheev|first = Artem|doi = 10.1177/002200278002400301}}</ref><br />
<br />
<br />
<br />
The prisoner's dilemma game can be used as a model for many [[#Real-life examples|real world situations]] involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activities.<br />
<br />
The prisoner's dilemma game can be used as a model for many real world situations involving cooperative behavior. In casual usage, the label "prisoner's dilemma" may be applied to situations not strictly matching the formal criteria of the classic or iterative games: for instance, those in which two entities could gain important benefits from cooperating or suffer from the failure to do so, but find it difficult or expensive—not necessarily impossible—to coordinate their activitie <br />
<br />
囚徒困境博弈可以作为许多现实中涉及合作行为的模型。在非正式用法中,“囚徒困境”一词可适用于不严格符合经典或迭代博弈的形式标准的情况: 例如,两个实体可以从合作中获得巨大利益或者会因为合作失败而遭受损失,但发现协调他们的活动很困难或者代价昂贵(并非是不可能的)。<br />
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<br />
<br />
==Strategy for the prisoner's dilemma==<br />
囚徒困境的策略<br />
<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
Two prisoners are separated into individual rooms and cannot communicate with each other.<br />
<br />
两名囚犯被分开关押在各自的房间里,不能相互交流。<br />
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The normal game is shown below:<br />
<br />
The normal game is shown below:<br />
<br />
正常的博弈如下:<br />
<br />
<br />
<br />
{| class="wikitable"<br />
<br />
{| class="wikitable"<br />
<br />
{ | class“ wikitable”<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! {{diagonal split header|<br />Prisoner A|Prisoner B}} !! Prisoner B stays silent<br>(''cooperates'') !! Prisoner B betrays<br>(''defects'')<br />
<br />
! !! Prisoner B stays silent<br>(cooperates) !! Prisoner B betrays<br>(defects)<br />
<br />
! {{diagonal split header|<br />犯人A|犯人B}}!!犯人B保持沉默<br>(''合作'') !! 犯人B背叛<br>(''背叛'')<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A stays silent<br>(''cooperates'')<br />
<br />
! Prisoner A stays silent<br>(cooperates)<br />
<br />
!犯人 a 保持沉默<br>(''合作'')<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
| Each serves 1 year|| Prisoner A: 3 years<br />Prisoner B: goes free<br />
<br />
|每人服刑1年||囚犯 A: 3年<br />囚犯 B: 无罪释放<br />
<br />
|-<br />
<br />
|-<br />
<br />
|-<br />
<br />
! Prisoner A betrays<br>(''defects'')<br />
<br />
! Prisoner A betrays<br>(defects)<br />
<br />
!犯人A背叛<br>(''背叛'')<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
| Prisoner A: goes free<br />Prisoner B: 3 years || Each serves 2 years<br />
<br />
|囚犯 A: 获释<br />囚犯 B: 3年||每人服刑2年<br />
<br />
|}<br />
<br />
|}<br />
<br />
|}<br />
<br />
<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by [[Dilemma#Use in logic|dilemma]]: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
It is assumed that both prisoners understand the nature of the game, have no loyalty to each other, and will have no opportunity for retribution or reward outside the game. Regardless of what the other decides, each prisoner gets a higher reward by betraying the other ("defecting"). The reasoning involves an argument by dilemma: B will either cooperate or defect. If B cooperates, A should defect, because going free is better than serving 1 year. If B defects, A should also defect, because serving 2 years is better than serving 3. So either way, A should defect. Parallel reasoning will show that B should defect.<br />
<br />
假设两个囚犯都了解博弈的本质,对彼此不忠诚,且在博弈之外没有机会得到报复或奖励。那么不管对方怎么决定,每个犯人背叛对方都会得到更高的奖励(“叛变”)。推理涉及一个进退两难的论点:B 要么合作,要么叛变。如果B合作,A 应该叛变,因为得到释放总比服刑1年好。如果 B叛变,A也应该叛变,因为服刑2年总比服刑3年好。所以不管怎样,A都应该叛变。并行推理表明B应该选择叛变。<br />
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Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a [[dominant strategy]]. Mutual defection is the only strong [[Nash equilibrium]] in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
Because defection always results in a better payoff than cooperation regardless of the other player's choice, it is a dominant strategy. Mutual defection is the only strong Nash equilibrium in the game (i.e. the only outcome from which each player could only do worse by unilaterally changing strategy). The dilemma, then, is that mutual cooperation yields a better outcome than mutual defection but is not the rational outcome because the choice to cooperate, from a self-interested perspective, is irrational.<br />
<br />
因为不管对方的选择如何,背叛总是比合作带来更好的回报,所以这是一个<font color="#ff8000">占优策略 dominant strategy</font>。相互背叛是博弈中唯一的强<font color="#ff8000">纳什均衡点 dominant strategy </font>(即每个参与者单方面的改变策略只能使自己的情况变糟)。因此,困境在于,虽然相互合作比相互背叛产生更好的结果,但它却不是理性的结果,因为从自我利益的角度来看,合作的选择是非理性的。<br />
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<br />
<br />
==Generalized form==<br />
<font color="#ff8000">广泛形态 Generalized form </font><br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
<br />
The structure of the traditional prisoner's dilemma can be generalized from its original prisoner setting. Suppose that the two players are represented by the colors red and blue, and that each player chooses to either "cooperate" or "defect".<br />
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传统囚徒困境的结构可以从其最初的囚徒环境中概括出来。假设两个玩家用红色和蓝色表示,并且每个玩家选择“合作”或“背叛”。<br />
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<br />
<br />
If both players cooperate, they both receive the reward ''R'' for cooperating. If both players defect, they both receive the punishment payoff ''P''. If Blue defects while Red cooperates, then Blue receives the temptation payoff ''T'', while Red receives the "sucker's" payoff, ''S''. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff ''S'', while Red receives the temptation payoff ''T''.<br />
<br />
If both players cooperate, they both receive the reward R for cooperating. If both players defect, they both receive the punishment payoff P. If Blue defects while Red cooperates, then Blue receives the temptation payoff T, while Red receives the "sucker's" payoff, S. Similarly, if Blue cooperates while Red defects, then Blue receives the sucker's payoff S, while Red receives the tem punishment payoffptation payoff T.<br />
<br />
如果两个玩家合作,他们都会因为合作而获得奖励''R''。如果两个参与人都叛变,他们都会受到惩罚''P''。 如果蓝方叛变而红方合作,那么蓝方得到诱惑回报''T'',而红方受到“上当受骗者”损失''S''。同样地,如果蓝方合作而红方叛变,那么蓝方得到上当受骗者的损失''S'',而红方得到诱惑支付''T''。<br />
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<br />
This can be expressed in [[Normal-form game|normal form]]:<br />
<br />
This can be expressed in normal form:<br />
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这可以用标准形式的博弈来表示:<br />
<br />
<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
{| class="wikitable" style="text-align:center"<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
|+ Canonical PD payoff matrix<br />
<br />
| + <font color="#ff8000">正则 PD 支付矩阵 Canonical PD payoff matrix </font> <br />
<br />
! {{diagonal split header|{{color|#009|Blue}}|{{color|#900|Red}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| ||transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|Defect}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
! {{diagonal split header|{{color|#009|蓝方}}|{{color|#900|红方}}}}<br />
<br />
! |}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
<br />
! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
<br />
|-<br />
<br />
! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
<br />
| {{diagonal split header|{{color|#009|''R''}}|{{color|#900|''R''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''S''}}|{{color|#900|''T''}}|transparent}}<br />
<br />
|-<br />
<br />
! scope="row" | {{color|#009|背叛}}<br />
<br />
| {{diagonal split header|{{color|#009|''T''}}|{{color|#900|''S''}}|transparent}}<br />
<br />
| {{diagonal split header|{{color|#009|''P''}}|{{color|#900|''P''}}|transparent}}<br />
<br />
|}<br />
<br />
<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
<br />
and to be a prisoner's dilemma game in the strong sense, the following condition must hold for the payoffs:<br />
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要成为强意义下的囚徒困境博弈,收益必须满足以下条件:<br />
<br />
<br />
<br />
:{{tmath|T > R > P > S}}<br />
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The payoff relationship {{tmath|R > P}} implies that mutual cooperation is superior to mutual defection, while the payoff relationships {{tmath|T > R}} and {{tmath|P > S}} imply that defection is the [[dominant strategy]] for both agents.<br />
<br />
The payoff relationship implies that mutual cooperation is superior to mutual defection, while the payoff relationships and imply that defection is the dominant strategy for both agents.<br />
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回报关系{{tmath|R > P}}意味着相互合作优于相互背叛,然而回报关系{{tmath|T > R}}和{{tmath|P > S}}也意味着相互背叛是双方的占优策略。<br />
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===Special case: donation game===<br />
特例:<font color="#ff8000">捐赠博弈 donation game </font><br />
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The "donation game"<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref> is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit ''b'' at a personal cost ''c'' with ''b'' > ''c''. Defection means offering nothing. The payoff matrix is thus<br />
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The "donation game" is a form of prisoner's dilemma in which cooperation corresponds to offering the other player a benefit b at a personal cost c with b > c. Defection means offering nothing. The payoff matrix is thus<br />
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捐赠博弈<ref name=Hilbe2013>{{cite journal|last=Hilbe|first=Christian |author2=Martin A. Nowak |author3=Karl Sigmund|title=Evolution of extortion in Iterated Prisoner's Dilemma games|journal=PNAS|date=April 2013|volume=110|issue=17|pages=6913–18|doi=10.1073/pnas.1214834110|pmid=23572576 |pmc=3637695 |bibcode=2013PNAS..110.6913H |arxiv=1212.1067}}</ref>是囚徒困境的一种形式,在这种博弈中,合作相当于以''b'' > ''c''条件下的个人成本''c''为另一方提供一个收益''b'',而叛变意味着什么也不提供。收益矩阵如下:<br />
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{| class="wikitable" style="text-align:center"<br />
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! {{diagonal split header|{{navy (color)|Blue}}|{{color|#900|Red}}}}<br />
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! scope="col" style="width:60px;" | {{color|#900|Cooperate}}<br />
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! scope="col" style="width:60px;" | {{color|#900|Defect}}<br />
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|-<br />
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! scope="row" style="width:60px;" | {{color|#009|Cooperate}}<br />
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| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|Defect}}<br />
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| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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{| class="wikitable" style="text-align:center"<br />
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! {{diagonal split header|{{navy (color)|蓝方}}|{{color|#900|红方}}}}<br />
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! scope="col" style="width:60px;" | {{color|#900|合作}}<br />
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! scope="col" style="width:60px;" | {{color|#900|背叛}}<br />
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|-<br />
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! scope="row" style="width:60px;" | {{color|#009|合作}}<br />
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| {{diagonal split header|{{color|#009|''b''-''c''}}|{{color|#900|''b''-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|-''c''}}|{{color|#900|''b''}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|背叛}}<br />
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| {{diagonal split header|{{color|#009|''b''}}|{{color|#900|-''c''}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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Note that {{tmath|2R>T+S}} (i.e. {{tmath|2(b-c)>b-c}}) which qualifies the donation game to be an iterated game (see next section).<br />
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Note that (i.e. ) which qualifies the donation game to be an iterated game (see next section).<br />
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请注意{{tmath|2R>T+S}}(即{{tmath|2(b-c)>b-c}})这使得捐赠博弈成为一个迭代博弈(见下一节)。<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The [[marginal utility]] of an apple to the orange-grower X is ''b'', which is higher than the marginal utility (''c'') of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is ''b'' while the marginal utility of an apple is ''c''. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of ''b''-''c''. If one "defects" and does not deliver as promised, the defector will receive a payoff of ''b'', while the cooperator will lose ''c''. If both defect, then neither one gains or loses anything.<br />
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The donation game may be applied to markets. Suppose X grows oranges, Y grows apples. The marginal utility of an apple to the orange-grower X is b, which is higher than the marginal utility (c) of an orange, since X has a surplus of oranges and no apples. Similarly, for apple-grower Y, the marginal utility of an orange is b while the marginal utility of an apple is c. If X and Y contract to exchange an apple and an orange, and each fulfills their end of the deal, then each receive a payoff of b-c. If one "defects" and does not deliver as promised, the defector will receive a payoff of b, while the cooperator will lose c. If both defect, then neither one gains or loses anything.<br />
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捐赠博弈可能适用于市场。假设种植者X 种橘子,种植者Y 种苹果。苹果对橙子种植者 X 的<font color="#ff8000">边际效用 marginal utility</font>是''b'',“b”比橙子的边际效用''c''高,因为X有橙子剩余而没有苹果。同样地,对于苹果种植者Y来说,橙子的边际效用是''b'',而苹果的边际效用是''c''。 如果X和Y签约交换一个苹果和一个橙子,并且每个人都完成了交易,那么每个人都会得到''b-c''的收益。如果一方违约没有按照承诺交货,那么这个违约者将得到''b''的收益,而合作者将失去''c''的收益。 如果两者都违约,那么谁也不会得到或失去任何东西。<br />
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==The iterated prisoner's dilemma==<br />
<font color="#ff8000">迭代囚徒困境 iterated prisoner's dilemma </font> {{more citations needed section|date=November 2012}}<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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If two players play prisoner's dilemma more than once in succession and they remember previous actions of their opponent and change their strategy accordingly, the game is called iterated prisoner's dilemma.<br />
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如果两个参与者连续进行多次囚徒困境博弈,他们记住对手先前的行动并相应地改变策略,这种博弈被称为迭代囚徒困境。<br />
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In addition to the general form above, the iterative version also requires that {{tmath|2R > T + S}}, to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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In addition to the general form above, the iterative version also requires that , to prevent alternating cooperation and defection giving a greater reward than mutual cooperation.<br />
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除了上面的一般形式之外,迭代版本还要求{{tmath|2R > T + S}},防止交替合作和背叛比相互合作有更大的回报。<br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "[[Peace war game|peace-war game]]".<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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The iterated prisoner's dilemma game is fundamental to some theories of human cooperation and trust. On the assumption that the game can model transactions between two people requiring trust, cooperative behaviour in populations may be modeled by a multi-player, iterated, version of the game. It has, consequently, fascinated many scholars over the years. In 1975, Grofman and Pool estimated the count of scholarly articles devoted to it at over 2,000. The iterated prisoner's dilemma has also been referred to as the "peace-war game".<br />
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迭代囚徒困境博弈是人类合作与信任的理论基础。假设博弈可以为两个需要信任的人之间的交易建模,那么群体中的合作行为也可以由多个参与者迭代的博弈模型来建模。因此,这些年来,它吸引了许多学者。1975年,葛夫曼 Grofman和普尔 Pool估计专门撰写有关该领域的学术文章超过2000篇。迭代囚徒困境也被称为“和平-战争博弈”。<ref name = Shy>{{cite book | title= Industrial Organization: Theory and Applications | publisher=Massachusetts Institute of Technology Press | first1= Oz | last1=Shy |url=https://books.google.com/?id=tr4CjJ5LlRcC&pg=PR13&dq=industrial+organization+theory+and+applications | year=1995 | isbn=978-0262193665 | accessdate=February 27, 2013}}</ref><br />
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If the game is played exactly ''N'' times and both players know this, then it is optimal to defect in all rounds. The only possible [[Nash equilibrium]] is to always defect. The proof is [[Mathematical induction|inductive]]: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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If the game is played exactly N times and both players know this, then it is optimal to defect in all rounds. The only possible Nash equilibrium is to always defect. The proof is inductive: one might as well defect on the last turn, since the opponent will not have a chance to later retaliate. Therefore, both will defect on the last turn. Thus, the player might as well defect on the second-to-last turn, since the opponent will defect on the last no matter what is done, and so on. The same applies if the game length is unknown but has a known upper limit.<br />
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如果这个游戏正好玩了N次,并且两个玩家都知道这一点,那么在所有回合中最佳的策略就是叛变。唯一可能的纳什均衡点就是永远叛变。证明是通过归纳法证出来的: 不妨假设一个人在最后一回合叛变,因为对手之后没有机会反击。因此,双方都会在最后一个回合叛变。所以玩家同样也会在倒数第二回合时叛变,因为无论采取什么策略,对手都会在倒数第一回合叛变,依此类推。如果博弈次数未知但次数有限的情况也同样如此。<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The [[superrational]] strategy in the iterated prisoner's dilemma with fixed ''N'' is to cooperate against a superrational opponent, and in the limit of large ''N'', experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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Unlike the standard prisoner's dilemma, in the iterated prisoner's dilemma the defection strategy is counter-intuitive and fails badly to predict the behavior of human players. Within standard economic theory, though, this is the only correct answer. The superrational strategy in the iterated prisoner's dilemma with fixed N is to cooperate against a superrational opponent, and in the limit of large N, experimental results on strategies agree with the superrational version, not the game-theoretic rational one.<br />
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与标准的囚徒困境不同,在迭代囚徒困境中,叛变策略是严重违反直觉的,以至于不能很好地预测人类玩家的行为。然而,在标准的经济理论中,这是唯一正确的答案。具有固定次数 N的迭代囚徒困境中的<font color="#ff8000">超理性 superrational</font>策略是与超理性对手进行合作,在N很大的限制下,实验结果的策略与超理性结果的策略一致,而不是博弈论的理性结果。<br />
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For [[cooperation]] to emerge between game theoretic rational players, the total number of rounds ''N'' must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by [[Robert Aumann]] in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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For cooperation to emerge between game theoretic rational players, the total number of rounds N must be unknown to the players. In this case "always defect" may no longer be a strictly dominant strategy, only a Nash equilibrium. Amongst results shown by Robert Aumann in a 1959 paper, rational players repeatedly interacting for indefinitely long games can sustain the cooperative outcome.<br />
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为了使合作在博弈论的理性参与者之间出现,参与者必须不知道回合总数N。在这种情况下,“总是叛变”可能不再是一个严格占优策略,而只是一个纳什均衡。罗伯特·奥曼 Robert Aumann在1959年的一篇论文中表明,理性参与者在无限多次的博弈中通过反复互动可以维持合作的结果。<br />
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According to a 2019 experimental study in the ''American Economic Review'' which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, [[Tit for tat|tit-for-tat]], and [[Grim trigger]]. Which strategy the subjects chose depended on the parameters of the game.<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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According to a 2019 experimental study in the American Economic Review which tested what strategies real-life subjects used in iterated prisoners' dilemma situations with perfect monitoring, the majority of chosen strategies were always defect, tit-for-tat, and Grim trigger. Which strategy the subjects chose depended on the parameters of the game.<br />
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根据《美国经济评论》于2019年进行的一项实验研究,该实验中通过完美的监控测试了现实中被用在迭代囚徒困境情况下的策略,监测选择的策略总是背叛,针锋相对的和 <font color="#ff8000"> 冷酷触发策略 Grim trigger</font>。受试者选择的策略取决于博弈的参数。<ref>{{Cite journal|last=Dal Bó|first=Pedro|last2=Fréchette|first2=Guillaume R.|date=2019|title=Strategy Choice in the Infinitely Repeated Prisoner's Dilemma|journal=American Economic Review|language=en|volume=109|issue=11|pages=3929–3952|doi=10.1257/aer.20181480|issn=0002-8282}}</ref><br />
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===Strategy for the iterated prisoner's dilemma===<br />
迭代囚徒困境下的策略<br />
Interest in the iterated prisoner's dilemma (IPD) was kindled by [[Robert Axelrod]] in his book ''[[The Evolution of Cooperation]]'' (1984). In it he reports on a tournament he organized of the ''N'' step prisoner's dilemma (with ''N'' fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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Interest in the iterated prisoner's dilemma (IPD) was kindled by Robert Axelrod in his book The Evolution of Cooperation (1984). In it he reports on a tournament he organized of the N step prisoner's dilemma (with N fixed) in which participants have to choose their mutual strategy again and again, and have memory of their previous encounters. Axelrod invited academic colleagues all over the world to devise computer strategies to compete in an IPD tournament. The programs that were entered varied widely in algorithmic complexity, initial hostility, capacity for forgiveness, and so forth.<br />
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罗伯特·阿克塞尔罗德 Robert Axelrod在他的著作《合作的进化》(1984)中激起了人们对迭代囚徒困境(IPD)的兴趣。在这篇文章中,他报道了自己组织的固定N次囚徒困境的比赛,参与者必须一次又一次地选择他们的共同策略,并且要记住他们之前的遭遇。阿克塞尔罗德邀请世界各地的学术界同仁设计计算机策略来参加IPD锦标赛。输入的程序在算法复杂性、最初敌意、宽恕能力等方面有很大差异。<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more [[altruism|altruistic]] strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by [[natural selection]].<br />
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Axelrod discovered that when these encounters were repeated over a long period of time with many players, each with different strategies, greedy strategies tended to do very poorly in the long run while more altruistic strategies did better, as judged purely by self-interest. He used this to show a possible mechanism for the evolution of altruistic behaviour from mechanisms that are initially purely selfish, by natural selection.<br />
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阿克塞尔罗德发现,当这些遭遇长时间在许多玩家身上重复发生时,每个玩家都有不同的策略,从长远来看,贪婪策略往往表现得非常糟糕,而更加利他的策略表现得更好,这完全是根据自身利益来判断的。他利用这一结果揭示了通过自然选择,从最初纯粹自私行为向利他行为进化的可能机制。<br />
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The winning [[deterministic algorithm|deterministic]] strategy was tit for tat, which [[Anatol Rapoport]] developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of [[BASIC]], and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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The winning deterministic strategy was tit for tat, which Anatol Rapoport developed and entered into the tournament. It was the simplest of any program entered, containing only four lines of BASIC, and won the contest. The strategy is simply to cooperate on the first iteration of the game; after that, the player does what his or her opponent did on the previous move. Depending on the situation, a slightly better strategy can be "tit for tat with forgiveness". When the opponent defects, on the next move, the player sometimes cooperates anyway, with a small probability (around 1–5%). This allows for occasional recovery from getting trapped in a cycle of defections. The exact probability depends on the line-up of opponents.<br />
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最终获胜的决定性策略是针锋相对策略,这是阿纳托尔·拉波波特 Anatol Rapoport开发并参加比赛的策略。这是所有参赛程序中最简单的一个,只有四行 BASIC 语言,并且赢得了比赛。策略很简单,就是在游戏的第一次迭代中进行合作; 在此之后,玩家将执行做他的对手在前一步中所做的事情。根据具体情况,一个稍微好一点的策略可以是“带着宽恕之心针锋相对”。当对手叛变时,在下一次博弈中,玩家有时还是会合作,但概率很小(大约1-5%)。这允许博弈偶尔能从陷入叛变循环中恢复过来。确切的概率取决于对手的安排。<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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By analysing the top-scoring strategies, Axelrod stated several conditions necessary for a strategy to be successful.<br />
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通过分析得分最高的战略,阿克塞尔罗德阐述了战略成功的几个必要条件。<br />
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; Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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Nice: The most important condition is that the strategy must be "nice", that is, it will not defect before its opponent does (this is sometimes referred to as an "optimistic" algorithm). Almost all of the top-scoring strategies were nice; therefore, a purely selfish strategy will not "cheat" on its opponent, for purely self-interested reasons first.<br />
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;友好:最重要的条件是策略必须是好的,也就是说,它不会在对手之前叛变(这有时被称为“乐观”算法)。几乎所有得分最高的策略都是友好的; 因此,一个纯粹的自私策略不会为了纯粹自身的利益而“欺骗”对手。<br />
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; Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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Retaliating: However, Axelrod contended, the successful strategy must not be a blind optimist. It must sometimes retaliate. An example of a non-retaliating strategy is Always Cooperate. This is a very bad choice, as "nasty" strategies will ruthlessly exploit such players.<br />
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;报复:然而,阿克塞尔罗德认为,成功的战略决不能是盲目的乐观主义。它有时必须进行报复。非报复策略的一个例子就是永远合作。这是一个非常糟糕的选择,因为“肮脏”的策略会无情地利用这些玩家。<br />
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; Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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Forgiving: Successful strategies must also be forgiving. Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to defect. This stops long runs of revenge and counter-revenge, maximizing points.<br />
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;宽容: 成功的策略也必须是宽容的。虽然玩家会报复,但如果对手不继续叛变,他们将再次回到合作的状态。这阻止了长时间的报复和反报复,最大限度地提高积分。<br />
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; Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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Non-envious: The last quality is being non-envious, that is not striving to score more than the opponent.<br />
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;不嫉妒: 最后一个品质是不嫉妒,不强求比对手得分更多。<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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The optimal (points-maximizing) strategy for the one-time PD game is simply defection; as explained above, this is true whatever the composition of opponents may be. However, in the iterated-PD game the optimal strategy depends upon the strategies of likely opponents, and how they will react to defections and cooperations. For example, consider a population where everyone defects every time, except for a single individual following the tit for tat strategy. That individual is at a slight disadvantage because of the loss on the first turn. In such a population, the optimal strategy for that individual is to defect every time. In a population with a certain percentage of always-defectors and the rest being tit for tat players, the optimal strategy for an individual depends on the percentage, and on the length of the game.<br />
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对于一次性的囚徒困境博弈,最优(点数最大化)策略就是简单的叛变; 正如上面所说,无论对手的构成如何,这都是正确的。然而,在迭代囚徒困境博弈中,最优策略取决于可能的对手的策略,以及他们对叛变和合作的反应。例如,考虑一个群体,其中每个人每次都会叛变,只有一个人遵循针锋相对的策略。那个人就会由于第一回合的失利而处于轻微的不利地位。在这样一个群体中,个体的最佳策略是每次都叛变。在一定比例的总是选择背叛的玩家和其余组成选择针锋相对策略的玩家的人群中,个人的最佳策略取决于这一比例和博弈的次数。<br />
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In the strategy called Pavlov, [[win-stay, lose-switch]], faced with a failure to cooperate, the player switches strategy the next turn.<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref> In certain circumstances,{{specify|date=November 2012}} Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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In the strategy called Pavlov, win-stay, lose-switch, faced with a failure to cooperate, the player switches strategy the next turn. In certain circumstances, Pavlov beats all other strategies by giving preferential treatment to co-players using a similar strategy.<br />
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在所谓的<font color="#ff8000">巴甫洛夫策略 Pavlov strategy</font>中,赢-保持,输-变换,面对一次合作失败,玩家将在下一次变换策略。<ref>http://www.pnas.org/content/pnas/93/7/2686.full.pdf</ref>在某些情况下,{{specify|date=November 2012}}巴甫洛夫通过使用类似策略给与合作者优惠待遇打败了其他所有策略。<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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Deriving the optimal strategy is generally done in two ways:<br />
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得出最佳策略通常有两种方法:<br />
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* [[Bayesian Nash equilibrium]]: If the statistical distribution of opposing strategies can be determined (e.g. 50% tit for tat, 50% always cooperate) an optimal counter-strategy can be derived analytically.{{efn|1=For example see the 2003 study<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref> for discussion of the concept and whether it can apply in real [[economic]] or strategic situations.}}<br />
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<font color="#ff8000">贝叶斯纳什均衡 Bayesian Nash equilibrium</font>:如果可以确定对立策略的统计分布(例如,50%针锋相对,50%总是合作),那么,可以通过分析得出最佳的反策略{{efn|1=例如2003年的研究<ref>{{cite web|url= http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|title=Bayesian Nash equilibrium; a statistical test of the hypothesis|url-status=dead|archive-url= https://web.archive.org/web/20051002195142/http://econ.hevra.haifa.ac.il/~mbengad/seminars/whole1.pdf|archive-date=2005-10-02|publisher=[[Tel Aviv University]]}}</ref>讨论这一概念以及它是否可以应用于实际经济或战略情况。}}<br />
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* [[Monte Carlo method|Monte Carlo]] simulations of populations have been made, where individuals with low scores die off, and those with high scores reproduce (a [[genetic algorithm]] for finding an optimal strategy). The mix of algorithms in the final population generally depends on the mix in the initial population. The introduction of mutation (random variation during reproduction) lessens the dependency on the initial population; empirical experiments with such systems tend to produce tit for tat players (see for instance Chess 1988),{{Clarify|date=August 2016}} but no analytic proof exists that this will always occur.<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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<font color="#ff8000">蒙特卡洛方法 Monte Carlo method </font>已经对种群进行了模拟,分数低的个体死亡,分数高的个体繁殖(<font color="#ff8000">遗传算法 genetic algorithm </font>用于寻找一个最佳策略)。最终群体中的算法组合通常取决于初始总体的组合。引入突变(繁殖过程中的随机变异)可以减少对初始种群的依赖性。使用这种系统进行经验性实验往往会为针锋相对的玩家带来麻烦(见Chess 1988),{{Clarify|date=August 2016}},但是没有分析证据表明这种情况会一直发生。<ref>{{Citation|last=Wu|first=Jiadong|title=Cooperation on the Monte Carlo Rule: Prisoner's Dilemma Game on the Grid|date=2019|work=Theoretical Computer Science|volume=1069|pages=3–15|editor-last=Sun|editor-first=Xiaoming|publisher=Springer Singapore|language=en|doi=10.1007/978-981-15-0105-0_1|isbn=978-981-15-0104-3|last2=Zhao|first2=Chengye|editor2-last=He|editor2-first=Kun|editor3-last=Chen|editor3-first=Xiaoyun}}</ref><br />
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Although tit for tat is considered to be the most [[robust]] basic strategy, a team from [[Southampton University]] in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start.<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref> Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show [[University of Southampton]]'s strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between [[computer program|software strategies]] (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian [[Evolutionarily stable strategy|ESS]] simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. [[Richard Dawkins]] showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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Although tit for tat is considered to be the most robust basic strategy, a team from Southampton University in England introduced a new strategy at the 20th-anniversary iterated prisoner's dilemma competition, which proved to be more successful than tit for tat. This strategy relied on collusion between programs to achieve the highest number of points for a single program. The university submitted 60 programs to the competition, which were designed to recognize each other through a series of five to ten moves at the start. Once this recognition was made, one program would always cooperate and the other would always defect, assuring the maximum number of points for the defector. If the program realized that it was playing a non-Southampton player, it would continuously defect in an attempt to minimize the score of the competing program. As a result, the 2004 Prisoners' Dilemma Tournament results show University of Southampton's strategies in the first three places, despite having fewer wins and many more losses than the GRIM strategy. (In a PD tournament, the aim of the game is not to "win" matches&nbsp;– that can easily be achieved by frequent defection). Also, even without implicit collusion between software strategies (exploited by the Southampton team) tit for tat is not always the absolute winner of any given tournament; it would be more precise to say that its long run results over a series of tournaments outperform its rivals. (In any one event a given strategy can be slightly better adjusted to the competition than tit for tat, but tit for tat is more robust). The same applies for the tit for tat with forgiveness variant, and other optimal strategies: on any given day they might not "win" against a specific mix of counter-strategies. An alternative way of putting it is using the Darwinian ESS simulation. In such a simulation, tit for tat will almost always come to dominate, though nasty strategies will drift in and out of the population because a tit for tat population is penetrable by non-retaliating nice strategies, which in turn are easy prey for the nasty strategies. Richard Dawkins showed that here, no static mix of strategies form a stable equilibrium and the system will always oscillate between bounds.}} this strategy ended up taking the top three positions in the competition, as well as a number of positions towards the bottom.<br />
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尽管针锋相对被认为是最有力的基本策略,来自英格兰南安普敦大学的一个团队在20周年的迭代囚徒困境竞赛中提出了一个新策略,这个策略被证明比针锋相对更为成功。这种策略依赖于程序之间的串通,以获得单个程序的最高分数。这所大学提交了60个程序,这些程序的设计目的是在比赛开始时通过一系列的5到10个动作来互相认识。<ref>{{cite press release|url= http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|publisher=University of Southampton|title=University of Southampton team wins Prisoner's Dilemma competition|date=7 October 2004|url-status=dead|archive-url= https://web.archive.org/web/20140421055745/http://www.southampton.ac.uk/mediacentre/news/2004/oct/04_151.shtml|archive-date=2014-04-21}}</ref>一旦认识建立,一个程序总是合作,另一个程序总是叛变,保证叛变者得到最多的分数。如果这个程序意识到它正在和一个非南安普顿的球员比赛,它会不断地叛变,试图最小化与之竞争的程序的得分。因此,2004年囚徒困境锦标赛的结果显示了南安普敦大学战略位居前三名,尽管它比冷酷战略赢得更少,输的更多。(在囚徒困境锦标赛中,比赛的目的不是“赢”比赛——这一点频繁叛变很容易实现)。此外,即使没有软件策略之间的暗中串通(南安普顿队利用了这一点) ,针锋相对并不总是任何特定锦标赛的绝对赢家; 更准确地说,它是在一系列锦标赛中的长期结果超过了它的竞争对手。(在任何一个事件中,一个给定的策略可以比针锋相对稍微更好地适应竞争,但是针锋相对更稳健)。这同样适用于带有宽恕变量的针锋相对,和其他最佳策略: 在任何特定的一天,他们可能不会“赢得”一个特定的混合反战略。另一种方法是使用达尔文 Darwinian的<font color="#ff8000"> ESS模拟 ESS simulation</font>。在这样的模拟中,针锋相对几乎总是占主导地位,尽管讨厌的策略会在人群中漂移,因为使用针锋相对策略的人群可以通过非报复性的好策略进行渗透,这反过来使他们容易成为讨厌策略的猎物。理查德·道金斯 Richard Dawkins指出,在这里,没有静态的混合策略会形成一个稳定的平衡,系统将始终在边界之间振荡。这种策略最终在比赛中获得了前三名的成绩,或者是接近垫底的成绩。<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of [[minmaxing]]). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book ''[[The Selfish Gene]]'', pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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This strategy takes advantage of the fact that multiple entries were allowed in this particular competition and that the performance of a team was measured by that of the highest-scoring player (meaning that the use of self-sacrificing players was a form of minmaxing). In a competition where one has control of only a single player, tit for tat is certainly a better strategy. Because of this new rule, this competition also has little theoretical significance when analyzing single agent strategies as compared to Axelrod's seminal tournament. However, it provided a basis for analysing how to achieve cooperative strategies in multi-agent frameworks, especially in the presence of noise. In fact, long before this new-rules tournament was played, Dawkins, in his book The Selfish Gene, pointed out the possibility of such strategies winning if multiple entries were allowed, but he remarked that most probably Axelrod would not have allowed them if they had been submitted. It also relies on circumventing rules about the prisoner's dilemma in that there is no communication allowed between the two players, which the Southampton programs arguably did with their opening "ten move dance" to recognize one another; this only reinforces just how valuable communication can be in shifting the balance of the game.<br />
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这种策略利用了这样一个事实,即在这场特殊的比赛中允许多个参赛项目,并且团队的表现由得分最高的项目来衡量(这意味着使用自我牺牲的项目是一种分数最大化的形式)。在一个只能控制一个玩家的比赛中,针锋相对当然是一个更好的策略。由于这一新规则的存在,与阿克塞尔罗德的具有深远影响的竞赛相比,这种竞赛在分析单个主体策略时也就没有什么理论意义。然而,它为在分析多主体框架下,特别是在存在干扰的情况下,如何实现协作策略提供了基础。事实上,早在这场新规则锦标赛开始之前,道金斯就在他的《自私的基因》一书中指出,如果允许多次参赛,这种策略就有可能获胜,但他说,如果提交这种策略的话,阿克塞尔罗德很可能不会允许。因为它依赖于规避囚徒困境的规则,即两个参与者之间不允许交流,南安普顿的项目可以说在开场的“十步舞”中就是这样做以认识对方的; 这只是强调了交流在改变游戏平衡方面的价值。<br />
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===Stochastic iterated prisoner's dilemma===<br />
随机的迭代囚徒困境<br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities".<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref> In an encounter between player ''X'' and player ''Y'', ''X'' 's strategy is specified by a set of probabilities ''P'' of cooperating with ''Y''. ''P'' is a function of the outcomes of their previous encounters or some subset thereof. If ''P'' is a function of only their most recent ''n'' encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that ''X'' will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which ''X'' cooperated and ''Y'' defected, then <math>P_{cd}</math> is the probability that ''X'' will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as ''P''={1,0,1,0}, in which ''X'' responds as ''Y'' did in the previous encounter. Another is the [[win–stay, lose–switch]] strategy written as ''P''={1,0,0,1}, in which ''X'' responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<ref name="Press2012"/><br />
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In a stochastic iterated prisoner's dilemma game, strategies are specified by in terms of "cooperation probabilities". In an encounter between player X and player Y, X 's strategy is specified by a set of probabilities P of cooperating with Y. P is a function of the outcomes of their previous encounters or some subset thereof. If P is a function of only their most recent n encounters, it is called a "memory-n" strategy. A memory-1 strategy is then specified by four cooperation probabilities: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>, where <math>P_{ab}</math> is the probability that X will cooperate in the present encounter given that the previous encounter was characterized by (ab). For example, if the previous encounter was one in which X cooperated and Y defected, then <math>P_{cd}</math> is the probability that X will cooperate in the present encounter. If each of the probabilities are either 1 or 0, the strategy is called deterministic. An example of a deterministic strategy is the tit for tat strategy written as P={1,0,1,0}, in which X responds as Y did in the previous encounter. Another is the win–stay, lose–switch strategy written as P={1,0,0,1}, in which X responds as in the previous encounter, if it was a "win" (i.e. cc or dc) but changes strategy if it was a loss (i.e. cd or dd). It has been shown that for any memory-n strategy there is a corresponding memory-1 strategy which gives the same statistical results, so that only memory-1 strategies need be considered.<br />
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在随机迭代<font color="#ff8000"> 囚徒困境prisoner's dilemma</font>博弈中,策略由“合作概率”来确定。<ref name=Press2012>{{cite journal|last1=Press|first1=WH|last2=Dyson|first2=FJ|title=Iterated Prisoner's Dilemma contains strategies that dominate any evolutionary opponent|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|date=26 June 2012|volume=109|issue=26|pages=10409–13|doi=10.1073/pnas.1206569109|pmid=22615375|pmc=3387070|bibcode=2012PNAS..10910409P}}</ref>在玩家''X''和玩家''Y''之间的遭遇中,''X''‘s的策略由一组与''Y''合作的概率''P''确定,''P''是他们之前遭遇的结果的函数,或者是其中的一些子集。如果''P''只是它们最近遇到次数 ''n''的函数,那么它被称为“记忆-n”策略。我们可以由四个联合概率指定一个记忆-1策略: <math>P=\{P_{cc},P_{cd},P_{dc},P_{dd}\}</math>,其中<math>P_{ab}</math>是在当前遭遇中基于先前联合的概率。如果每个概率都是1或0,这种策略称为确定性策略。确定性策略的一个例子是针锋相对策略,写成 p {1,0,1,0} ,其中 x 的反应和 y 在前一次遭遇中的反应一样。另一种是胜-保持-败-转换策略,它被写成 p {1,0,0,1} ,在这种策略中,如果 x 获得胜利(即:cc 或 dc),x会做出与上一次遭遇一样的反应 ,但如果失败,x会改变策略(即cd 或 dd)。研究表明,对于任何一种记忆-n 策略,存在一个相应的记忆-1策略,这个策略给出相同的统计结果,因此只需要考虑记忆-1策略。<ref name="Press2012"/><br />
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If we define ''P'' as the above 4-element strategy vector of ''X'' and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of ''Y'', a transition matrix ''M'' may be defined for ''X'' whose ''ij'' th entry is the probability that the outcome of a particular encounter between ''X'' and ''Y'' will be ''j'' given that the previous encounter was ''i'', where ''i'' and ''j'' are one of the four outcome indices: ''cc'', ''cd'', ''dc'', or ''dd''. For example, from ''X'' 's point of view, the probability that the outcome of the present encounter is ''cd'' given that the previous encounter was ''cd'' is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for ''Q'' are from ''Y'' 's point of view: a ''cd'' outcome for ''X'' is a ''dc'' outcome for ''Y''.) Under these definitions, the iterated prisoner's dilemma qualifies as a [[stochastic process]] and ''M'' is a [[stochastic matrix]], allowing all of the theory of stochastic processes to be applied.<ref name="Press2012"/><br />
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If we define P as the above 4-element strategy vector of X and <math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math> as the 4-element strategy vector of Y, a transition matrix M may be defined for X whose ij th entry is the probability that the outcome of a particular encounter between X and Y will be j given that the previous encounter was i, where i and j are one of the four outcome indices: cc, cd, dc, or dd. For example, from X 's point of view, the probability that the outcome of the present encounter is cd given that the previous encounter was cd is equal to <math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>. (The indices for Q are from Y 's point of view: a cd outcome for X is a dc outcome for Y.) Under these definitions, the iterated prisoner's dilemma qualifies as a stochastic process and M is a stochastic matrix, allowing all of the theory of stochastic processes to be applied.<br />
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如果我们将''P''定义为''X''的上述4元策略向量,并将<math>Q=\{Q_{cc},Q_{cd},Q_{dc},Q_{dd}\}</math>定义为''Y''的4元策略向量,则对于''X''可以定义一个转移矩阵''M'',其第ij项是''X''和''Y''之间特定相遇的结果为j的概率,给定i,其中i和j是cc、cd、dc或dd 四个结果索引中的一个。例如,从''X''的角度来看,如果给定''cd'',那么这次的结果是''cd''的概率等于<math>M_{cd,cd}=P_{cd}(1-Q_{dc})</math>。(''Q''的指标是 从''Y''的角度: ''X''的''cd''结果是''Y''的''dc''结果)在这些定义下,重复的囚徒困境被定义为一个随机过程,''M''是一个随机矩阵,允许应用所有的随机过程理论。<ref name="Press2012"/><br />
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One result of stochastic theory is that there exists a stationary vector ''v'' for the matrix ''M'' such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that ''v'' is normalized so that the sum of its four components is unity. The ''ij'' th entry in <math>M^n</math> will give the probability that the outcome of an encounter between ''X'' and ''Y'' will be ''j'' given that the encounter ''n'' steps previous is ''i''. In the limit as ''n'' approaches infinity, ''M'' will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing ''j'' which will be independent of ''i''. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that ''v'' is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to ''v''. Thus the stationary vector specifies the equilibrium outcome probabilities for ''X''. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From ''X'' 's point of view), the equilibrium payoffs for ''X'' and ''Y'' can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.<br />
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One result of stochastic theory is that there exists a stationary vector v for the matrix M such that <math>v\cdot M=v</math>. Without loss of generality, it may be specified that v is normalized so that the sum of its four components is unity. The ij th entry in <math>M^n</math> will give the probability that the outcome of an encounter between X and Y will be j given that the encounter n steps previous is i. In the limit as n approaches infinity, M will converge to a matrix with fixed values, giving the long-term probabilities of an encounter producing j which will be independent of i. In other words, the rows of <math>M^\infty</math> will be identical, giving the long-term equilibrium result probabilities of the iterated prisoners dilemma without the need to explicitly evaluate a large number of interactions. It can be seen that v is a stationary vector for <math>M^n</math> and particularly <math>M^\infty</math>, so that each row of <math>M^\infty</math> will be equal to v. Thus the stationary vector specifies the equilibrium outcome probabilities for X. Defining <math>S_x=\{R,S,T,P\}</math> and <math>S_y=\{R,T,S,P\}</math> as the short-term payoff vectors for the {cc,cd,dc,dd} outcomes (From X 's point of view), the equilibrium payoffs for X and Y can now be specified as <math>s_x=v\cdot S_x</math> and <math>s_y=v\cdot S_y</math>, allowing the two strategies P and Q to be compared for their long term payoffs.<br />
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随机理论的一个结果是,矩阵''M''存在一个平稳向量''v''使得<math>v\cdot M=v</math>成立。一般地,我们可以指定''v''是标准化的,因此它的4个组成部分之和为1。the equilibrium payoffs for and can now be specified as and, allowing the two strategies ''P'' and ''Q'' to be compared for their long term payoffs.第''ij''项<math>M^n</math>给出了''X''和''Y''相遇的结果的概率为''j'',给定前面相遇''n''步的概率是''i''。当''n''趋于无穷时,''M''收敛于一个具有固定值的矩阵,并且''j''趋向一个长期概率,与''i''独立。换句话说, <math>M^\infty</math>的行将是相同的,从而给出了重复囚徒困境的长期均衡结果概率,而不需要明确地计算大量的相互作用。可以看出,''v''是<math>M^n</math>特别是<math>M^\infty</math>, 的平稳向量,因此<math>M^\infty</math>的每一行都等于''v''。因此平稳向量指定了''X''的均衡结果概率。定义<math>S_x=\{R,S,T,P\}</math>和<math>S_y=\{R,T,S,P\}</math>作为{cc,cd,dc,dd}结果的短期收益向量(从''X''的角度来看) ,现在可以将''X''和''Y''的均衡收益指定为<math>s_x=v\cdot S_x</math>和<math>s_y=v\cdot S_y</math>,使得''P''、''Q''两种策略的长期收益可以比较。<br />
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====Zero-determinant strategies====<br />
<font color="#ff8000">零决定策略 Zero-determinant strategies</font><br />
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[[File:IPD Venn.svg|right|thumb|upright=2.5|The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram]]. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and [[weak selection]]. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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The relationship between zero-determinant (ZD), cooperating and defecting strategies in the iterated prisoner's dilemma (IPD) illustrated in a [[Venn diagram. Cooperating strategies always cooperate with other cooperating strategies, and defecting strategies always defect against other defecting strategies. Both contain subsets of strategies that are robust under strong selection, meaning no other memory-1 strategy is selected to invade such strategies when they are resident in a population. Only cooperating strategies contain a subset that are always robust, meaning that no other memory-1 strategy is selected to invade and replace such strategies, under both strong and weak selection. The intersection between ZD and good cooperating strategies is the set of generous ZD strategies. Extortion strategies are the intersection between ZD and non-robust defecting strategies. Tit-for-tat lies at the intersection of cooperating, defecting and ZD strategies.]]<br />
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<font color="#ff8000">维恩图 Venn diagram</font>中讨论了<font color="#ff8000">迭代囚徒困境 iterated prisoner's dilemma</font>(IPD)中零决定策略(ZD)、合作策略和背叛策略之间的关系。合作策略总是与其他合作策略相互配合,而背叛策略总是与其他背叛策略相抵触。这两种策略都包都含在强选择下稳健的策略子集,这意味着当它们驻留在一个种群中时,没有选择其他的记忆-1策略来入侵此策略。只有合作策略包含在始终稳健的策略子集,意味着无论选择强项还是弱项,都不会选择其他任何记忆-1策略来入侵和替换此策略。零决定策略和良好的合作策略之间的交集是一组宽松的零决定策略。勒索策略是零决定策略和非稳健背叛策略的交集。针锋相对是合作、背叛和零决定策略的交集。<br />
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In 2012, [[William H. Press]] and [[Freeman Dyson]] published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies.<ref name="Press2012"/> The long term payoffs for encounters between ''X'' and ''Y'' can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector ''v''. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in ''f'', it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where ''U''={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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In 2012, William H. Press and Freeman Dyson published a new class of strategies for the stochastic iterated prisoner's dilemma called "zero-determinant" (ZD) strategies. The long term payoffs for encounters between X and Y can be expressed as the determinant of a matrix which is a function of the two strategies and the short term payoff vectors: <math>s_x=D(P,Q,S_x)</math> and <math>s_y=D(P,Q,S_y)</math>, which do not involve the stationary vector v. Since the determinant function <math>s_y=D(P,Q,f)</math> is linear in f, it follows that <math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math> (where U={1,1,1,1}). Any strategies for which <math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math> is by definition a ZD strategy, and the long term payoffs obey the relation <math>\alpha s_x+\beta s_y+\gamma=0</math>.<br />
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2012年,威廉·H·普莱斯 William H. Press和弗里曼·戴森 Freeman Dyson针对随机迭代囚徒困境提出了一类新的策略,称为“零决定”策略。<ref name="Press2012"/>''X''和''Y''之间的长期收益可以表示为一个矩阵的决定因素,它是两个策略和短期收益向量的函数: <math>s_x=D(P,Q,S_x)</math>和<math>s_y=D(P,Q,S_y)</math>,不涉及平稳向量''v''。 由于行列式函数<math>s_y=D(P,Q,f)</math>在''f''中是线性的,因此可以推出<math>\alpha s_x+\beta s_y+\gamma=D(P,Q,\alpha S_x+\beta S_y+\gamma U)</math>(其中''U''={1,1,1,1})。任何策略的<math>D(P,Q,\alpha S_x+\beta S_y+\gamma U)=0</math>被定义为零决定策略,长期收益服从关系式<math>\alpha s_x+\beta s_y+\gamma=0</math>。<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of [[ultimatum game]]. Specifically, ''X'' is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of ''Y'' 's strategy, offering an opportunity for ''X'' to "extort" player ''Y'' (and vice versa). (It turns out that if ''X'' tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.<ref name="Press2012"/>)<br />
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Tit-for-tat is a ZD strategy which is "fair" in the sense of not gaining advantage over the other player. However, the ZD space also contains strategies that, in the case of two players, can allow one player to unilaterally set the other player's score or alternatively, force an evolutionary player to achieve a payoff some percentage lower than his own. The extorted player could defect but would thereby hurt himself by getting a lower payoff. Thus, extortion solutions turn the iterated prisoner's dilemma into a sort of ultimatum game. Specifically, X is able to choose a strategy for which <math>D(P,Q,\beta S_y+\gamma U)=0</math>, unilaterally setting <math>s_y</math> to a specific value within a particular range of values, independent of Y 's strategy, offering an opportunity for X to "extort" player Y (and vice versa). (It turns out that if X tries to set <math>s_x</math> to a particular value, the range of possibilities is much smaller, only consisting of complete cooperation or complete defection.)<br />
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针锋相对是一种零决定策略,在不获得超越其他玩家优势的意义下是“公平”的。然而,零决定策略空间还包含这样的策略:在两个玩家的情况下,可以允许一个玩家单方面设置另一个玩家的分数,或者强迫进化的玩家获得比他自己的分数低一些的收益。被勒索的玩家可能会背叛,但会因此获得较低的回报并且受到伤害。因此,勒索的解决方案将迭代囚徒困境转化为一种<font color="#ff8000">最后通牒博弈 ultimatum game </font>。具体来说,''X''能够选择一种策略,对于这种策略,<math>D(P,Q,\beta S_y+\gamma U)=0</math>单方面地将<math>s_y</math>设置为一个特定值范围内的特定值,与''Y''的策略无关,为''X''提供了“勒索”玩家''Y''的机会(反之亦然)。(事实证明,如果''X''试图将<math>s_x</math>设置为一个特定的值,那么可能的范围要小得多,只包括完全合作或完全叛变。<ref name="Press2012"/>)<br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not [[evolutionarily stable strategy|evolutionarily stable]]. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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An extension of the IPD is an evolutionary stochastic IPD, in which the relative abundance of particular strategies is allowed to change, with more successful strategies relatively increasing. This process may be accomplished by having less successful players imitate the more successful strategies, or by eliminating less successful players from the game, while multiplying the more successful ones. It has been shown that unfair ZD strategies are not evolutionarily stable. The key intuition is that an evolutionarily stable strategy must not only be able to invade another population (which extortionary ZD strategies can do) but must also perform well against other players of the same type (which extortionary ZD players do poorly, because they reduce each other's surplus).<br />
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迭代囚徒困境的一个扩展是进化的随机迭代囚徒困境,其中允许特定策略的相对丰度改变,更成功的策略相对增加。这个过程可以通过让不太成功的玩家模仿更成功的策略,或者通过从游戏中淘汰不太成功的玩家,同时让更成功的玩家成倍增加。研究表明,不公平的零决定策略不是进化稳定策略。关键的直觉告诉我们,进化稳定策略不仅要能够入侵另一个群体(这是勒索零决定策略可以做到的) ,而且还要在同类型的其他玩家面前表现良好(勒索零决定策略玩家表现不佳,因为他们减少了彼此的盈余)。<ref>{{cite journal|last=Adami|first=Christoph|author2=Arend Hintze|title=Evolutionary instability of Zero Determinant strategies demonstrates that winning isn't everything|journal=Nature Communications|volume=4|year=2013|page=3|arxiv=1208.2666|doi=10.1038/ncomms3193|pmid=23903782|pmc=3741637|bibcode=2013NatCo...4.2193A}}</ref><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and [[win–stay, lose–switch]] agents.<ref name=Hilbe2013 /><br />
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Theory and simulations confirm that beyond a critical population size, ZD extortion loses out in evolutionary competition against more cooperative strategies, and as a result, the average payoff in the population increases when the population is larger. In addition, there are some cases in which extortioners may even catalyze cooperation by helping to break out of a face-off between uniform defectors and win–stay, lose–switch agents.<br />
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理论和模拟证实,超过一个临界种群规模,零决定勒索在与更多合作策略的进化竞争中会失败,因此,种群越大,种群的平均收益就越大。此外,在某些情况下,勒索者甚至可能通过帮助打破统一的背叛者与使用“赢-保持-输”策略的转换玩家之间的对峙而促进合作。<ref name=Hilbe2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies ''is'' both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the [[Prisoner's dilemma#Special case: Donation game|donation game]] by Alexander Stewart and Joshua Plotkin in 2013.<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref> Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013)<ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<ref name=Stewart2013 /><br />
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While extortionary ZD strategies are not stable in large populations, another ZD class called "generous" strategies is both stable and robust. In fact, when the population is not too small, these strategies can supplant any other ZD strategy and even perform well against a broad array of generic strategies for iterated prisoner's dilemma, including win–stay, lose–switch. This was proven specifically for the donation game by Alexander Stewart and Joshua Plotkin in 2013. Generous strategies will cooperate with other cooperative players, and in the face of defection, the generous player loses more utility than its rival. Generous strategies are the intersection of ZD strategies and so-called "good" strategies, which were defined by Akin (2013) to be those for which the player responds to past mutual cooperation with future cooperation and splits expected payoffs equally if he receives at least the cooperative expected payoff. Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.<br />
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虽然勒索零决定策略在人口众多的情况下并不稳定,但另一种宽松的零决定策略既稳定又稳健。事实上,当人口不算太少的时候,这些策略可以取代任何其他零决定策略,甚至在一系列针对迭代囚徒困境的广泛通用策略(包括“获胜-保持-输”的转换策略)中表现良好。亚历山大·斯图尔特 Alexander Stewart和约书亚·普洛特金 Joshua Plotkin在2013年的捐赠博弈中证明了这一点。<ref name=Stewart2013>{{cite journal|last=Stewart|first=Alexander J.|author2=Joshua B. Plotkin|title=From extortion to generosity, evolution in the Iterated Prisoner's Dilemma|journal=[[Proceedings of the National Academy of Sciences of the United States of America]]|year=2013|doi=10.1073/pnas.1306246110|pmid=24003115|volume=110|issue=38|pages=15348–53|bibcode=2013PNAS..11015348S|pmc=3780848}}</ref>宽松的策略会与其他合作的玩家合作,面对背叛,慷慨的玩家比他的对手失去更多的效用。宽松策略是零决定策略和所谓的“好”策略的交集,阿金(2013) <ref name=Akin2013>{{cite arxiv|last=Akin|first=Ethan|title=Stable Cooperative Solutions for the Iterated Prisoner's Dilemma|year=2013|page=9|class=math.DS|eprint=1211.0969}} {{bibcode|2012arXiv1211.0969A}}</ref> Among good strategies, the generous (ZD) subset performs well when the population is not too small. If the population is very small, defection strategies tend to dominate.将这两种策略定义为玩家对过去的相互合作作出回应,并在至少获得合作预期收益的情况下平均分配预期收益的策略。在好的策略中,当总体不太小时,宽松(零决定)子集表现良好。如果总体很少,背叛策略往往占主导地位。<ref name=Stewart2013 /><br />
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===Continuous iterated prisoner's dilemma===<br />
<font color="#ff8000">连续迭代囚徒困境 Continuous iterated prisoner's dilemma </font> <br />
Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref> found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from [[Assortative mating|assorting]] with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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Most work on the iterated prisoner's dilemma has focused on the discrete case, in which players either cooperate or defect, because this model is relatively simple to analyze. However, some researchers have looked at models of the continuous iterated prisoner's dilemma, in which players are able to make a variable contribution to the other player. Le and Boyd found that in such situations, cooperation is much harder to evolve than in the discrete iterated prisoner's dilemma. The basic intuition for this result is straightforward: in a continuous prisoner's dilemma, if a population starts off in a non-cooperative equilibrium, players who are only marginally more cooperative than non-cooperators get little benefit from assorting with one another. By contrast, in a discrete prisoner's dilemma, tit for tat cooperators get a big payoff boost from assorting with one another in a non-cooperative equilibrium, relative to non-cooperators. Since nature arguably offers more opportunities for variable cooperation rather than a strict dichotomy of cooperation or defection, the continuous prisoner's dilemma may help explain why real-life examples of tit for tat-like cooperation are extremely rare in nature (ex. Hammerstein<ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)<br />
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关于迭代囚徒困境的研究大多集中在离散情况下,在这种情况下,参与者要么合作,要么背叛,因为这个模型分析起来比较简单。然而,一些研究人员已经研究了连续迭代囚徒困境模型,在这个模型中,玩家能够对另一个玩家做出可变的贡献。乐 Le和博伊德 Boyd<ref>{{cite journal | last1 = Le | first1 = S. | last2 = Boyd | first2 = R. |name-list-format=vanc| year = 2007 | title = Evolutionary Dynamics of the Continuous Iterated Prisoner's Dilemma | url = | journal = Journal of Theoretical Biology | volume = 245 | issue = 2| pages = 258–67 | doi = 10.1016/j.jtbi.2006.09.016 | pmid = 17125798 }}</ref>发现,在这种情况下,合作比离散迭代的囚徒困境更难发展。这个结果的基本直觉很简单: 在一个持续的囚徒困境中,如果一个人群开始处于非合作均衡状态,那么与非合作者相比,合作程度稍高的玩家不会从相互配合中获益。相比之下,在离散的囚徒困境中,相对于非合作者,针锋相对的合作者在非合作均衡中相互配合会获得巨大的回报。由于自然界可以提供更多的机会来进行各种各样的合作,而不是严格地将合作或背叛分为两类,因此连续的囚徒困境可以帮助解释为什么现实生活中针锋相对的合作的例子在自然界中极其罕见。(例如,哈默斯坦 Hammerstein <ref>Hammerstein, P. (2003). Why is reciprocity so rare in social animals? A protestant appeal. In: P. Hammerstein, Editor, Genetic and Cultural Evolution of Cooperation, MIT Press. pp. 83–94. </ref>)。<br />
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even though tit for tat seems robust in theoretical models.<br />
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even though tit for tat seems robust in theoretical models.<br />
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尽管在理论模型中,针锋相对策略似乎是稳健的。<br />
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===Emergence of stable strategies===<br />
<font color="#ff8000">稳定策略的出现 Emergence of stable strategies </font> <br />
Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies.<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref> Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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Players cannot seem to coordinate mutual cooperation, thus often get locked into the inferior yet stable strategy of defection. In this way, iterated rounds facilitate the evolution of stable strategies. Iterated rounds often produce novel strategies, which have implications to complex social interaction. One such strategy is win-stay lose-shift. This strategy outperforms a simple Tit-For-Tat strategy&nbsp;– that is, if you can get away with cheating, repeat that behavior, however if you get caught, switch.<br />
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玩家似乎不能协调相互合作,因此常常陷入劣等而稳定的背叛策略。这样,迭代回合可以促进稳定策略的发展。<ref>{{cite book|last=Spaniel|first=William|title=Game Theory 101: The Complete Textbook|year=2011}}</ref>迭代回合往往产生新颖的策略,这对复杂的社会互动有影响。其中一个策略就是“赢-保持-输”的转变。这个策略比一个简单的针锋相对策略要好&nbsp;–也就是说,如果你能逃脱作弊的惩罚,就重复这个行为,如果你被抓住了,就改变策略。<ref>{{cite journal|last=Nowak|first=Martin|author2=Karl Sigmund|title=A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game|journal=Nature|year=1993|volume=364|issue=6432|doi=10.1038/364056a0|pages=56–58|pmid=8316296|bibcode=1993Natur.364...56N}}</ref><br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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The only problem of this tit-for-tat strategy is that they are vulnerable to signal error. The problem arises when one individual cheats in retaliation but the other interprets it as cheating. As a result of this, the second individual now cheats and then it starts a see-saw pattern of cheating in a chain reaction.<br />
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这种针锋相对策略的唯一问题是它们很容易出现信号错误。当一个人因报复而作弊,而另一个人将其单纯解释为欺骗时,就会出现问题。结果,第二个人现在作弊,然后在接下来的连锁反应中开始了反复交替的作弊模式。<br />
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==Real-life examples==<br />
现实生活的例子<br />
The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the [[social science]]s such as [[economics]], [[politics]], and [[sociology]], as well as to the biological sciences such as [[ethology]] and [[evolutionary biology]]. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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The prisoner setting may seem contrived, but there are in fact many examples in human interaction as well as interactions in nature that have the same payoff matrix. The prisoner's dilemma is therefore of interest to the social sciences such as economics, politics, and sociology, as well as to the biological sciences such as ethology and evolutionary biology. Many natural processes have been abstracted into models in which living beings are engaged in endless games of prisoner's dilemma. This wide applicability of the PD gives the game its substantial importance.<br />
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囚犯的环境似乎是人为的,但实际上,在人类交往以及自然界的交互中有许多具有相同收益矩阵的例子。因此,囚徒困境是经济学、政治学、社会学等社会科学以及动物行为学、进化生物学等生物学研究的热点问题。许多自然过程都被抽象为生物进行无休止的囚徒困境博弈的模型。囚徒困境这种广泛的适用性让博弈变得非常重要。<br />
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===Environmental studies===<br />
环境研究<br />
In [[environmental studies]], the PD is evident in crises such as global [[climate change|climate-change]]. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb [[Carbon dioxide|{{Co2}}]] emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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In environmental studies, the PD is evident in crises such as global climate-change. It is argued all countries will benefit from a stable climate, but any single country is often hesitant to curb Carbon dioxide| emissions. The immediate benefit to any one country from maintaining current behavior is wrongly perceived to be greater than the purported eventual benefit to that country if all countries' behavior was changed, therefore explaining the impasse concerning climate-change in 2007.<br />
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在环境研究中,囚徒困境在诸如全球气候变化等危机中显而易见。有人认为,所有国家都将从稳定的气候中受益,但是每一个国家通常都在限制二氧化碳排放方面犹豫不决。人们错误地认为,如果所有国家的行为都改变,任何一个国家保持目前的行为所带来的直接好处都会大于所谓的最终好处,这就解释了2007年气候变化方面的僵局。<ref>{{cite news|newspaper=[[The Economist]]|url=http://www.economist.com/finance/displaystory.cfm?story_id=9867020|title=Markets & Data|date=2007-09-27}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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An important difference between climate-change politics and the prisoner's dilemma is uncertainty; the extent and pace at which pollution can change climate is not known. The dilemma faced by government is therefore different from the prisoner's dilemma in that the payoffs of cooperation are unknown. This difference suggests that states will cooperate much less than in a real iterated prisoner's dilemma, so that the probability of avoiding a possible climate catastrophe is much smaller than that suggested by a game-theoretical analysis of the situation using a real iterated prisoner's dilemma.<br />
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气候变化政治与囚徒困境之间的一个重要区别是不确定性; 污染对气候变化的影响程度和速度尚不清楚。因此,政府面临的困境不同于囚徒困境,因为合作的回报是未知的。这种差异表明,各国之间的合作远远少于真正的迭代囚徒困境中的合作,因此避免可能发生的气候灾难的可能性远远小于使用真正的迭代囚徒困境博弈论情景分析<ref>{{cite web|last=Rehmeyer|first=Julie|title=Game theory suggests current climate negotiations won't avert catastrophe|url=https://www.sciencenews.org/article/game-theory-suggests-current-climate-negotiations-won%E2%80%99t-avert-catastrophe|work=Science News|publisher=Society for Science & the Public|date=2012-10-29}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of [[Michael Porter]]'s hypothesis, in which government regulation of competing firms is substantial.<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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Osang and Nandy (2003) provide a theoretical explanation with proofs for a regulation-driven win-win situation along the lines of Michael Porter's hypothesis, in which government regulation of competing firms is substantial.<br />
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欧桑 Osang和南迪 Nandy (2003)提供了一个理论解释,并根据迈克尔·波特 Michael Porter的假设,即政府对竞争企业的监管是实质性的,证明了监管驱动的双赢局面。<ref>{{cite thesis|type=paper|url= http://faculty.smu.edu/tosang/pdf/regln0803.pdf|first=Thomas|last=Osang|first2=Arundhati|last2=Nandyyz|date=August 2003|title=Environmental Regulation of Polluting Firms: Porter's Hypothesis Revisited}}</ref><br />
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===Animals===<br />
动物<br />
Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, [[guppy|guppies]] inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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Cooperative behavior of many animals can be understood as an example of the prisoner's dilemma. Often animals engage in long term partnerships, which can be more specifically modeled as iterated prisoner's dilemma. For example, guppies inspect predators cooperatively in groups, and they are thought to punish non-cooperative inspectors.<br />
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许多动物的合作行为可以理解为囚徒困境的一个例子。通常动物会建立长期的伙伴关系,这种关系可以更具体地模拟为迭代囚徒困境。例如,孔雀鱼成群结队地合作监察捕食者,它们被认为是在惩罚不合作的监察者。<br />
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[[Vampire bats]] are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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Vampire bats are social animals that engage in reciprocal food exchange. Applying the payoffs from the prisoner's dilemma can help explain this behavior:<br />
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吸血蝙蝠是从事相互的食物交换的群居动物。应用囚徒困境收益可以帮助解释这种行为: <ref>{{cite book|last=Dawkins|first=Richard|title=The Selfish Gene|year=1976|publisher=Oxford University Press}}</ref><br />
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* C/C: "Reward: I get blood on my unlucky nights, which saves me from starving. I have to give blood on my lucky nights, which doesn't cost me too much."<br />
* 合作/合作:"回报:我在不幸运的晚上得到了能让我果腹的血,那在幸运的晚上我也应该分出点血,那不会花费多少。"<br />
* D/C: "Temptation: You save my life on my poor night. But then I get the added benefit of not having to pay the slight cost of feeding you on my good night."<br />
* 背叛/合作:"诱惑:你在我的不幸的夜里救了我,但在我的幸运夜我不会给你血,那样我会活的更好。"<br />
* C/D: "Sucker's Payoff: I pay the cost of saving your life on my good night. But on my bad night you don't feed me and I run a real risk of starving to death."<br />
* 合作/叛变:"可怜者的回报:在我的幸运夜我救了你的命,但在我的不幸夜里你没有救我,我有饿死的风险。"<br />
* D/D: "Punishment: I don't have to pay the slight costs of feeding you on my good nights. But I run a real risk of starving on my poor nights."<br />
* 叛变/叛变:"惩罚:我在我的幸运夜里不必付出代价来救你,但我在我的不幸夜里有挨饿的风险。"<br />
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===Psychology===<br />
心理学<br />
In [[addiction]] research / [[behavioral economics]], [[George Ainslie (psychologist)|George Ainslie]] points out<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref> that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, ''defecting'' means ''relapsing'', and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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In addiction research / behavioral economics, George Ainslie points out that addiction can be cast as an intertemporal PD problem between the present and future selves of the addict. In this case, defecting means relapsing, and it is easy to see that not defecting both today and in the future is by far the best outcome. The case where one abstains today but relapses in the future is the worst outcome&nbsp;– in some sense the discipline and self-sacrifice involved in abstaining today have been "wasted" because the future relapse means that the addict is right back where he started and will have to start over (which is quite demoralizing, and makes starting over more difficult). Relapsing today and tomorrow is a slightly "better" outcome, because while the addict is still addicted, they haven't put the effort in to trying to stop. The final case, where one engages in the addictive behavior today while abstaining "tomorrow" will be familiar to anyone who has struggled with an addiction. The problem here is that (as in other PDs) there is an obvious benefit to defecting "today", but tomorrow one will face the same PD, and the same obvious benefit will be present then, ultimately leading to an endless string of defections.<br />
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在成瘾研究/行为经济学中,乔治·安斯利 George Ainslie指出<ref>{{cite book |first=George|last=Ainslie |title=Breakdown of Will |year=2001 |isbn=978-0-521-59694-7}}</ref>,可以将成瘾视为成瘾者现在和未来自我之间的跨期囚徒困境问题。在这种情况下,背叛意味着复发,很容易看出,目前和未来都没有背叛是迄今为止最好的结果。如果一个人今天戒了,但在将来又复吸,这是最糟糕的结果&nbsp;–从某种意义上来说,今天戒瘾所包含的纪律和自我牺牲已经被“浪费”了,因为未来的复吸意味着瘾君子又回到了他开始的地方,他将被迫重新开始(这相当令人沮丧,也使得重新开始更加困难)。今天和明天复发是一个稍微“好一点”的结果,因为尽管瘾君子仍然上瘾,但他们没有努力去尝试停止。最后一种情况是,现在与成瘾斗争的任何人都会熟悉现在的成瘾行为,而在明天放弃。这里的问题是(和其他囚徒困境问题一样),背叛“今天”有一个明显的好处,但明天这个人将面临同样的囚徒困境问题,同样明显的好处是背叛,最终导致一连串无休止的背叛。<br />
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[[John Gottman]] in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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John Gottman in his research described in "the science of trust" defines good relationships as those where partners know not to enter the (D,D) cell or at least not to get dynamically stuck there in a loop.<br />
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约翰·高特曼 John Gottman在他的研究《信任的科学》中将良好的关系定义为伙伴知道不进入(背叛,背叛)牢房中或者至少不要陷入这样的动态循环关系中。<br />
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===Economics===<br />
经济学<br />
The prisoner's dilemma has been called the ''[[Escherichia coli|E. coli]]'' of social psychology, and it has been used widely to research various topics such as [[Oligopoly|oligopolistic]] competition and collective action to produce a collective good.<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref> <br />
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The prisoner's dilemma has been called the E. coli of social psychology, and it has been used widely to research various topics such as oligopolistic competition and collective action to produce a collective good. <br />
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囚徒困境被称为社会心理学中的“大肠杆菌”,它被广泛用于研究寡头垄断竞争和集体行动来产生集体利益等问题。<ref>{{Cite journal|last=Axelrod|first=Robert|date=1980|title=Effective Choice in the Prisoner's Dilemma|journal=The Journal of Conflict Resolution|volume=24|issue=1|pages=3–25|issn=0022-0027|jstor=173932|doi=10.1177/002200278002400101|url=https://semanticscholar.org/paper/fd1ab82470446bfb12c39f0c577644291027cf76}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When [[cigarette advertising]] was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. <ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref> This analysis is likely to be pertinent in many other business situations involving advertising. <ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref><br />
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Advertising is sometimes cited as a real-example of the prisoner's dilemma. When cigarette advertising was legal in the United States, competing cigarette manufacturers had to decide how much money to spend on advertising. The effectiveness of Firm A's advertising was partially determined by the advertising conducted by Firm B. Likewise, the profit derived from advertising for Firm B is affected by the advertising conducted by Firm A. If both Firm A and Firm B chose to advertise during a given period, then the advertisement from each firm negates the other's, receipts remain constant, and expenses increase due to the cost of advertising. Both firms would benefit from a reduction in advertising. However, should Firm B choose not to advertise, Firm A could benefit greatly by advertising. Nevertheless, the optimal amount of advertising by one firm depends on how much advertising the other undertakes. As the best strategy is dependent on what the other firm chooses there is no dominant strategy, which makes it slightly different from a prisoner's dilemma. The outcome is similar, though, in that both firms would be better off were they to advertise less than in the equilibrium. Sometimes cooperative behaviors do emerge in business situations. For instance, cigarette manufacturers endorsed the making of laws banning cigarette advertising, understanding that this would reduce costs and increase profits across the industry. This analysis is likely to be pertinent in many other business situations involving advertising.<br />
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广告有时被认为是囚徒困境的一个真实例子。当香烟广告在美国是合法的时候,相互竞争的香烟制造商必须决定在广告上花多少钱。公司A的广告效果部分取决于公司B的广告效果。同样,公司B的广告带来的利润也受到公司A的广告影响。如果公司A和公司B都选择在给定的时间段内做广告,那么一家公司的广告就会抵消另一方的广告,倘若收入保持不变,费用就会因广告成本而增加。两家公司都将从广告减少中获益。然而,如果B公司选择不做广告,A公司就可以通过广告获得巨大的利益。尽管如此,一家公司的最佳广告数量仍取决于另一家公司的广告投放量。由于最佳策略取决于其他公司的选择,因此这里没有占主导地位的策略,这使得它与囚徒困境略有不同。但结果是相似的,如果两家公司的广告都少于均衡状态,他们的处境会更好。有时合作行为确实会在商业环境中出现。例如,香烟制造商支持立法禁止香烟广告,因为这将降低成本并增加整个行业的利润。<ref>{{Citation needed|reason=This reference doesn't mention or support the claimed historical account.|date=December 2012}}</ref><ref>{{efn|1=This argument for the development of cooperation through trust is given in ''[[The Wisdom of Crowds]]'', where it is argued that long-distance [[capitalism]] was able to form around a nucleus of [[Religious Society of Friends|Quakers]], who always dealt honourably with their business partners. (Rather than defecting and reneging on promises&nbsp;– a phenomenon that had discouraged earlier long-term unenforceable overseas contracts). It is argued that dealings with reliable merchants allowed the [[meme]] for cooperation to spread to other traders, who spread it further until a high degree of cooperation became a profitable strategy in general [[commerce]]}} </ref>这种分析可能适用于许多其他涉及广告的商业情况。<ref>{{Citation needed|reason=This doesn't sound like cooperation|date=November 2012}}</ref> <br />
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Without enforceable agreements, members of a [[cartel]] are also involved in a (multi-player) prisoner's dilemma.<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. [[Anti-trust]] authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for [[consumer]]s.<br />
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Without enforceable agreements, members of a cartel are also involved in a (multi-player) prisoner's dilemma. 'Cooperating' typically means keeping prices at a pre-agreed minimum level. 'Defecting' means selling under this minimum level, instantly taking business (and profits) from other cartel members. Anti-trust authorities want potential cartel members to mutually defect, ensuring the lowest possible prices for consumers.<br />
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没有可强制执行的协议,卡特尔 cartel的成员国也会陷入(多玩家)囚徒困境。<ref>{{Cite book|last1=Nicholson|first=Walter|year=2000|title=Intermediate microeconomics and its application|edition=8th|location=Fort Worth, TX|publisher=Dryden Press : Harcourt College Publishers|isbn=978-0-030-25916-6}}</ref> “合作”通常意味着将价格保持在预先商定的最低水平。“背叛”意味着低于最低价格水平销售,并立即从其他卡特尔成员那里获得业务(和利润)。反垄断机构希望潜在的卡特尔成员相互背叛,确保消费者获得尽可能低的价格。<br />
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===Sport===<br />
运动<br />
[[Doping in sport]] has been cited as an example of a prisoner's dilemma.<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Doping in sport has been cited as an example of a prisoner's dilemma.<br />
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体育运动中的兴奋剂被认为是囚徒困境的一个例子。<ref name="wired">{{cite journal|last=Schneier |first=Bruce |url=https://www.wired.com/opinion/2012/10/lance-armstrong-and-the-prisoners-dilemma-of-doping-in-professional-sports/ |title=Lance Armstrong and the Prisoners' Dilemma of Doping in Professional Sports &#124; Wired Opinion |journal=Wired |publisher=Wired.com |date=2012-10-26 |accessdate=2012-10-29}}</ref><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<ref name="wired" /><br />
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Two competing athletes have the option to use an illegal and/or dangerous drug to boost their performance. If neither athlete takes the drug, then neither gains an advantage. If only one does, then that athlete gains a significant advantage over their competitor, reduced by the legal and/or medical dangers of having taken the drug. If both athletes take the drug, however, the benefits cancel out and only the dangers remain, putting them both in a worse position than if neither had used doping.<br />
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两名参赛运动员可以选择使用非法或危险药物来提高成绩。如果两个运动员都没有服用这种药物,那么他们都不会获得优势。如果只有一个人这样做,那么这个运动员就比他们的竞争对手获得了明显的优势,但由于法律或服用药物的医疗风险,这种优势会减少。然而,如果两名运动员都服用了这种药物,那么好处就被抵消了,只剩下风险,这使得他们的处境比没有服用兴奋剂的情况更加糟糕。<ref name="wired" /><br />
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===International politics===<br />
国际政治<br />
In [[international politics|international political theory]], the Prisoner's Dilemma is often used to demonstrate the coherence of [[strategic realism]], which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given [[anarchy (international relations)|international anarchy]]. A classic example is an arms race like the [[Cold War]] and similar conflicts.<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref> During the Cold War the opposing alliances of [[NATO]] and the [[Warsaw Pact]] both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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In international political theory, the Prisoner's Dilemma is often used to demonstrate the coherence of strategic realism, which holds that in international relations, all states (regardless of their internal policies or professed ideology), will act in their rational self-interest given international anarchy. A classic example is an arms race like the Cold War and similar conflicts. During the Cold War the opposing alliances of NATO and the Warsaw Pact both had the choice to arm or disarm. From each side's point of view, disarming whilst their opponent continued to arm would have led to military inferiority and possible annihilation. Conversely, arming whilst their opponent disarmed would have led to superiority. If both sides chose to arm, neither could afford to attack the other, but both incurred the high cost of developing and maintaining a nuclear arsenal. If both sides chose to disarm, war would be avoided and there would be no costs.<br />
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在国际政治理论中,囚徒困境经常被用来证明战略现实主义的一致性,这种战略现实主义认为,在国际关系中,由于国际无政府状态,所有国家(无论其国内政策或公开宣称的意识形态如何)都会为了自身的理性利益来行动。一个典型的例子是类似冷战和类似冲突的军备竞赛。<ref>{{cite journal| title = Arms races as iterated prisoner's dilemma games | author = Stephen J. Majeski | journal = Mathematical and Social Sciences | volume = 7 | issue = 3 | pages = 253–66 | year = 1984 | doi=10.1016/0165-4896(84)90022-2}}</ref>在冷战期间,北约和华约组织的对立联盟都可以选择武装或解除武装。从双方的观点来看,解除武装而对手继续武装可能会导致军事劣势和被歼灭。相反,如果选择武装而对手已经解除了武装,那么就会获得优势。如果双方都选择武装自己,那么任何一方都承担不起攻击对方的代价,但是双方都为发展和维持核武库付出了高昂的代价。如果双方都选择裁军,战争就可以避免,也不会有任何代价。<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a [[War of attrition (game)|war of attrition]] for the next thirty years until the Soviet Union could not withstand the economic cost.<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref> The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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Although the 'best' overall outcome is for both sides to disarm, the rational course for both sides is to arm, and this is indeed what happened. Both sides poured enormous resources into military research and armament in a war of attrition for the next thirty years until the Soviet Union could not withstand the economic cost. The same logic could be applied in any similar scenario, be it economic or technological competition between sovereign states.<br />
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虽然最好的结果是双方解除武装,但是双方的理性选择是武装起来,事实也的确如此。在接下来的三十年里,双方都在军事研究和武器装备的消耗战上投入了大量的资源,直到苏联无法承受经济损失。<ref>{{Citation|last=Kuhn|first=Steven|title=Prisoner's Dilemma|date=2019|url=https://plato.stanford.edu/archives/win2019/entries/prisoner-dilemma/|encyclopedia=The Stanford Encyclopedia of Philosophy|editor-last=Zalta|editor-first=Edward N.|edition=Winter 2019|publisher=Metaphysics Research Lab, Stanford University|access-date=2020-04-12}}</ref>同样的逻辑也适用于任何类似的情况,无论是主权国家之间的经济竞争还是技术竞争。<br />
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===Multiplayer dilemmas===<br />
<font color="#ff8000">多玩家困境 Multiplayer dilemmas</font><br />
Many real-life dilemmas involve multiple players.<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref> Although metaphorical, [[Garrett Hardin|Hardin's]] [[tragedy of the commons]] may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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Many real-life dilemmas involve multiple players. Although metaphorical, Hardin's tragedy of the commons may be viewed as an example of a multi-player generalization of the PD: Each villager makes a choice for personal gain or restraint. The collective reward for unanimous (or even frequent) defection is very low payoffs (representing the destruction of the "commons"). A commons dilemma most people can relate to is washing the dishes in a shared house. By not washing dishes an individual can gain by saving his time, but if that behavior is adopted by every resident the collective cost is no clean plates for anyone.<br />
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许多现实生活中的困境牵涉到多个参与者。<ref>Gokhale CS, Traulsen A. Evolutionary games in the multiverse. Proceedings of the National Academy of Sciences. 2010 Mar 23. 107(12):5500–04.</ref>尽管具有隐喻性,但哈丁的<font color="#ff8000">公地悲剧 tragedy of the commons</font>可以看作是囚徒困境多个参与者的一个例子: 每个村民做出选择是为了个人利益还是克制。对于一致(甚至频繁)叛变的集体回报是非常低的(代表了对“公共资源”的破坏)。大多数人可能会遇到的公地困境是在一个共用的房子里洗碗。通过不洗碗,个人可以节省时间,但如果每个居民都选择这种行为,那么集体的代价是任何人都没有干净的盘子。<br />
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The commons are not always exploited: [[William Poundstone]], in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to [[Excludability|take a paper without paying]] (''defecting'') but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by [[Elinor Ostrom]], winner of the 2009 [[Nobel Memorial Prize in Economic Sciences]], hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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The commons are not always exploited: William Poundstone, in a book about the prisoner's dilemma (see References below), describes a situation in New Zealand where newspaper boxes are left unlocked. It is possible for people to take a paper without paying (defecting) but very few do, feeling that if they do not pay then neither will others, destroying the system. Subsequent research by Elinor Ostrom, winner of the 2009 Nobel Memorial Prize in Economic Sciences, hypothesized that the tragedy of the commons is oversimplified, with the negative outcome influenced by outside influences. Without complicating pressures, groups communicate and manage the commons among themselves for their mutual benefit, enforcing social norms to preserve the resource and achieve the maximum good for the group, an example of effecting the best case outcome for PD.<br />
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公共资源并不总是被利用: 威廉·庞德斯通 William Poundstone在一本关于囚徒困境的书(见下文参考文献)中描述了新西兰的一种情况,信箱没有上锁。人们可以不付钱就拿报纸(背叛) ,但很少有人这样做,他们觉得如果他们不付钱,那么其他人也不会付钱,这会摧毁整个系统。2009年诺贝尔经济学奖获得者埃莉诺·奥斯特罗姆 Elinor Ostrom随后的研究认为公地悲剧过于简单化,其负面结果会受到外部影响。在没有复杂压力的情况下,团体之间为了共同利益进行沟通和管理,执行社会规范以保护资源并为团体实现最大利益,这是实现囚徒困境最佳结果的一个例子。<ref>{{cite web|url=http://volokh.com/2009/10/12/elinor-ostrom-and-the-tragedy-of-the-commons/ |title=The Volokh Conspiracy " Elinor Ostrom and the Tragedy of the Commons |publisher=Volokh.com |date=2009-10-12 |accessdate=2011-12-17}}</ref><br />
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==Related games==<br />
相关博弈<br />
===Closed-bag exchange===<br />
<font color="#ff8000">封闭袋子交换 Closed-bag exchange </font><br />
[[File:Prisoner's Dilemma briefcase exchange (colorized).svg|thumb|The prisoner's dilemma as a briefcase exchange]]<br />
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The prisoner's dilemma as a briefcase exchange<br />
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囚徒困境是一个公文包式的交换<br />
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[[Douglas Hofstadter]]<ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref> once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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Douglas Hofstadter once suggested that people often find problems such as the PD problem easier to understand when it is illustrated in the form of a simple game, or trade-off. One of several examples he used was "closed bag exchange":<br />
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侯世达 Douglas Hofstadter <ref name="dh">{{cite book | first=Douglas R. | last=Hofstadter| authorlink=Douglas Hofstadter | title= Metamagical Themas: questing for the essence of mind and pattern | publisher= Bantam Dell Pub Group| year=1985 | isbn=978-0-465-04566-2|chapter= Ch.29 ''The Prisoner's Dilemma Computer Tournaments and the Evolution of Cooperation''.| title-link=Metamagical Themas}}</ref>曾经指出,人们通常会发现诸如囚徒困境的问题,比如,当它以一个简单囚徒困境博弈的形式,或者以权衡的方式表现出来时,会更容易理解。他使用的几个例子之一是“封闭袋子交换” :<br />
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{{quote|Two people meet and exchange closed bags, with the understanding that one of them contains money, and the other contains a purchase. Either player can choose to honor the deal by putting into his or her bag what he or she agreed, or he or she can defect by handing over an empty bag.}}<br />
两人相遇并交换包裹,事先知道一个包里装着钱,一个装着订单。任一玩家都可选择尊重交易,放入事先约定的东西;也可以选择背叛,交换空的公文包。<br />
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Defection always gives a game-theoretically preferable outcome.<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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Defection always gives a game-theoretically preferable outcome.<br />
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背叛总是会带来一个理论上更可取的结果。<ref>{{Cite web|url=https://users.auth.gr/kehagiat/Research/GameTheory/06GamesToPlay/Prisoner%27s_dilemma.htm#Closed_Bag_Exchange|title=Prisoner's dilemma - Wikipedia, the free encyclopedia|website=users.auth.gr|access-date=2020-04-12}}</ref><br />
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===''Friend or Foe?''===<br />
朋友还是敌人?<br />
''[[Friend or Foe? (TV series)|Friend or Foe?]]'' is a game show that aired from 2002 to 2005 on the [[Game Show Network]] in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, ''Friend or Foe'' has a rewards model between prisoner's dilemma and the [[Chicken (game)|game of Chicken]].<br />
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Friend or Foe? is a game show that aired from 2002 to 2005 on the Game Show Network in the US. It is an example of the prisoner's dilemma game tested on real people, but in an artificial setting. On the game show, three pairs of people compete. When a pair is eliminated, they play a game similar to the prisoner's dilemma to determine how the winnings are split. If they both cooperate (Friend), they share the winnings 50–50. If one cooperates and the other defects (Foe), the defector gets all the winnings and the cooperator gets nothing. If both defect, both leave with nothing. Notice that the reward matrix is slightly different from the standard one given above, as the rewards for the "both defect" and the "cooperate while the opponent defects" cases are identical. This makes the "both defect" case a weak equilibrium, compared with being a strict equilibrium in the standard prisoner's dilemma. If a contestant knows that their opponent is going to vote "Foe", then their own choice does not affect their own winnings. In a specific sense, Friend or Foe has a rewards model between prisoner's dilemma and the game of Chicken.<br />
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朋友还是敌人?是一个竞赛节目,从2002年至2005年在美国的Game show Network播出。这是囚徒困境博弈在真人身上测试的一个例子,只是在人为的环境中。在游戏节目中,有三对选手参加比赛。当一对被淘汰时,他们会玩一个类似囚徒困境的游戏来决定奖金如何分配。如果他们都合作(朋友) ,他们分享奖金50-50。如果一方合作而另一方背叛(敌人) ,那么叛变者将得到所有的奖金,而合作者将一无所获。如果双方都背叛,那么双方都将一无所有。请注意,奖励矩阵与上面给出的标准矩阵略有不同,因为“双方都背叛”和“合作而对方背叛”情况下的奖励是相同的。与标准囚徒困境中的严格均衡相比,这使得“两个都背叛”情况成为一个弱均衡。如果一个参赛者知道他们的对手将投票给“敌人” ,那么他们自己的选择不会影响他们自己的奖金。从特定意义上讲,“朋友还是敌人”节目在囚徒困境和“胆小鬼”博弈之间有一个奖励模型。<br />
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The rewards matrix is<br />
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The rewards matrix is<br />
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奖励矩阵是<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Friend"<br />(cooperate)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"Foe"<br />(defect)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"Friend"<br />(cooperate)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"Foe"<br />(defect)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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{| class="wikitable"<br />
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! {{diagonal split header|{{color|#009|Pair 1}}|{{color|#900|Pair 2}}}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"朋友"<br />(合作)}}<br />
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! scope="col" style="width:6em;" | {{color|#900|"敌人"<br />(背叛)}}<br />
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|-<br />
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! scope="row" style="width:6em;" | {{color|#009|"朋友"<br />(合作)}}<br />
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| {{diagonal split header|{{color|#009|1}}|{{color|#900|1}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|2}}|transparent}}<br />
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|-<br />
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! scope="row" | {{color|#009|"敌人"<br />(背叛)}}<br />
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| {{diagonal split header|{{color|#009|2}}|{{color|#900|0}}|transparent}}<br />
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| {{diagonal split header|{{color|#009|0}}|{{color|#900|0}}|transparent}}<br />
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|}<br />
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This payoff matrix has also been used on the [[United Kingdom|British]] [[television]] programmes ''Trust Me'', ''[[Shafted]]'', ''[[The Bank Job (TV series)|The Bank Job]]'' and ''[[Golden Balls]]'', and on the [[United States|American]] shows ''[[Bachelor Pad]]'' and ''[[Take It All (game show)|Take It All]]''. Game data from the ''[[Golden Balls]]'' series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
<br />
This payoff matrix has also been used on the British television programmes Trust Me, Shafted, The Bank Job and Golden Balls, and on the American shows Bachelor Pad and Take It All. Game data from the Golden Balls series has been analyzed by a team of economists, who found that cooperation was "surprisingly high" for amounts of money that would seem consequential in the real world, but were comparatively low in the context of the game.<br />
<br />
英国电视节目《相信我》、《阴影》、《银行工作》和《黄金球》以及美国电视节目《单身公寓》和《全部拿走》也采用了这种奖励矩阵。一个经济学家团队分析了“金球奖”系列的游戏数据,他们发现,现实生活中,合作对于金额而言“惊人地高” ,但在游戏的背景下,相对较低。<ref>{{cite journal | ssrn=1592456 | title=Split or Steal? Cooperative Behavior When the Stakes Are Large | author=Van den Assem, Martijn J. | journal=Management Science |date=January 2012 | volume=58 | issue=1 | pages=2–20 | doi=10.1287/mnsc.1110.1413| url=http://faculty.chicagobooth.edu/richard.thaler/research/pdf/Split%20or%20Steal%20Cooperative%20Behavior%20When%20the%20Stakes%20Are%20Large.pdf }}</ref><br />
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<br />
===Iterated snowdrift===<br />
<font color="#ff8000">迭代雪堆 Iterated snowdrift </font><br />
{{main|snowdrift game}}<br />
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Researchers from the [[University of Lausanne]] and the [[University of Edinburgh]] have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a [[chicken game]], it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a [[snowdrift]], each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
<br />
Researchers from the University of Lausanne and the University of Edinburgh have suggested that the "Iterated Snowdrift Game" may more closely reflect real-world social situations. Although this model is actually a chicken game, it will be described here. In this model, the risk of being exploited through defection is lower, and individuals always gain from taking the cooperative choice. The snowdrift game imagines two drivers who are stuck on opposite sides of a snowdrift, each of whom is given the option of shoveling snow to clear a path, or remaining in their car. A player's highest payoff comes from leaving the opponent to clear all the snow by themselves, but the opponent is still nominally rewarded for their work.<br />
<br />
来自洛桑大学和爱丁堡大学的研究人员认为,“迭代雪堆游戏”可能更能反映现实世界的社会状况。虽然这个模型实际上是一个胆小鬼博弈。在这个模型中,由于背叛可以降低被剥削的风险,个体总是从合作选择中获益。这个雪堆游戏可以设想两个司机被困在雪堆的两侧,每个司机都可以选择铲雪清理道路,或者留在自己的车里。一个玩家的最高回报来自于让对手清除所有的积雪,但是仍然可以从对手的工作中得到回报。<br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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This may better reflect real world scenarios, the researchers giving the example of two scientists collaborating on a report, both of whom would benefit if the other worked harder. "But when your collaborator doesn’t do any work, it’s probably better for you to do all the work yourself. You’ll still end up with a completed project."<br />
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这可能更好地反映了现实世界的情景,研究人员举了两位科学家合作完成一份报告的例子,如果另一位科学家更加努力地工作,这两位科学家都会受益。“但当你的合作者不做任何工作时,你自己完成所有的工作可能会更好。你最终还是会完成一个项目。” <ref>{{cite web|last=Kümmerli|first=Rolf|title='Snowdrift' game tops 'Prisoner's Dilemma' in explaining cooperation|url=http://phys.org/news111145481.html|accessdate=11 April 2012}}</ref><br />
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{|<br />
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|-<br />
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{| class="wikitable" style="text-align: center;"<br />
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|+ Example snowdrift payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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|-<br />
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! Cooperates<br />
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| 200, 200 || 100, 300<br />
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|-<br />
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! Defects<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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||<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ Example PD payouts (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! Cooperates !! Defects<br />
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|-<br />
<br />
! Cooperates<br />
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| 200, 200 || -100, 300<br />
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|-<br />
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! Defects<br />
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| 300, -100 || 0, 0<br />
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|}<br />
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{|<br />
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|-<br />
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|<br />
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{| class="wikitable" style="text-align: center;"<br />
<br />
|+ 迭代雪堆的支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
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|-<br />
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! 合作<br />
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| 200, 200 || 100, 300<br />
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|-<br />
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! 背叛<br />
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| 300, 100 || 0, 0<br />
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|}<br />
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{| class="wikitable" style="text-align: center;margin-left:2em;"<br />
<br />
|+ 囚徒困境支出示例 (A, B)<br />
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! {{diagonal split header|&nbsp;A|B&nbsp;}} !! 合作 !! 背叛<br />
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|-<br />
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! 合作<br />
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| 200, 200 || -100, 300<br />
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|-<br />
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! 背叛<br />
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| 300, -100 || 0, 0<br />
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|}<br />
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===Coordination games===<br />
<font color="#ff8000">协调博弈 Coordination games</font><br />
{{main|coordination games}}<br />
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In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local [[left- and right-hand traffic]] convention helps to co-ordinate their actions.<br />
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In coordination games, players must coordinate their strategies for a good outcome. An example is two cars that abruptly meet in a blizzard; each must choose whether to swerve left or right. If both swerve left, or both right, the cars do not collide. The local left- and right-hand traffic convention helps to co-ordinate their actions.<br />
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在协调博弈中,参与者必须协调自己的策略以获得一个好的结果。一个例子是两辆车在暴风雪中突然相遇,每辆车必须选择是左转还是右转。如果两辆车都向左转弯,或者都向右转弯,那么两辆车就不会相撞。当地的左右向交通惯例有助于协调他们的行动。<br />
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Symmetrical co-ordination games include [[Stag hunt]] and [[Bach or Stravinsky]].<br />
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Symmetrical co-ordination games include Stag hunt and Bach or Stravinsky.<br />
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对称的协调游戏包括猎鹿 Stag hunt和巴赫 Bach或斯特拉文斯基 Stravinsky。<br />
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===Asymmetric prisoner's dilemmas===<br />
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<font color="#ff8000">不对称的囚徒困境 Asymmetric prisoner's dilemmas</font><br />
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A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an [[alibi]], whence the term "alibi game".<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
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A more general set of games are asymmetric. As in the prisoner's dilemma, the best outcome is co-operation, and there are motives for defection. Unlike the symmetric prisoner's dilemma, though, one player has more to lose and/or more to gain than the other. Some such games have been described as a prisoner's dilemma in which one prisoner has an alibi, whence the term "alibi game".<br />
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一个更一般的博弈集是不对称的。就像在囚徒困境中一样,最好的结果是合作,而背叛是有动机的。与对称的囚徒困境不同的是一个玩家比另一个玩家有更多的损失或收获。这样的博弈被描述为囚徒困境,其中一个囚徒有不在场证明,这就是术语“不在场证明游戏”的由来。<ref>{{cite conference|last1=Robinson |first1=D.R. |last2=Goforth |first2=D.J. |title=Alibi games: the Asymmetric Prisoner' s Dilemmas |date=May 5, 2004 |url=https://economics.ca/2004/papers/0359.pdf |conference=Meetings of the Canadian Economics Association, Toronto, June 4-6, 2004}}</ref><br />
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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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In experiments, players getting unequal payoffs in repeated games may seek to maximize profits, but only under the condition that both players receive equal payoffs; this may lead to a stable equilibrium strategy in which the disadvantaged player defects every X games, while the other always co-operates. Such behaviour may depend on the experiment's social norms around fairness.<br />
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在实验中,在重复博弈中获得不均等收益的参与者可能会寻求利润最大化,但是前提是两个玩家都必须获得均等的收益。这可能会导致一个稳定的均衡策略,即弱势参与者在每隔X场博弈中都会背叛,而另一个参与者总是保持合作。这种行为可能取决于实验围绕公平的社会规范。<ref>{{cite chapter|last1=Beckenkamp |first1=Martin |last2=Hennig-Schmidt |first2=Heike |last3=Maier-Rigaud |first3=Frank P. |chapter=Cooperation in Symmetric and Asymmetric Prisoner's Dilemma Games |date=March 4, 2007 |chapter-url=http://homepage.coll.mpg.de/pdf_dat/2006_25online.pdf |title=[[Max Planck Institute for Research on Collective Goods]]}}</ref><br />
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==Software==<br />
软件<br />
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
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Several software packages have been created to run prisoner's dilemma simulations and tournaments, some of which have available source code.<br />
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已经有一些可以用来运行囚徒困境模拟和比赛的软件包,其中一些有可用的源代码。<br />
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* The source code for the [[The Evolution of Cooperation|second tournament]] run by Robert Axelrod (written by Axelrod and many contributors in [[Fortran]]) is available [http://www-personal.umich.edu/~axe/research/Software/CC/CC2.html online]<br />
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* [https://web.archive.org/web/19991010053242/http://www.lifl.fr/IPD/ipd.frame.html Prison], a library written in [[Java (programming language)|Java]], last updated in 1998<br />
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* [https://github.com/Axelrod-Python/Axelrod Axelrod-Python], written in [[Python (programming language)|Python]]<br />
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* [http://selborne.nl/ipd/ play the Iterative Prisoner's Dilemma in the browser], play against strategies or let strategies play against other strategies<br />
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==In fiction==<br />
在小说中<br />
[[Hannu Rajaniemi]] set the opening scene of his ''[[The Quantum Thief]]'' trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in [[mathematical physics]]&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, ''[[The Fractal Prince]]'' and ''[[The Causal Angel]]'', published in 2012 and 2014, respectively.<br />
<br />
Hannu Rajaniemi set the opening scene of his The Quantum Thief trilogy in a "dilemma prison". The main theme of the series has been described as the "inadequacy of a binary universe" and the ultimate antagonist is a character called the All-Defector. Rajaniemi is particularly interesting as an artist treating this subject in that he is a Cambridge-trained mathematician and holds a PhD in mathematical physics&nbsp;– the interchangeability of matter and information is a major feature of the books, which take place in a "post-singularity" future. The first book in the series was published in 2010, with the two sequels, The Fractal Prince and The Causal Angel, published in 2012 and 2014, respectively.<br />
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汉努·拉贾尼埃米 Hannu Rajaniemi将他的《量子窃贼》三部曲的开场场景设置在一个“囚徒困境”中。该系列的主题被描述为“双重宇宙的不足” ,最终的对手是一个叫做全面背叛者的角色。作为一个处理这个问题的艺术家,拉贾尼埃米尤其有趣,因为他是剑桥大学培养的数学家,拥有数学物理学博士学位——物质和信息的可互换性是这本书的一个主要特征,它发生在<font color="#ff8000">后奇点post-singularity</font>的未来。该系列的第一本书于2010年出版,其续集《分形王子》和《因果天使》分别于2012年和2014年出版。<br />
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A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game ''[[Zero Escape: Virtue's Last Reward]]'' and a minor part in its 2016 sequel ''[[Zero Escape: Zero Time Dilemma]]''.<br />
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A game modeled after the (iterated) prisoner's dilemma is a central focus of the 2012 video game Zero Escape: Virtue's Last Reward and a minor part in its 2016 sequel Zero Escape: Zero Time Dilemma.<br />
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一个(迭代)囚徒困境博弈的模型是2012年电子游戏《零度逃脱: 美德的最后奖励》的重点,也是2016年续集《零度逃脱: 极限脱出刻之困境》的一个次要部分。<br />
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In ''The Mysterious Benedict Society and the Prisoner's Dilemma'' by [[Trenton Lee Stewart]], the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
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In The Mysterious Benedict Society and the Prisoner's Dilemma by Trenton Lee Stewart, the main characters start by playing a version of the game and escaping from the "prison" altogether. Later they become actual prisoners and escape once again.<br />
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在特伦顿·李·斯图尔特 Trenton Lee Stewart的《神秘的本尼迪克特社会和囚徒困境》中,主要角色从玩一个版本的游戏开始,然后一起逃离“监狱”。后来他们变成了真正的囚犯,再次越狱。<br />
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In ''[[The Adventure Zone]]: Balance'' during ''The Suffering Game'' subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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In The Adventure Zone: Balance during The Suffering Game subarc, the player characters are twice presented with the prisoner's dilemma during their time in two liches' domain, once cooperating and once defecting.<br />
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在冒险区: 苦难游戏的平衡中,玩家角色在他们在两个领域的时间内两次呈现出囚徒困境,一次是合作,一次是背叛。<br />
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In the 8th novel from the author James S. A. Corey [[Tiamat's Wrath]] . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. {{cn|date=April 2020}}<br />
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In the 8th novel from the author James S. A. Corey Tiamat's Wrath . Winston Duarte explains the prisoners dilemma in his 14-year-old daughter, Teresa, to train her in strategic thinking. <br />
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在作者詹姆斯·S·A·科里·提亚玛特 James S. A. Corey Tiamat的《愤怒》中的第八部小说中,温斯顿•杜阿尔特 Winston Duarte向他14岁的女儿特蕾莎 Teresa解释了她面临的囚徒困境,来训练她的战略思维能力。<br />
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==See also==<br />
请参阅<br />
{{div col|colwidth=18em}}<br />
<br />
* [[Abilene paradox]]<br />
<font color="#ff8000"> 阿背伦悖论</font><br />
* [[Centipede game]]<br />
<font color="#ff8000"> 蜈蚣博弈</font><br />
* [[Christmas truce]]<br />
<font color="#ff8000"> 圣诞休战</font><br />
* [[Folk theorem (game theory)]]<br />
<font color="#ff8000"> 无名氏定理(博弈论)/font><br />
* [[Free-rider problem]]<br />
<font color="#ff8000"> 搭便车问题</font><br />
* [[Hobbesian trap]]<br />
]<font color="#ff8000"> 霍布斯主义陷阱</font><br />
* [[Innocent prisoner's dilemma]]<br />
<font color="#ff8000"> 无辜囚徒困局</font><br />
* [[Liar Game]]<br />
<font color="#ff8000">说谎者博弈</font><br />
* [[Optional prisoner's dilemma]]<br />
<font color="#ff8000"> 可选择囚徒困境</font><br />
* [[Robert H. Frank#Prisoner's dilemma and cooperation|Prisoner's dilemma and cooperation]]<br />
罗伯特·H·弗兰克囚徒的困境和合作|<font color="#ff8000"> 囚徒困境</font>和合作<br />
* [[Public goods game]]<br />
<font color="#ff8000"> 公共商品博弈</font><br />
* [[Gift-exchange game]]<br />
<font color="#ff8000"> 互利博弈</font><br />
* [[Reciprocal altruism]]<br />
<font color="#ff8000"> 相互利他行为</font><br />
* [[Social preferences]]<br />
<font color="#ff8000"> 社会偏好</font><br />
* [[Swift trust theory]]<br />
<font color="#ff8000"> 快速信任理论</font><br />
* [[Unscrupulous diner's dilemma]]<br />
]<font color="#ff8000"> 无道德食客困境</font><br />
{{div col end}}<br />
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==References==<br />
==参考==<br />
{{notelist}}<br />
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{{reflist|colwidth=30em}}<br />
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<br />
<br />
==Further reading==<br />
==拓展阅读==<br />
{{refbegin|30em}}<br />
<br />
* [[S.M. Amadae|Amadae, S.]] (2016). 'Prisoner's Dilemma,' ''Prisoners of Reason.'' [[Cambridge University Press]], NY, pp.&nbsp;24–61.<br />
<br />
* {{cite book |first1=Robert |last1=Aumann |authorlink=Robert Aumann |chapter=Acceptable points in general cooperative ''n''-person games |editor1-first=R. D. |editor1-last=Luce |editor2-first=A. W. |editor2-last=Tucker |title=Contributions to the Theory 23 of Games IV |series=Annals of Mathematics Study |volume=40 |pages=287–324 |publisher=Princeton University Press |location=Princeton NJ |year=1959 |mr=0104521}}<br />
<br />
* [[Robert Axelrod|Axelrod, R.]] (1984). ''[[The Evolution of Cooperation]]''. {{isbn|0-465-02121-2}}<br />
<br />
* [[Cristina Bicchieri|Bicchieri, Cristina]] (1993). Rationality and Coordination. [[Cambridge University Press]].<br />
<br />
* {{cite journal |first1=David M. |last1=Chess |date=December 1988 |title=Simulating the evolution of behavior: the iterated prisoners' dilemma problem |url=http://www.complex-systems.com/pdf/02-6-4.pdf |journal=Complex Systems |volume=2 |issue=6 |pages=663–70}}<br />
<br />
* [[Melvin Dresher|Dresher, M.]] (1961). ''The Mathematics of Games of Strategy: Theory and Applications'' [[Prentice-Hall]], Englewood Cliffs, NJ.<br />
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* Greif, A. (2006). ''Institutions and the Path to the Modern Economy: Lessons from Medieval Trade.'' Cambridge University Press, [[Cambridge]], UK.<br />
<br />
* [[Anatol Rapoport|Rapoport, Anatol]] and Albert M. Chammah (1965). ''Prisoner's Dilemma''. [[University of Michigan Press]].<br />
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{{refend}}<br />
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<br />
<br />
==External links==<br />
外部链接<br />
*{{Commonscat-inline}}<br />
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* [http://plato.stanford.edu/entries/prisoner-dilemma/ Prisoner's Dilemma (''Stanford Encyclopedia of Philosophy'')]<br />
<br />
* [http://www.msri.org/ext/larryg/pages/15.htm The Bowerbird's Dilemma] The Prisoner's Dilemma in ornithology&nbsp;– mathematical cartoon by Larry Gonick.<br />
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* [https://www.youtube.com/watch?v=_1SEXTVsxjk The Prisoner's Dilemma] The Prisoner's Dilemma with Lego minifigures.<br />
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* {{cite encyclopedia |last1=Dixit |first1=Avinash |authorlink1=Avinash Dixit |last2= Nalebuff |first2=Barry |authorlink2=Barry Nalebuff |editor=[[David R. Henderson]]|encyclopedia=[[Concise Encyclopedia of Economics]] |title=Prisoner's Dilemma |url=http://www.econlib.org/library/Enc/PrisonersDilemma.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0865976658 |oclc=237794267}}<br />
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* [http://gametheory101.com/The_Prisoner_s_Dilemma.html Game Theory 101: Prisoner's Dilemma]<br />
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* [https://www.youtube.com/watch?v=I71mjZefg8g Dawkins: Nice Guys Finish First]<br />
<br />
* [https://axelrod.readthedocs.io/en/stable/ Axelrod] Iterated Prisoner's Dilemma [[Python (programming language)|Python]] library<br />
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* [http://gametheorygames.nl/index.html Play the Iterated Prisoner's Dilemma on gametheorygames.nl]<br />
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* [https://web.archive.org/web/20141011014608/http://demo.otree.org/demo/Prisoner%27s+Dilemma/ Play Prisoner's Dilemma on ''oTree''] (N/A 11-5-17)<br />
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* Nicky Case's [https://web.archive.org/web/20181229222135/https://ncase.me/trust/ Evolution of Trust], an example of the donation game<br />
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* [http://iterated-prisoners-dilemma.info Iterated Prisoner's Dilemma online game] by Wayne Davis<br />
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{{Decision theory paradoxes}}<br />
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[[Category:Non-cooperative games]]<br />
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Category:Non-cooperative games<br />
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Category:Thought experiments<br />
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[[Category:Dilemmas]]<br />
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Category:Dilemmas<br />
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[[Category:Social psychology]]<br />
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Category:Social psychology<br />
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类别: 社会心理学<br />
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[[Category:Moral psychology]]<br />
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Category:Moral psychology<br />
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范畴: 道德心理学<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Prisoner's dilemma]]. Its edit history can be viewed at [[囚徒困境/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=20950行为经济学2021-01-17T15:40:20Z<p>Vicky:/* Criticism 批评 */</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受到决策问题的可操作性、他们自己的认知局限性和可用时间的限制。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型。它补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论——即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''所能解释的一切。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman因为他“将心理学研究的见解整合到经济科学中——关于不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了损失厌恶的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
<br />
Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
<br />
:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
。<br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
。<br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
<br />
该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
。<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
<br />
Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
<br />
'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
<br />
<br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
<br />
|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
<br />
和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
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== Notable people 著名人物==<br />
<br />
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<br />
=== Economics 经济学===<br />
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{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
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* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
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* [[Linda C. Babcock]]<br />
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* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
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* [[David Laibson]]<br />
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* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
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* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
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* [[Larry Summers]]<br />
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* [[Richard Thaler]]<br />
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{{div col end}}<br />
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=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
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* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
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* [[Andrei Shleifer]]<br />
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* [[Robert Vishny]]<br />
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{{div col end}}<br />
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<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
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{{div col end}}<br />
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== See also 参见==<br />
<br />
{{Wikipedia books|Finance}} <br />
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{{div col|colwidth=30em}}<br />
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* [[Adaptive market hypothesis]] 适应性市场假设<br />
<br />
* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
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* [[Behavioralism]] 行为主义<br />
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* [[Behavioral analysis of markets]] 市场的行为分析<br />
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* [[Behavioral operations research]] 行为运筹学<br />
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*[[Big Five personality traits]] 大五人格<br />
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* [[Confirmation bias]] 确认偏差<br />
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* [[Cultural economics]] 文化经济学<br />
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* [[Culture change]] 文化变迁<br />
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* [[Economic sociology]] 经济社会学<br />
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* [[Emotional bias]] 情绪偏差<br />
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* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
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* [[Hindsight bias]] 后见之明偏差<br />
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* ''[[Homo reciprocans]]'' “人属”<br />
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* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
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* [[List of cognitive biases]] 认知偏差列表<br />
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* [[Market sentiment]] 市场情绪<br />
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* [[Methodological individualism]] 方法论个人主义<br />
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* [[Nudge theory]] “助推”理论<br />
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* [[Observational techniques]] 可观察的技术<br />
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* [[Praxeology]] 人类行为学<br />
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* [[Priority heuristic]] 齐当别启发式<br />
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* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
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* [[Repugnancy costs]] 厌恶成本<br />
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* [[Socioeconomics]] 社会经济学<br />
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* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
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{{div col end}}<br />
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<br />
== Citations ==<br />
<br />
{{reflist|30em}}<br />
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<br />
<br />
== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
<br />
* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
<br />
* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
<br />
* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
<br />
* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
<br />
* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
<br />
* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
<br />
* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
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** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
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** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
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** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
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** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
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* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
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* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
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* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
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* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
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* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
<br />
* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
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* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
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* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
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* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
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* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
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* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
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* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
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* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
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* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
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* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
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* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
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* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
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*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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== External links ==<!-- This section is linked from Behavioral finance --><br />
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外部链接! -- 这一部分链接来自行为金融学 -- <br />
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{{wikiquote}}<br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E8%A1%8C%E4%B8%BA%E7%BB%8F%E6%B5%8E%E5%AD%A6&diff=20949行为经济学2021-01-17T15:32:17Z<p>Vicky:</p>
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<div>此词条由嘉树初步翻译,已由和光同尘审校。<br />
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{{Economics sidebar}}<br />
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{{Nudge Theory}}<br />
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[[File:Nudge.jpg|thumb|right|200px|The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.]]<br />
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The behavioral economics concept of "nudging" people's behavior and actions is often illustrated with this urinal with a housefly image embossed in the enamel; the image "nudges" users into improving their aim, which lowers cleaning costs.<br />
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'''<font color = 'ff8000'>助推 nudging</font>'''人类行为这一行为经济学概念,通常用这个釉面装饰了家蝇图像的小便器来说明; 这个图像可以“助推”使用者优化他们的目标,从而降低清洁成本。<br />
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'''Behavioral economics''' studies the effects of [[psychological]], [[cognitive bias|cognitive]], emotional, cultural and social factors on the [[decision making|decisions]] of individuals and institutions and how those decisions vary from those implied by classical economic theory.<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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Behavioral economics studies the effects of psychological, cognitive, emotional, cultural and social factors on the decisions of individuals and institutions and how those decisions vary from those implied by classical economic theory<ref name="ssrn.com">{{cite journal|ssrn=2040946|title=A Behavioral Framework for Securities Risk|publisher =SSRN|last = Lin|first = Tom C. W. |date = 16 April 2012|journal = Seattle University Law Review}}</ref><ref name=":0">{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|last2=Teitelbaum|first2=Joshua|date=2018-03-30|title=Research Handbook on Behavioral Law and Economics|url=https://scholarship.law.bu.edu/books/35|journal=Books}}</ref><br />
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'''<font color = 'ff8000'>行为经济学Behavioral economics</font>'''研究'''<font color = 'ff8000'>心理psychological</font>'''、'''<font color = 'ff8000'>认知emotional</font>'''、情感、文化和社会因素如何影响个人和机构的决策,以及这些决策与经典经济理论暗示下产生的决策有怎样的差别。<br />
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Behavioral economics is primarily concerned with the [[bounded rationality|bounds]] of [[rationality]] of [[economic agent]]s. Behavioral models typically integrate insights from [[psychology]], [[neuroscience]] and [[Microeconomics|microeconomic theory]].<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref> The study of behavioral economics includes how [[Market (economics)|market]] decisions are made and the mechanisms that drive [[public choice]]. The three prevalent themes in behavioral economics are:{{sfn|Shefrin|2002}}<br />
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Behavioral economics is primarily concerned with the bounds of rationality of economic agents. Behavioral models typically integrate insights from psychology, neuroscience and microeconomic theory. The study of behavioral economics includes how market decisions are made and the mechanisms that drive public choice. The three prevalent themes in behavioral economics are:<br />
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行为经济学主要研究经济行为主体的'''<font color = 'ff8000'>理性边界bounded rationality</font>'''。行为模型通常会整合'''<font color = 'ff8000'>心理学psychology</font>'''、'''<font color = 'ff8000'>神经科学neuroscience</font>'''和'''<font color = 'ff8000'>微观经济学理论microeconomic theory</font>'''的观点<ref>{{cite web|title=Search of ''behavioural economics'' |url=http://www.dictionaryofeconomics.com/search_results?q=behavioural+economics+&edition=current&button_search=GO}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref name="MintonKahle2013">{{cite book|first1=Elizabeth A. |last1=Minton|first2=Lynn R. |last2=Kahle|title=Belief Systems, Religion, and Behavioral Economics: Marketing in Multicultural Environments|url={{google books |plainurl=y |id=hk5pngEACAAJ}}|year=2013|publisher=Business Expert Press|isbn=978-1-60649-704-3}}</ref>。行为经济学研究包括'''<font color = 'ff8000'>市场决策market decisions</font>'''是如何做出的,以及驱动'''<font color = 'ff8000'>公共选择public choice</font>'''的机制。行为经济学中三个流行的主题是:{{sfn|Shefrin|2002}}<br />
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* [[Heuristics in judgment and decision making|Heuristics]]: Humans make 95% of their decisions using mental shortcuts or [[rules of thumb]].{{Citation needed|date=May 2020}}<br />
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* [[Framing (social sciences)|Framing]]: The collection of [[anecdote]]s and [[stereotype]]s that make up the mental filters individuals rely on to understand and respond to events.<br />
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* [[Market anomaly|Market inefficiencies]]: These include [[price mechanism|mis-pricing]] and [[rationality|non-rational decision making]].<br />
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* '''<font color = 'ff8000'>判断和决策的启发式Heuristics in judgment and decision making</font>''':人类95% 的决策都是通过'''<font color = 'ff8000'>思维捷径mental shortcuts</font>'''或依据'''<font color = 'ff8000'>经验法则rules of thumb</font>'''做出的{{Citation needed|date=May 2020}}。<br />
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* '''<font color = 'ff8000'>框架效应Framing</font>''': 由'''<font color = 'ff8000'>轶事奇闻anecdote</font>'''和'''<font color = 'ff8000'>刻板印象stereotype</font>'''构成的'''<font color = 'ff8000'>心理过滤器mental filters</font>'''是人们理解和应对事件的依仗。<br />
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* '''<font color = 'ff8000'>市场异象Market anomaly</font>''':包括'''<font color = 'ff8000'>价格机制price mechanism</font>'''和'''<font color = 'ff8000'>理性rationality</font>'''。<br />
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In 2002, psychologist [[Daniel Kahneman]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref> In 2013, economist [[Robert J. Shiller]] received the [[Nobel Memorial Prize in Economic Sciences]] "for his empirical analysis of asset prices" (within the field of [[#Behavioral finance|behavioral finance]]).<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref> In 2017, economist [[Richard Thaler]] was awarded the [[Nobel Memorial Prize in Economic Sciences]] for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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In 2002, psychologist Daniel Kahneman was awarded the Nobel Memorial Prize in Economic Sciences "for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty." In 2013, economist Robert J. Shiller received the Nobel Memorial Prize in Economic Sciences "for his empirical analysis of asset prices" (within the field of behavioral finance). In 2017, economist Richard Thaler was awarded the Nobel Memorial Prize in Economic Sciences for "his contributions to behavioral economics and his pioneering work in establishing that people are predictably irrational in ways that defy economic theory."<br />
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2002年,心理学家丹尼尔 · 卡尼曼 Daniel Kahneman被授予诺贝尔经济学奖,“因为他将心理学研究的成果整合到经济科学中,特别是关于不确定条件下人类的判断和决策<ref name="Winners2002">{{cite web|url=http://nobelprize.org/nobel_prizes/economics/laureates/2002/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2002|publisher=Nobel Foundation|accessdate=2008-10-14}}</ref>。”2013年,经济学家罗伯特·希勒 Robert J. Shiller因“对资产价格的实证分析”(属于金融学领域)而获得诺贝尔经济学奖<ref>{{cite web|url=https://www.nobelprize.org/nobel_prizes/economic-sciences/laureates/2013/|title=The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2013|publisher=Nobel Foundation|accessdate=2016-07-01}}</ref>。2017年经济学家理查德·泰勒 Richard Thaler因为他“对行为经济学的贡献,以及他在不符合经济学原理的人类可预测性非理性行为方面的开创性工作”而被授予诺贝尔经济学奖<ref>{{Cite news|url=https://www.nytimes.com/2017/10/09/business/nobel-economics-richard-thaler.html|title=Nobel in Economics is Awarded to Richard Thaler|last=Appelbaum|first=Binyamin|date=2017-10-09|work=The New York Times|access-date=2017-11-04}}</ref><ref>{{Cite news|url=http://lucidez.pe/economia/richard-thaler-y-el-auge-de-la-economia-conductual-por-marco-carrasco/|title=Richard Thaler y el auge de la Economía Conductual|last=Carrasco-Villanueva|first=Marco|date=2017-10-18|language=es|work=Lucidez|access-date=2018-10-31}}</ref><br />
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== History 历史==<br />
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[[File:Adam Smith The Muir portrait.jpg|thumb|140px|[[Adam Smith]], author of ''The Wealth of Nations'' (1776) and ''The Theory of Moral Sentiments'' (1759).]]<br />
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[[Adam Smith, author of The Wealth of Nations (1776) and The Theory of Moral Sentiments (1759).]]<br />
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[亚当·斯密Adam Smith,《'''<font color = 'ff8000'>国富论The Wealth of Nations</font>'''》(1776)和《'''<font color = 'ff8000'>道德情操论The Theory of Moral Sentiments</font>'''》(1759)的作者]<br />
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During the [[classical economics|classical period]] of economics, microeconomics was closely linked to psychology. For example, [[Adam Smith]] wrote ''[[The Theory of Moral Sentiments]]'', which proposed psychological explanations of individual behavior, including concerns about fairness and [[justice (economics)|justice]].<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref> [[Jeremy Bentham]] wrote extensively on the psychological underpinnings of [[utility]]. Then, during the development of [[neo-classical economics]], economists sought to reshape the discipline as a [[natural science]], deducing behavior from assumptions about the nature of economic agents. They developed the concept of [[homo economicus]], whose behavior was fundamentally rational.<br />
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During the classical period of economics, microeconomics was closely linked to psychology. For example, Adam Smith wrote The Theory of Moral Sentiments, which proposed psychological explanations of individual behavior, including concerns about fairness and justice. Jeremy Bentham wrote extensively on the psychological underpinnings of utility. Then, during the development of neo-classical economics, economists sought to reshape the discipline as a natural science, deducing behavior from assumptions about the nature of economic agents. They developed the concept of homo economicus, whose behavior was fundamentally rational.<br />
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在'''<font color = 'ff8000'>古典经济学classical economice</font>'''时期,微观经济学与心理学有着密切的联系。例如,Adam Smith的《道德情操论》提出了个人行为的心理学解释,包括一些对公平和正义的想法<ref>{{cite journal |first1=Nava |last1=Ashraf |first2=Colin F. |last2=Camerer |first3=George |last3=Loewenstein |year=2005 |title=Adam Smith, Behavioral Economist |journal=[[Journal of Economic Perspectives]] |volume=19 |issue=3 |url=http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |doi=10.1257/089533005774357897 |pages=131–45 |access-date=2011-12-20 |archive-url=https://web.archive.org/web/20120417093442/http://webserver1.pugetsound.edu/facultypages/gmilam/courses/econ291/readings/ASmithBenEcon.pdf |archive-date=2012-04-17 |url-status=dead }}.</ref>。杰里米·边沁 Jeremy Bentham写了大量文章来讨论'''<font color = 'ff8000'>效用utility</font>'''的心理学基础。然后,在'''<font color = 'ff8000'>新古典主义经济学neo-classical economics</font>'''的发展过程中,通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断行为,经济学家试图将该学科重塑为一门自然科学,即通过对经济行为主体性质的'''<font color = 'ff8000'>假设assumptions</font>'''来推断主体行为。他们提出了'''<font color = 'ff8000'>经济人homo economicus</font>'''的概念——经济人的行为基本上是理性的。<br />
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Neo-classical economists did incorporate psychological explanations: this was true of [[Francis Edgeworth]], [[Vilfredo Pareto]] and [[Irving Fisher]]. '''Economic psychology''' emerged in the 20th century in the works of [[Gabriel Tarde]],<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref> [[George Katona]],<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref> and [[Laszlo Garai]].<ref name="Garai" /> [[Expected utility]] and [[discounted utility]] models began to gain acceptance, generating testable [[hypotheses]] about decision-making given [[uncertainty]] and [[intertemporal consumption]], respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by [[Maurice Allais]], for example, in setting out the [[Allais paradox]], a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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Neo-classical economists did incorporate psychological explanations: this was true of Francis Edgeworth, Vilfredo Pareto and Irving Fisher. Economic psychology emerged in the 20th century in the works of Gabriel Tarde, George Katona, and Laszlo Garai. Expected utility and discounted utility models began to gain acceptance, generating testable hypotheses about decision-making given uncertainty and intertemporal consumption, respectively. Observed and repeatable anomalies eventually challenged those hypotheses, and further steps were taken by Maurice Allais, for example, in setting out the Allais paradox, a decision problem he first presented in 1953 that contradicts the expected utility hypothesis.<br />
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新古典主义经济学家的确纳入了心理学的解释:埃奇沃斯Francis Edgeworth、帕累托Vilfredo Pareto和费舍Irving Fisher就是如此。'''<font color = 'ff8000'>经济心理学Economic psychology</font>'''在20世纪加布里埃尔·塔德 Gabriel Tarde<ref>{{cite web |last=Tarde |first=G. |url = http://classiques.uqac.ca/classiques/tarde_gabriel/psycho_economique_t1/psycho_eco_t1.html |title=Psychologie économique |year=1902 |language = French}}</ref>,乔治·卡托纳 George Katona<ref name="Katona2011">{{cite book|first=George |last=Katona|title=The Powerful Consumer: Psychological Studies of the American Economy|url={{google books |plainurl=y |id=jmdEywAACAAJ}}|year= 2011|publisher=Literary Licensing, LLC|isbn=978-1-258-21844-7}}</ref>和拉斯洛·加莱 Laszlo Garai<ref name="Garai" />的著作中出现。''<font color = 'ff8000'>期望效用模型Expected utility models</font>'''和''<font color = 'ff8000'>折扣效用模型discounted utility models</font>'''开始被接受,在存在'''<font color = 'ff8000'>不确定性uncertainty</font>'''和'''<font color = 'ff8000'>跨期消费intertemporal consumption</font>'''的情况下生成有关决策的假设。然而一些人们观察到的、频繁重复的异常情况最终挑战了这些假说。研究者为此采取了进一步的步骤。例如,莫里斯•阿莱Maurice Allais设定了'''<font color = 'ff8000'>阿莱悖论Allais paradox</font>'''。Allais在1953年第一次提出这个决策问题,并用以反对期望效用假说。<br />
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In the 1960s [[cognitive psychology]] began to shed more light on the brain as an information processing device (in contrast to [[behaviorism|behaviorist]] models). Psychologists in this field, such as Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref> [[Amos Tversky]] and [[Daniel Kahneman]] began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. [[Mathematical psychology]] reflects a longstanding interest in preference transitivity and the measurement of utility.{{sfn|Luce|2000}}<br />
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In the 1960s cognitive psychology began to shed more light on the brain as an information processing device (in contrast to behaviorist models). Psychologists in this field, such as Ward Edwards, Amos Tversky and Daniel Kahneman began to compare their cognitive models of decision-making under risk and uncertainty to economic models of rational behavior. Mathematical psychology reflects a longstanding interest in preference transitivity and the measurement of utility.<br />
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在20世纪60年代,'''<font color = 'ff8000'>认知心理学cognitive psychology</font>'''开始给予大脑这一信息处理设备(与行为主义模型相对)更多的关注。这一领域的心理学家,如爱德华兹Ward Edwards,<ref name=ward>{{cite web|title=Ward Edward Papers|publisher=Archival Collections|url=http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080416235453/http://www.usc.edu/libraries/archives/arc/libraries/collections/records/427home.html|archivedate=2008-04-16|url-status=dead}}</ref>、阿莫斯 · 特沃斯基Amos Tversky和Daniel Kahneman开始将在一定风险性和不确定性下做决策的认知模型与理性行为的经济模型进行比较。'''<font color = 'ff8000'>数学心理学Mathematical psychology</font>'''反映了长期以来研究者对'''<font color = 'ff8000'>偏好传递性preference transitivity</font>'''和'''<font color = 'ff8000'>效用度量measurement of utility</font>'''的兴趣{{sfn|Luce|2000}}。<br />
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=== Bounded rationality 有限理性===<br />
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[[File:Herbert simon red complete.jpg|thumb|left|140px|[[Herbert A. Simon]], winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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[[Herbert A. Simon, winner of the 1975 Turing award and the 1978 Nobel Prize in economics]]<br />
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'''<font color = 'ff8000'>赫伯特·西蒙Herbert A. Simon</font>''',1975年图灵奖和1978年诺贝尔经济学奖得主<br />
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[[Bounded rationality]] is the idea that when individuals make decisions, their [[rationality]] is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as [[satisficer]]s, seeking a satisfactory solution rather than an optimal one. [[Herbert A. Simon]] proposed bounded rationality as an alternative basis for the mathematical modeling of [[decision-making]]. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available.<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref> Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<ref name=bounded_rationality_1999/><br />
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Bounded rationality is the idea that when individuals make decisions, their rationality is limited by the tractability of the decision problem, their cognitive limitations and the time available. Decision-makers in this view act as satisficers, seeking a satisfactory solution rather than an optimal one. Herbert A. Simon proposed bounded rationality as an alternative basis for the mathematical modeling of decision-making. It complements "rationality as optimization", which views decision-making as a fully rational process of finding an optimal choice given the information available. Simon used the analogy of a pair of scissors, where one blade represents human cognitive limitations and the other the "structures of the environment", illustrating how minds compensate for limited resources by exploiting known structural regularity in the environment.<br />
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'''<font color = 'ff8000'>有限理性Bounded rationality</font>'''是指,当个体做出决策时,他们的理性受到决策问题的可操作性、他们自己的认知局限性和可用时间的限制。这种观点认为,决策者像'''<font color = 'ff8000'>满意者satisficers</font>'''一样寻求一个令自己满意的解决方案,而不是寻求最佳的解决方案。Herbert A. Simon提出以有限理性为基础替代传统的决策数学模型。它补充了“理性即优化”(即决策是一个完全理性的,基于已有信息获取最佳选择的过程)的观点<ref name=bounded_rationality_1999>{{cite book|url={{google books |plainurl=y |id=dVMq5UoYS3YC}} |first=Gerd|last=Gigerenzer|first2=Reinhard|last2=Selten|title=Bounded Rationality: The Adaptive Toolbox|publisher=MIT Press|year=2002|isbn=978-0-262-57164-7}}</ref>。Simon用一把剪刀做类比。剪刀的一个刀片代表人类认知的局限性,另一个刀片代表” '''<font color = 'ff8000'>环境结构structures of the environment</font>'''” ,以此来说明人类思维是如何利用已知的环境结构规律来弥补资源有限这一问题的<ref name=bounded_rationality_1999/>。<br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from [[Cass Sunstein]] and [[Richard Thaler]]'s ''[[Nudge (book)|Nudge]]''.<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref> Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of ''Nudge'' have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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Bounded rationality implicates the idea that humans take shortcuts that may lead to suboptimal decision-making. Behavioral economists engage in mapping the decision shortcuts that agents use in order to help increase the effectiveness of human decision-making. One treatment of this idea comes from Cass Sunstein and Richard Thaler's Nudge. Sunstein and Thaler recommend that choice architectures are modified in light of human agents' bounded rationality. A widely cited proposal from Sunstein and Thaler urges that healthier food be placed at sight level in order to increase the likelihood that a person will opt for that choice instead of less healthy option. Some critics of Nudge have lodged attacks that modifying choice architectures will lead to people becoming worse decision-makers.<br />
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有限理性意味着,走捷径的策略可能导致人们做出次优决策。行为经济学家从事主体决策捷径的绘制工作,以帮助人们提高决策的有效性。关于这个观点的一种论述来自卡斯 · 桑斯坦Cass Sunstein和Richard Thaler的《'''<font color = 'ff8000'>“助推”Nudge</font>'''》一书<ref name =nudge>{{cite book|title=Nudge: Improving Decisions about Health, Wealth, and Happiness|isbn=978-0-14-311526-7|oclc=791403664|date=April 8, 2008|publisher=Yale University Press|authors=Thaler, Richard H., Sunstein, Cass R.|title-link=Nudge (book)}}</ref><ref>{{cite book|title=Choice Architecture|authors=Thaler, Richard H., Sunstein, Cass R. and Balz, John P.|doi=10.2139/ssrn.1583509|ssrn=1583509|date=April 2, 2010}}</ref>。Sunstein和Thaler建议,'''<font color = 'ff8000'>选项结构choice architectures</font>'''应该根据人类的有限理性进行修改。Sunstein和Thaler提出的一个被广泛引用的建议是,为了增加人们选择健康食品而不是不健康食品的可能性,应该把健康食品放在人们的视线范围内。一些对《助推》持批评态度的人则指出,修改选项结构将导致人们成为更糟糕的决策者<ref>{{cite web|last1=Wright|first1=Joshua|first2=Douglas|last2=Ginsberg|title=Free to Err?: Behavioral Law and Economics and its Implications for Liberty|url=http://www.libertylawsite.org/liberty-forum/free-to-err-behavioral-law-and-economics-and-its-implications-for-liberty/|date=February 16, 2012|work=Library of Law & Liberty}}</ref><ref>{{cite book|last1=Sunstein|first1=Cass|title=Going to Extremes: How Like Minds Unite and Divide|url={{google books |plainurl=y |id=jEWplxVkEEEC}}|isbn = 9780199793143|publisher = Oxford University Press |date =2009 }}</ref><br />
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=== Prospect theory 前景理论===<br />
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[[File:Daniel KAHNEMAN.jpg|thumb|200px|[[Daniel Kahneman]], winner of the 2002 Nobel Prize in economics]]<br />
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[[Daniel Kahneman, winner of the 2002 Nobel Prize in economics]]<br />
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[Daniel Kahneman,2002年诺贝尔经济学奖得主]<br />
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In 1979, Kahneman and Tversky published ''[[prospect theory|Prospect Theory]]: An Analysis of Decision Under Risk'', that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory.{{sfn|Kahneman|Diener|2003}} Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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In 1979, Kahneman and Tversky published Prospect Theory: An Analysis of Decision Under Risk, that used cognitive psychology to explain various divergences of economic decision making from neo-classical theory. Prospect theory has two stages: an editing stage and an evaluation stage.<br />
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1979年,Kahneman和Tversky发表了《'''<font color = 'ff8000'>前景理论: 风险下的决策分析Prospect Theory: An Analysis of Decision Under Risk</font>'''》一文,该文利用认知心理学解读了新古典主义经济决策理论中的多种分歧。'''<font color = 'ff8000'>前景理论 Prospect theory </font>'''分为两个阶段:'''<font color = 'ff8000'>编辑阶段editing stage</font>'''和'''<font color = 'ff8000'>评估阶段evaluation stage</font>'''。<br />
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In the editing stage, risky situations are simplified using various [[heuristic]]s. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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In the editing stage, risky situations are simplified using various heuristics. In the evaluation phase, risky alternatives are evaluated using various psychological principles that include:<br />
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在编辑阶段,人们使用各种启发式简化风险情况。在评估阶段,人们利用各种心理学原则对风险选项进行评估,这些原则中包括:<br />
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*[[Reference dependence]]: When evaluating outcomes, the decision maker considers a "reference level." Outcomes are then compared to the reference point and classified as "gains" if greater than the reference point and "losses" if less than the reference point.<br />
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* '''<font color = 'ff8000'>参考依赖Reference dependence</font>''':评估结果时,决策者会确定一个“参考水平”,然后将结果与参考点进行比较。如果结果大于参考点则归类为”收益” ,如果小于参考点则为”损失”。<br />
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* [[Loss aversion]]: Losses are avoided more than equivalent gains are sought. In their 1992 paper, Kahneman and Tversky found the median coefficient of loss aversion to be about 2.25, i.e., losses hurt about 2.25 times more than equivalent gains reward.<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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'''<font color = 'ff8000'>损失厌恶Loss aversion</font>''':相比追求等价的收益,人们更倾向于规避损失。在1992年的论文中,Kahneman和Tversky发现损失厌恶系数的中位数大约是2.25。也就是说,损失造成的伤害是同等收益的2.25倍<ref name="TverskyKahneman1992">{{cite journal|first1=Amos |last1=Tversky |first2=Daniel |last2=Kahneman |year=1992 |title=Advances in Prospect Theory: Cumulative Representation of Uncertaintly |journal=Journal of Risk and Uncertainty |volume=5 |issue=4 | pages=297–323|issn=0895-5646|doi=10.1007/BF00122574}}[https://link.springer.com/article/10.1007/BF00122574 Abstract.]</ref><br />
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* Non-linear probability weighting: Decision makers overweigh small probabilities and underweigh large probabilities—this gives rise to the inverse-S shaped "probability weighting function."<br />
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* 非线性概率加权:决策者重小概率而轻大概率——这就产生了反 S 型的“'''<font color = 'ff8000'>概率加权函数probability weighting function</font>'''”。<br />
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* Diminishing sensitivity to gains and losses: As the size of the gains and losses relative to the reference point increase in absolute value, the [[marginal utility|marginal]] effect on the decision maker's utility or satisfaction falls.<br />
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* 对收益和损失的'''<font color = 'ff8000'>敏感度sensitivity</font>'''递减:当收益和损失的大小相对于参考点的绝对值增加时,对决策者的效用或满意度产生影响的'''<font color = 'ff8000'>边际效用marginal utility</font>'''就会减弱。<br />
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Prospect theory is able to explain everything that the two main existing decision theories—[[Expected utility hypothesis|expected utility theory]] and [[Rank-dependent expected utility|rank dependent utility]] theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include [[Backward bending supply curve of labour|backward bending labor supply curves]], asymmetric price elasticities, [[tax evasion]] and co-movement of stock prices and consumption.<br />
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Prospect theory is able to explain everything that the two main existing decision theories—expected utility theory and rank dependent utility theory—can explain. Further, prospect theory has been used to explain phenomena that existing decision theories have great difficulty in explaining. These include backward bending labor supply curves, asymmetric price elasticities, tax evasion and co-movement of stock prices and consumption.<br />
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前景理论能够解释已有的两个主要决策理论——即'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''和'''<font color = 'ff8000'>等级依赖效用理论rank dependent utility theory</font>'''所能解释的一切。此外,前景理论也能被用来解释现有决策理论难以解释的现象。这些现象包括'''<font color = 'ff8000'>后弯的劳动力供给曲线backward bending labor supply curves</font>'''、'''<font color = 'ff8000'>不对称的价格弹性price elasticities</font>'''、'''<font color = 'ff8000'>逃税tax evasion</font>'''以及股票价格和消费的'''<font color = 'ff8000'>共同波动co-movement</font>'''。<br />
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In 1992, in the ''Journal of Risk and Uncertainty'', Kahneman and Tversky gave a revised account of prospect theory that they called [[cumulative prospect theory]].<ref name="TverskyKahneman1992" /> The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in [[John Quiggin]]'s rank-dependent utility theory.<br />
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In 1992, in the Journal of Risk and Uncertainty, Kahneman and Tversky gave a revised account of prospect theory that they called cumulative prospect theory. The new theory eliminated the editing phase in prospect theory and focused just on the evaluation phase. Its main feature was that it allowed for non-linear probability weighting in a cumulative manner, which was originally suggested in John Quiggin's rank-dependent utility theory.<br />
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1992年,在《'''<font color = 'ff8000'>风险与不确定性Risk and Uncertainty</font>'''》期刊上,Kahneman和Tversky对前景理论进行了修正,并将修正结果称之为'''<font color = 'ff8000'>累积前景理论cumulative prospect theory</font>'''<ref name="TverskyKahneman1992" />。新理论消除了前景理论中的编辑阶段,只注重评估阶段。它的主要特点是允许以累积的方式对概率进行非线性的加权,而这个想法最初出现于约翰 · 奎金John Quiggin的等级依赖效用理论中。<br />
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Psychological traits such as [[Overconfidence effect|overconfidence]], [[Affective forecasting#Projection bias|projection bias]], and the effects of limited attention are now part of the theory. Other developments include a conference at the [[University of Chicago]],{{sfn|Hogarth|Reder|1987}} a special behavioral economics edition of the ''[[Quarterly Journal of Economics]]'' ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref><br />
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Psychological traits such as overconfidence, projection bias, and the effects of limited attention are now part of the theory. Other developments include a conference at the University of Chicago, a special behavioral economics edition of the Quarterly Journal of Economics ("In Memory of Amos Tversky"), and Kahneman's 2002 Nobel Prize for having "integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty."<br />
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一些心理特征,如'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>投射偏差projection bias</font>'''和有限的注意力等现已经成为这个理论的一部分。其他进展包括:在芝加哥大学举行的一次会议,《'''<font color = 'ff8000'>经济学季刊Quarterly Journal of Economics</font>'''》上的一期行为经济学特刊《'''<font color = 'ff8000'>纪念阿莫斯 · 特沃斯基 In Memory of Amos Tversky</font>'''》,以及Kahneman因为他“将心理学研究的见解整合到经济科学中——关于不确定条件下的人类判断和决策尤为重要”而获得的2002年诺贝尔奖<ref name=kahneman>{{cite web|title=Nobel Laureates 2002|publisher=Nobelprize.org|url=http://nobelprize.org/nobel_prizes/lists/2002.html|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080410071445/http://nobelprize.org/nobel_prizes/lists/2002.html|archivedate=10 April 2008 |url-status=live}}</ref>。<br />
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=== Intertemporal choice 跨期选择===<br />
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{{See also|Dynamic inconsistency}}<br />
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[[File:David_laibson_2007.jpg|thumb|left|140px|[[David Laibson]], professor of economics at [[Harvard University]]]]<br />
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[[David Laibson, professor of economics at Harvard University]]<br />
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[哈佛大学经济学教授大卫 · 莱布森David Laibson]<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by [[George Ainslie (psychologist)|George Ainslie]]'s [[hyperbolic discounting]]—one of the prominently studied observations—and further developed by [[David Laibson]], Ted O'Donoghue and [[Matthew Rabin]]. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time ''t'' and ''t+1'' will be low at time ''t-1'' when ''t'' is the near future, but high at time ''t'' when ''t'' is the present and time ''t+1'' is the near future.<br />
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Behavioral economics has been applied to intertemporal choice, which is defined as making a decision and having the effects of such decision happening in a different time. Intertemporal choice behavior is largely inconsistent, as exemplified by George Ainslie's hyperbolic discounting—one of the prominently studied observations—and further developed by David Laibson, Ted O'Donoghue and Matthew Rabin. Hyperbolic discounting describes the tendency to discount outcomes in the near future more than outcomes in the far future. This pattern of discounting is dynamically inconsistent (or time-inconsistent), and therefore inconsistent with basic models of rational choice, since the rate of discount between time t and t+1 will be low at time t-1 when t is the near future, but high at time t when t is the present and time t+1 is the near future.<br />
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行为经济学已经被应用到跨期选择中。跨期选择是指在某个时间点做出决策,在另一个时间点获得该决策所产生的效果。跨期选择行为在很大程度上是不一致的,乔治 · 安斯利George Ainslie的'''<font color = 'ff8000'>双曲折扣hyperbolic discounting</font>'''就是一个很好的例子——大卫 · 莱布森David Laibson、泰德 · 奥多诺霍Ted O'Donoghue和马修 · 拉宾Matthew Rabin则进一步发展了这个想法。双曲折扣描述了一种倾向,即与遥远的未来相比,人们更倾向于对在较近的未来会产生的结果打折扣。这种折扣模式在动态上是不一致的(或者说是在时间上不一致的),因此它与理性选择的基本模型不一致——因为时间 t 和 t + 1之间的折扣率比在时间 t-1 和t 时低(当t是较近的未来时),但是也会更高(在时间 t 为现在, 而 t + 1 为较近的未来时)。<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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This pattern can also be explained through models of sub-additive discounting that distinguish the delay and interval of discounting: people are less patient (per-time-unit) over shorter intervals regardless of when they occur.<br />
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这种模式也可以通过'''<font color = 'ff8000'>次加法sub-additive</font>'''折扣模型来解释,这种模型区分了折扣的延迟和折扣的时间间隔:无论折扣何时发生,人们在较短的折扣时间间隔内都缺乏耐心。<br />
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=== Other areas of research 研究的其他领域===<br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. [[Ernst Fehr]], [[Armin Falk]], and Rabin studied [[distributive justice|fairness]], [[inequity aversion]] and [[reciprocal altruism]], weakening the neoclassical assumption of perfect [[selfishness]]. This work is particularly applicable to wage setting. The work on "intrinsic motivation by [[Uri Gneezy|Gneezy]] and Rustichini and "identity" by [[George Akerlof|Akerlof]] and [[Rachel Kranton|Kranton]] assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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Other branches of behavioral economics enrich the model of the utility function without implying inconsistency in preferences. Ernst Fehr, Armin Falk, and Rabin studied fairness, inequity aversion and reciprocal altruism, weakening the neoclassical assumption of perfect selfishness. This work is particularly applicable to wage setting. The work on "intrinsic motivation by Gneezy and Rustichini and "identity" by Akerlof and Kranton assumes that agents derive utility from adopting personal and social norms in addition to conditional expected utility. According to Aggarwal, in addition to behavioral deviations from rational equilibrium, markets are also likely to suffer from lagged responses, search costs, externalities of the commons, and other frictions making it difficult to disentangle behavioral effects in market behavior.<br />
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行为经济学的其他分支丰富了效用函数模型,但并不蕴含偏好的不一致性。恩斯特·费尔 Ernst Fehr、阿明·福柯 Armin Falk和 拉宾 Rabin 研究了公平、'''<font color = 'ff8000'>不公平厌恶inequity aversion</font>'''和'''<font color = 'ff8000'>互惠利他reciprocal altruism</font>''',削弱了新古典主义中'''<font color = 'ff8000'>完美自私perfect selfishness</font>'''的假设。这项工作特别适用于工资确定这一问题。Gneezy 、 Rustichini 关于“'''<font color = 'ff8000'>内在动机intrinsic motivation</font>'''”和 Akerlof 、 Kranton 关于“'''<font color = 'ff8000'>认同identity</font>'''”的工作都假定,主体除了从'''<font color = 'ff8000'>条件期望效用conditional expected utility</font>'''中获得效用以外,也会从个人和社会规范中获得效用。根据埃格瓦尔 Aggarwal的观点,除了行为偏离'''<font color = 'ff8000'>合理均衡rational equilibrium</font>''',市场还可能受到'''<font color = 'ff8000'>响应滞后 lagged responses</font>''','''<font color = 'ff8000'>搜索成本search costs</font>''','''<font color = 'ff8000'>极端情况externalities of the commons</font>'''以及其他'''<font color = 'ff8000'>冲突frictions</font>'''的影响,这使研究者难以从市场行为中区分'''<font color = 'ff8000'>(个人的)</font>''''''<font color = 'ff8000'>行为效应behavioral effect</font>'''<ref>{{cite journal|last1=Aggarwal|first1=Raj|title=Animal Spirits in Financial Economics: A Review of Deviations from Economic Rationality|journal=International Review of Financial Analysis|date=2014|volume=32|issue=1|pages=179–87|doi=10.1016/j.irfa.2013.07.018}}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an [[illusion of control]], and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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"Conditional expected utility" is a form of reasoning where the individual has an illusion of control, and calculates the probabilities of external events and hence their utility as a function of their own action, even when they have no causal ability to affect those external events.<br />
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“条件期望效用”是一种个人自认为拥有'''<font color = 'ff8000'>掌控权 illusion of control </font>'''的错觉,并根据他们自己的行为去计算外部事件发生的概率,进而自己得出效用结果,即使他们没有能力影响外部事件<ref>{{cite journal|doi=10.2307/3791450|author=Grafstein R|title=Rationality as Conditional Expected Utility Maximization|journal=Political Psychology|volume=16|issue=1|pages=63–80|year=1995|jstor=3791450}}</ref><ref>{{cite journal|doi=10.1016/0010-0285(92)90015-T|author=Shafir E, Tversky A|title=Thinking through uncertainty: nonconsequential reasoning and choice|journal=Cognitive Psychology|volume=24|issue=4|pages=449–74|year=1992|pmid=1473331 }}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as [[Dan Ariely]]'s ''[[Predictably Irrational]].'' Practitioners of the discipline have studied quasi-public policy topics such as [[Broadband mapping in the United States|broadband mapping]].<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Behavioral economics caught on among the general public with the success of books such as Dan Ariely's Predictably Irrational. Practitioners of the discipline have studied quasi-public policy topics such as broadband mapping.<br />
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行为经济学随着丹·埃利里Dan Ariely的《'''<font color = 'ff8000'>怪诞行为学Predictably Irrational</font>'''》等书籍的成功而在普通大众中流行起来。该学科的从业者研究了'''<font color = 'ff8000'>宽带制图broadband mapping</font>'''等'''<font color = 'ff8000'>准公共政策专题quasi-public policy topics</font>'''<ref name=twsA2faa4>{{cite web|title=US National Broadband Plan: good in theory|publisher=Telco 2.0|quote=... Sara Wedeman's awful experience with this is instructive....|date=March 17, 2010|url=http://www.telco2.net/blog/2010/03/us_national_broadband_plan_qui.html|accessdate=2010-09-23}}</ref><ref name=twsA2xx>{{cite news|first1=Gordon |last1=Cook |first2=Sara |last2=Wedeman|title=Connectivity, the Five Freedoms, and Prosperity|publisher=Community Broadband Networks|date=July 1, 2009|url=http://www.muninetworks.org/reports/cook-report-broadband-mapping-connectivity-five-freedoms-and-prosperity|accessdate=2010-09-23}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in [[artificial intelligence]] and [[machine learning]]. The Silicon Valley-based start-up Singularities is using the [[AGM postulates]] proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a [[symbolic logic]] to create a "machine learning and deduction engine that uses the latest [[data science]] and [[big data]] algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications for behavioral economics include the modeling of the consumer decision-making process for applications in artificial intelligence and machine learning. The Silicon Valley-based start-up Singularities is using the AGM postulates proposed by Alchourrón, Gärdenfors, and Makinson—the formalization of the concepts of beliefs and change for rational entities—in a symbolic logic to create a "machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs."<br />
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行为经济学的应用包括,在人工智能和机器学习中对消费者决策过程建模。硅谷公司奇点Singularities在使用阿尔肖伦 Alchourrón、加登弗斯Gärdenfors和梅金森 Makinson 提出的AGM假设,即信念概念的形式化和理性实体的改变,在符号逻辑中创建一个“使用最新的数据科学和大数据算法的机器学习和演绎引擎,以生成捕捉客户的行为和想法的内容和条件规则(即一些'''<font color = 'ff8000'>反事实推理counterfactuals</font>''' ) 。” <ref>{{cite web|title=Singluarities Our Company|publisher=Singular Me, LLC|quote=... machine learning and deduction engine that uses the latest data science and big data algorithms in order to generate the content and conditional rules (counterfactuals) that capture customer's behaviors and beliefs....|date=2017|url=https://www.singularities.com/our-company|accessdate=2017-07-12|archive-url=https://web.archive.org/web/20171112074640/https://www.singularities.com/our-company|archive-date=2017-11-12|url-status=dead}}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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Applications of behavioral economics also exist in other disciplines, for example in the area of supply chain management.<br />
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行为经济学的应用也存在于其他学科,例如'''<font color = 'ff8000'>供应链管理supply chain management</font>'''<ref>{{cite journal | last1 = Schorsch | first1 = Timm | last2 = Marcus Wallenburg | first2 = Carl | last3 = Wieland | first3 = Andreas | year = 2017 | title = The human factor in SCM: Introducing a meta-theory of behavioral supply chain management | url = | journal = International Journal of Physical Distribution & Logistics Management | volume = 47 | issue = | pages = 238–262 | doi = 10.1108/IJPDLM-10-2015-0268 }}</ref><br />
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=== Natural experiments 自然实验===<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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From a biological point of view, human behaviors are essentially the same during crises accompanied by stock market crashes and during bubble growth when share prices exceed historic highs. During those periods, most market participants see something new for themselves, and this inevitably induces a stress response in them with accompanying changes in their endocrine profiles and motivations. The result is quantitative and qualitative changes in behavior. This is one example where behavior affecting economics and finance can be observed and variably-contrasted using behavioral economics.<br />
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从生物学的角度来看,不管是股市崩溃的危机期还是股价超过历史高点的泡沫增长期,人类行为的本质是一致的。在这些时期,大多数市场参与者看到了对自己有用的新东西,这不可避免地引发了压力反应,内分泌系统和心理动机也随之发生变化。而最终结果就是人的行为发生定量和定性的变化。这是一个典型的运用行为经济学来观察、对比人类行为是如何影响经济和金融的例子。<br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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Behavioral economics' usefulness applies beyond environments similar to stock exchanges. Selfish-reasoning, 'adult behaviors', and similar, can be identified within criminal-concealment(s), and legal-deficiencies and neglect of different types can be observed and discovered. Awareness of indirect consequence (or lack of), at least in potential with different experimental models and methods, can be used as well—behavioral economics' potential uses are broad, but its reliability needs scrutiny. Underestimation of the role of novelty as a stressor is the primary shortcoming of current approaches for market research. It is necessary to account for the biologically determined diphasisms of human behavior in everyday low-stress conditions and in response to stressors.<br />
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行为经济学不仅在类似证券交易所的环境中会发挥作用。我们可以在'''<font color = 'ff8000'>犯罪隐瞒行为criminal-concealment</font>'''中发现'''<font color = 'ff8000'>自私推理Selfish-reasoning</font>'''、“'''<font color = 'ff8000'>成人行为adult behaviors</font>'''”以及不同类型的法律缺陷和疏忽。需要明确的是不同实验模型和方法具有利用间接后果的认识(或缺乏)的的能力——至少是潜力。行为经济学的潜在用途是广泛的,但需要审查其可靠性。低估'''<font color = 'ff8000'>新异novelty</font>'''作为一种压力源的作用是目前市场研究方法的主要缺点。研究方法有必要解释在日常低应激条件下和应对应激源的时候,人类行为中具有的由生物学所决定的'''<font color = 'ff8000'>双相性diphasisms</font>'''<ref name="Sarapultsev, A. 2014" /> Limitations of experimental methods (e.g. randomized control trials) and their use in economics were famously analyzed by Angus Deaton.<ref>{{cite web |last1=Blattman |first1=Christopher |title=Why Angus Deaton Deserved the Nobel Prize in Economics |url=https://foreignpolicy.com/2015/10/12/why-angus-deaton-deserved-the-nobel-prize-in-economics/ |website=Foreign Policy |accessdate=18 February 2020}}</ref><br />
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== Criticism 批评==<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 批评的前两段语句不太通顺,最新英文维基百科的原文和翻译附在这两段之下<br />
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Critics of behavioral economics typically stress the [[rationality]] of economic agents.<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref> A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Critics of behavioral economics typically stress the rationality of economic agents. A fundamental critique is provided by Maialeh (2019) who argues that no behavioral research can establish an economic theory. Examples provided on this account include pillars of behavioral economics such as satisficing behavior or prospect theory, which are confronted from the neoclassical perspective of utility maximization and expected utility theory respectively. The author shows that behavioral findings are hardly generalizable and that they do not disprove typical mainstream axioms related to rational behavior.<br />
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行为经济学的批评通常强调经济行为主体的'''<font color = 'ff8000'>理性rationality</font>'''<ref>{{cite journal |last1= Myagkov |last2= Plott |year=1997 |title=Exchange Economies and Loss Exposure: Experiments Exploring Prospect Theory and Competitive Equilibria in Market Environments |url=http://authors.library.caltech.edu/43961/1/exchange%20economies%20and%20loss%20exposure.pdf}}</ref>。玛亚莱Maaialeh (2019)提供了一个基本的批评,他认为没有行为研究可以建立一个经济学理论。这些例子包括,行为经济学的支柱:从新古典主义的反面分别挑战'''<font color = 'ff8000'>效用最大化utility maximization</font>'''和'''<font color = 'ff8000'>期望效用理论expected utility theory</font>'''的'''<font color = 'ff8000'>满意行为satisficing behavior</font>'''和'''<font color = 'ff8000'>前景理论prospect theory</font>'''。作者向读者展示,行为研究结果很难被推广,而且它们不能否定理性行为有关的典型主流公理<ref>{{cite journal |last1=Maialeh |first1=Robin |title=Generalization of results and neoclassical rationality: unresolved controversies of behavioural economics methodology |journal=Quality & Quantity |date=2019 |volume=53 |issue=4 |pages=1743–1761 |doi=10.1007/s11135-019-00837-1 }}</ref><br />
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Others note that cognitive theories, such as [[prospect theory]], are models of [[decision-making]], not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.{{citation needed|date=May 2010}} Others argue that decision-making models, such as the [[Endowment effect|endowment effect theory]], that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions.<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents. Others argue that decision-making models, such as the endowment effect theory, that have been widely accepted behavioral economists may be erroneously established as a consequence of poor experimental design practices that do not adequately control subject misconceptions. <br />
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其他人则指出,前景理论等认知理论是决策模型,而不是推广化的经济行为。它们只适用于向实验参与者或调查对象提出的一次性的决策问题。其他人认为决策模型,如已被广泛接受的'''<font color = 'ff8000'>禀赋效应理论endowment effect theory</font>''',行为经济学家,可能被错误地建立为糟糕的实验设计实践的后果,没有充分控制受试者的错误概念<ref name=":0" /><ref>{{Cite journal|last=Klass|first=Greg|last2=[[Kathryn Zeiler|Zeiler]]|first2=Kathryn|date=2013-01-01|title=Against Endowment Theory: Experimental Economics and Legal Scholarship|url=https://scholarship.law.bu.edu/faculty_scholarship/199|journal=UCLA Law Review|volume=61|issue=1|pages=2}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2011-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Reply|url=https://scholarship.law.bu.edu/faculty_scholarship/521|journal=American Economic Review|volume=101|pages=1012}}</ref><ref>{{Cite journal|last=[[Kathryn Zeiler|Zeiler]]|first=Kathryn|date=2005-01-01|title=The Willingness to Pay-Willingness to Accept Gap, the 'Endowment Effect,' Subject Misconceptions, and Experimental Procedures for Eliciting Valuations|url=https://scholarship.law.bu.edu/faculty_scholarship/781|journal=American Economic Review|volume=95|pages=530}}</ref> <br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 以下是最新英文维基原文<br />
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Critics of behavioral economics typically stress the rationality of economic agents.[32] They contend that experimentally observed behavior has limited application to market situations, as learning opportunities and competition ensure at least a close approximation of rational behavior.<br />
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行为经济学的批评者通常强调经济主体的理性。他们认为,实验观察到的行为在市场环境中的应用有限,这是因为学习机会和竞争至少能确保他们接近理性。<br />
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Others note that cognitive theories, such as prospect theory, are models of decision-making, not generalized economic behavior, and are only applicable to the sort of once-off decision problems presented to experiment participants or survey respondents.<br />
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另一些人指出,认知理论,如前景理论,是决策模型而不是广义的经济行为。它们只适用于向实验参与者或调查对象提出的那种一次性决策问题。<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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A notable concern is that despite a great deal of rhetoric, no unified behavioral theory has yet been espoused: behavioral economists have proposed no unified theory.<br />
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一个值得关注的问题是,尽管有大量的修饰与措辞,但仍然没有一个统率性的行为理论得到支持,也就是说,行为经济学家还没有提出统一的理论。<br />
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[[David Gal]] has argued that many of these issues stem from behavioral economics being too concerned with understanding ''how'' behavior deviates from standard economic models rather than with understanding ''why'' people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of [[science]]. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref><br />
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David Gal has argued that many of these issues stem from behavioral economics being too concerned with understanding how behavior deviates from standard economic models rather than with understanding why people behave the way they do. Understanding why behavior occurs is necessary for the creation of generalizable knowledge, the goal of science. He has referred to behavioral economics as a "triumph of marketing" and particularly cited the example of loss aversion.<br />
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大卫·加尔David Gal认为,这些争论中的许多问题源于行为经济学过分执着于分析行为是如何偏离标准经济模型,而不是理解人们为什么会这样做。理解特定行为发生的原因对于归纳性知识的诞生很必要——这也是科学的目标。他还将行为经济学称为“市场营销的胜利” ,并特别提到了'''<font color = 'ff8000'>损失规避loss aversion</font>'''的例子<ref>{{Cite news|url=https://www.nytimes.com/2018/10/06/opinion/sunday/behavioral-economics.html|title=Opinion {{!}} Why Is Behavioral Economics So Popular?|access-date=2018-11-16|language=en}}</ref>。<br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively. Economists typically stress [[revealed preference]]s over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of [[systemic bias]]es, strategic behavior and lack of incentive compatibility.{{citation needed|date=May 2010}} Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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Traditional economists are skeptical of the experimental and survey-based techniques that behavioral economics uses extensively.Economists typically stress revealed preferences over stated preferences (from surveys) in the determination of economic value. Experiments and surveys are at risk of systemic biases, strategic behavior and lack of incentive compatibility. Some researchers point out that participants of experiments conducted by behavioural economists are not representative enough and drawing broad conclusions on the basis of such experiments is not possible. An acronym WEIRD has been coined in order to describe the studies participants - as those, who come from Western, Educated, Industrialized, Rich, and Democratic societies.<br />
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传统经济学家对行为经济学广泛使用的实验和调查技术持怀疑态度。经济学家通常会强调,在决定经济价值时,与显示性偏好相比,他们更偏向于展示(来自调查的)陈诉偏好。实验和调查具有'''<font color = 'ff8000'>系统偏差systemic biases</font>'''、'''<font color = 'ff8000'>策略行为strategic behavior</font>'''和缺乏'''<font color = 'ff8000'>激励相容incentive compatibility</font>'''的风险。一些研究人员指出,行为经济学实验的参与者代表性不够,因此具有广泛适用性的结论不可能在此类实验的基础上得出。为了描述这些研究的参与者——这些有着'''<font color = 'ff8000'>西方的Western</font>'''、'''<font color = 'ff8000'>受过教育的Educated</font>'''、'''<font color = 'ff8000'>工业化的Industrialized</font>'''、'''<font color = 'ff8000'>富裕的Rich</font>'''和'''<font color = 'ff8000'>民主的Democratic</font>'''社会背景的实验参与者,被人们描述为 :WEIRD(各个单词首字母的集合)<ref>Joseph Henrich, Steven J. Heine, Ara Norenzayan, The weirdest people in the world?, „Behavioral and brain sciences”, 2010.</ref><br />
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=== Responses 回应===<br />
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[[Matthew Rabin]]{{sfn|Rabin|1998|pp=11–46}} dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between [[experimental economics]] and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating [[neuroeconomics]], which is entirely experimental and has not been verified in the field.{{citation needed|date=May 2010}}<br />
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Matthew Rabin dismisses these criticisms, countering that consistent results typically are obtained in multiple situations and geographies and can produce good theoretical insight. Behavioral economists, however, responded to these criticisms by focusing on field studies rather than lab experiments. Some economists see a fundamental schism between experimental economics and behavioral economics, but prominent behavioral and experimental economists tend to share techniques and approaches in answering common questions. For example, behavioral economists are investigating neuroeconomics, which is entirely experimental and has not been verified in the field.<br />
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Matthew Rabin{{sfn|Rabin|1998|pp=11–46}}反驳了这些批评。他认为一致的结果通常是在多种情况和复杂地理环境下获得的,并且可以由此产生很好的理论洞察力。然而,行为经济学家则将对这些批评的回应重点放在'''<font color = 'ff8000'>田野研究field studies</font>'''而不是实验室实验上。一些经济学家认为'''<font color = 'ff8000'>实验经济学 experimental economics</font>'''和行为经济学之间存在根本的分歧,但一些杰出的行为和实验经济学家倾向于在一些共同问题上作出交叉性的回答。例如,行为经济学家正在研究'''<font color = 'ff8000'>神经经济学neuroeconomics</font>'''——它是完全实验性的且尚未在该领域得到验证{{citation needed|date=May 2010}}。<br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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The epistemological, ontological, and methodological components of behavioral economics are increasingly debated, in particular by historians of economics and economic methodologists.<br />
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行为经济学的'''<font color = 'ff8000'>认识论epistemological</font>'''、'''<font color = 'ff8000'>本体论ontological</font>'''和'''<font color = 'ff8000'>方法论methodological</font>'''饱受争议,尤其是在经济学史学家和经济方法论学家这里<ref>{{Cite news|url=https://www.exploring-economics.org/en/orientation/behavioral-economics/|title=Behavioral Economics |website= Exploring Economics|access-date=|last1 = Kersting|first1 = Felix|last2= Obst|first2= Daniel|date = 10 April 2016|language=en}}</ref><br />
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According to some researchers,<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref> when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref> because, "Stress is the nonspecific body response to any demands presented to it."<ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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According to some researchers, when studying the mechanisms that form the basis of decision-making, especially financial decision-making, it is necessary to recognize that most decisions are made under stress because, "Stress is the nonspecific body response to any demands presented to it."<br />
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一些研究人员表示<ref name="Sarapultsev, A. 2014">{{cite journal|last1=Sarapultsev |first1=A. |last2= Sarapultsev |first2=P. |year=2014 |title=Novelty, Stress, and Biological Roots in Human Market Behavior |journal=Behavioral Sciences |volume=4 |issue=1 |pages=53–69 |doi=10.3390/bs4010053|pmid=25379268 |pmc=4219248 }}</ref>,在研究构成决策基础的机制(尤其是财务决策)时,有必要认识到大多数决策都是在压力状态下做出的<ref>{{cite book|last=Zhukov |first=D.A. |title=Biologija Povedenija |work= Gumoral’nye Mehanizmy [Biology of Behavior. Humoral Mechanisms]; |publisher=Rech |location=St. Petersburg, Russia |year=2007}}</ref>,因为“压力是一种面对任务时人所做出的非特定的身体反应。” <ref name="Selye2013">{{cite book|first=Hans|last=Selye |title=Stress in Health and Disease|url={{google books |plainurl=y |id=wrfYBAAAQBAJ}}|year= 2013|publisher=Elsevier Science|isbn=978-1-4831-9221-5}}</ref><br />
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== Applied issues 应用问题==<br />
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=== Nudge theory “助推”理论===<br />
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{{Main|Nudge theory}}<br />
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[[File:Richard Thaler Chatham.jpg|thumb|140px|[[Richard Thaler]], winner of the 2017 Nobel Prize in economics]]<br />
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[[Richard Thaler, winner of the 2017 Nobel Prize in economics]]<br />
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[理查德 · 泰勒 Richard Thaler,2017年诺贝尔经济学奖得主]<br />
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'''Nudge''' is a concept in [[behavioral science]], [[political theory]] and [[economics]] which proposes [[positive reinforcement]] and indirect suggestions as ways to [[Social influence|influence]] the behavior and [[decision making]] of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as [[education]], [[legislation]] or [[enforcement]]. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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Nudge is a concept in behavioral science, political theory and economics which proposes positive reinforcement and indirect suggestions as ways to influence the behavior and decision making of groups or individuals. Nudging contrasts with other ways to achieve compliance, such as education, legislation or enforcement. The concept has influenced British and American politicians. Several nudge units exist around the world at the national level (UK, Germany, Japan and others) as well as at the international level (OECD, World Bank, UN).<br />
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'''<font color = 'ff8000'>“助推”Nudge</font>'''是行为科学、政治理论和经济学中的一个概念,该理论提出'''<font color = 'ff8000'>正强化positive reinforcement</font>'''和'''<font color = 'ff8000'>间接暗示indirect suggestions</font>'''可以影响群体或个体行为与决策。“助推”与其他实现'''<font color = 'ff8000'>依从compliance</font>'''的方式,比如教育、立法或执法,形成了鲜明对比。这个概念已经影响了英国和美国的政治家。在世界各地,国家层面(英国、德国、日本和其他国家)和国际层面(经济合作与发展组织OECD、世界银行、联合国),都存在一些'''<font color = 'ff8000'> “助推”单位nudge units</font>'''。<br />
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The first formulation of the term and associated principles was developed in [[cybernetics]] by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>). It also drew on methodological influences from clinical [[psychotherapy]] tracing back to [[Gregory Bateson]], including contributions from [[Milton Erickson]], [[Paul Watzlawick|Watzlawick]], [[John Weakland|Weakland]] and Fisch, and [[Bill O'Hanlon]].<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref> In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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The first formulation of the term and associated principles was developed in cybernetics by James Wilk before 1995 and described by Brunel University academic D. J. Stewart as "the art of the nudge" (sometimes referred to as micronudges). It also drew on methodological influences from clinical psychotherapy tracing back to Gregory Bateson, including contributions from Milton Erickson, Watzlawick, Weakland and Fisch, and Bill O'Hanlon. In this variant, the nudge is a microtargetted design geared towards a specific group of people, irrespective of the scale of intended intervention.<br />
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詹姆斯·沃尔夫 James Wilk 早在1995年以前就在控制论中首次提出了这一术语和相关原则,布鲁内尔大学的学者 斯图尔特 D. J. Stewart 称之为'''<font color = 'ff8000'>“助推”的艺术the art of the “nudge”</font>'''(有时称为'''<font color = 'ff8000'>“微推”micronudges</font>'''<ref>{{citation | author=Wilk, J. | year=1999 | chapter=Mind, nature and the emerging science of change: An introduction to metamorphology. | editor1=G. Cornelis|editor2=S. Smets|editor2-link= Sonja Smets |editor3=J. Van Bendegem | title=EINSTEIN MEETS MAGRITTE: An Interdisciplinary Reflection on Science, Nature, Art, Human Action and Society: Metadebates on science | volume=6 | pages=71–87 | publisher=Springer Netherlands | doi=10.1007/978-94-017-2245-2_6| isbn=978-90-481-5242-1 }}</ref>)。它还受到了临床心理治疗方法论的影响,这些方法可以追溯到Gregory Bateson,包括米尔顿·埃里克森Milton Erickson,沃兹拉维克Watzlawick,威克兰Weakland,菲施Fisch,和比尔·奥汉隆Bill O'Hanlon的研究<ref>{{citation | author1=O'Hanlon, B.|author2=Wilk, J. | year=1987 | title=Shifting contexts : The generation of effective psychotherapy. | publisher=New York, N.Y.: Guilford Press.}}</ref>。在这个变体中,”助推”是一个针对特定人群的'''<font color = 'ff8000'>微观目标设计 microtargetted design</font>''',而不考虑预期干预的规模。<br />
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In 2008, [[Richard Thaler]] and [[Cass Sunstein]]'s book ''[[Nudge (book)|Nudge: Improving Decisions About Health, Wealth, and Happiness]]'' brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health.<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref> The authors refer to influencing behaviour without coercion as [[libertarian paternalism]] and the influencers as choice architects.<ref name=speak /> Thaler and Sunstein defined their concept as:<br />
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In 2008, Richard Thaler and Cass Sunstein's book Nudge: Improving Decisions About Health, Wealth, and Happiness brought nudge theory to prominence. It also gained a following among US and UK politicians, in the private sector and in public health. The authors refer to influencing behaviour without coercion as libertarian paternalism and the influencers as choice architects. Thaler and Sunstein defined their concept as:<br />
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2008年,Richard Thaler和Cass Sunstein的书《'''<font color = 'ff8000'>“助推”:我们如何做出最佳选择Nudge: Improving Decisions About Health, Wealth, and Happiness</font>'''》让”助推”理论得到了重视。它还赢得了部分美国和英国的政界人士、私营部门以及公共卫生领域人员的追随<ref>See: [http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think Dr. Jennifer Lunt and Malcolm Staves] {{Webarchive|url=https://web.archive.org/web/20120430212840/http://www.shponline.co.uk/features-content/full/cpd-article-nudge-nudge-think-think |date=2012-04-30 }}</ref>。两位作者把非强制的影响施加过程称为'''<font color = 'ff8000'>自由意志的家长作风libertarian paternalism</font>''',称影响者为'''<font color = 'ff8000'>选择建筑师choice architects</font>'''<ref name=speak /> 。Thaler和Sunstein将他们的理论定义为:<br />
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{{quote|''A nudge, as we will use the term, is any aspect of the [[choice architecture]] that alters people's behavior in a predictable way without forbidding any options or significantly changing their economic incentives. To count as a mere nudge, the intervention must be easy and cheap to avoid. Nudges are not mandates. Putting fruit at eye level counts as a nudge. Banning junk food does not.''}}<br />
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正如我们将要提到的那样,“助推”是指'''<font color = 'ff8000'>选项结构choice architecture</font>'''中的任意一个,即在不禁止任何选择,也不颠覆人们经济动机的条件下以可预测的方式改变人的行为。而只有能被轻易做到的干预才能被算作一次“助推”。“助推”不是命令。把水果放在眼睛所在的高度算是“助推”,禁止垃圾食品就不是。<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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In this form, drawing on behavioral economics, the nudge is more generally applied to influence behaviour.<br />
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在这种形式下,借鉴行为经济学,“助推”能够更广泛地应用于行为影响。<br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room [[urinal]]s at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<ref name="nudge" /><br />
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One of the most frequently cited examples of a nudge is the etching of the image of a housefly into the men's room urinals at Amsterdam's Schiphol Airport, which is intended to "improve the aim."<br />
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人们经常引用的一个”助推”例子是,在阿姆斯特丹史基浦机场的男厕所小便池里画了家蝇的图象。这么做的目的是“'''<font color = 'ff8000'>优化目标improve the aim</font>'''” <ref name="nudge" />。<br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome.<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref> An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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Nudging techniques aim to use judgmental heuristics to our advantage. In other words, a nudge alters the environment so that when heuristic, or System 1, decision-making is used, the resulting choice will be the most positive or desired outcome. An example of such a nudge is switching the placement of junk food in a store, so that fruit and other healthy options are located next to the cash register, while junk food is relocated to another part of the store.<br />
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“助推”技巧的目的是利用判断启发式给我们提供好处。换句话说,”助推”改变了环境,所以当使用了启发式,也就是系统1来做决策的时候,往往就会出现最积极的或最想要的结果<ref>{{cite journal|last1=Campbell-Arvai|first1=V|last2=Arvai|first2=J.|last3=Kalof|first3=L.|title=Motivating sustainable food choices: the role of nudges, value orientation, and information provision|journal=Environment and Behavior|date=2014|volume=46|issue=4|pages=453–475|url=https://www.researchgate.net/publication/272996812|doi=10.1177/0013916512469099}}</ref>。一个例子就是,改变一些产品在商店里的位置——将健康食物放在收银机旁边,把垃圾食品搬到别部分<ref>{{cite journal|last1=Kroese|first1=F.|last2=Marchiori|first2=D.|last3=de Ridder|first3=D.|title=Nudging healthy food choices: a field experiment at the train station|journal=Journal of Public Health|date=2016|volume=38|issue=2|pages=e133–7|url=https://academic.oup.com/jpubhealth/article-pdf/38/2/e133/6869936/fdv096.pdf|doi=10.1093/pubmed/fdv096|pmid=26186924}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the [[Office of Information and Regulatory Affairs]].<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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In 2008, the United States appointed Sunstein, who helped develop the theory, as administrator of the Office of Information and Regulatory Affairs.<br />
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2008年,美国任命帮助完善该理论的Sunstein为信息和管理事务办公室Office of Information and Regulatory Affairs的管理员<ref name=speak>{{cite news|url=https://www.theguardian.com/politics/blog/2008/aug/22/davidcameron.conservatives|title=Speak 'Nudge': The 10 key phrases from David Cameron's favorite book|author=Andrew Sparrow|newspaper=[[The Guardian]]|date=2008-08-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite news|url=http://business.timesonline.co.uk/tol/business/career_and_jobs/article4330267.ece|title=Why Barack Obama and David Cameron are keen to 'nudge' you|newspaper=[[The Times]]|author=Carol Lewis |date=2009-07-22|accessdate=2009-09-09 | location=London}}</ref><ref>{{cite magazine|url=http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|title=Nudge, nudge: meet the Cameroons' new guru|magazine=[[The Spectator]]|author=James Forsyth|date=2009-07-16|accessdate=2009-09-09|url-status=dead|archiveurl=https://web.archive.org/web/20090124222449/http://www.spectator.co.uk/the-magazine/features/839676/nudge-nudge-meet-the-cameroons-new-guru.thtml|archivedate=2009-01-24}}</ref><br />
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Notable applications of nudge theory include the formation of the British [[Behavioural Insights Team]] in 2010. It is often called the "Nudge Unit", at the British [[Cabinet Office]], headed by [[David Halpern (psychologist)|David Halpern]].<ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Notable applications of nudge theory include the formation of the British Behavioural Insights Team in 2010. It is often called the "Nudge Unit", at the British Cabinet Office, headed by David Halpern.<br />
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“助推”理论的主要应用包括2010年英国行为洞察小组British Behavioural Insights Team的成立。它从属于戴维·哈珀恩David Halpern领导的英国内阁办公室British Cabinet Office,常被称为“'''<font color = 'ff8000'>“助推”小组Nudge Unit</font>'''” <ref>{{cite web|url=https://www.behaviouralinsights.co.uk/about-us/|title=Who we are |website = The Behavioural Insights Team}}</ref><br />
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Both Prime Minister [[David Cameron]] and President [[Barack Obama]] sought to employ nudge theory to advance [[domestic policy]] goals during their terms.<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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Both Prime Minister David Cameron and President Barack Obama sought to employ nudge theory to advance domestic policy goals during their terms.<br />
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英国首相戴维·卡梅伦David Cameron和美国前总统·奥巴马Barack Obama都试图在任期内运用”助推”理论来实现国内政策目标<ref>{{cite news|url=https://www.independent.co.uk/news/uk/politics/first-obama-now-cameron-embraces-nudge-theory-2050127.html|title=First Obama, now Cameron embraces 'nudge theory'|date=12 August 2010|newspaper=The Independent}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref><br />
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In Australia, the government of New South Wales established a Behavioural Insights community of practice.<br />
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在澳大利亚,新南威尔士州政府建立了一个行为洞察实践社区Behavioural Insights community of practice<ref>{{cite web |url= http://bi.dpc.nsw.gov.au/|title=Behavioural Insights|publisher =Department of Premier and Cabinet|website=bi.dpc.nsw.gov.au}}</ref>。<br />
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Nudge theory has also been applied to [[business management]] and [[corporate culture]], such as in relation to [[Environment, health and safety|health, safety and environment]] (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Nudge theory has also been applied to business management and corporate culture, such as in relation to health, safety and environment (HSE) and human resources. Regarding its application to HSE, one of the primary goals of nudge is to achieve a "zero accident culture."<br />
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“助推”理论也被应用于企业管理和企业文化,包括健康、安全、环境(health, safety and environment, HSE)、人力资源等领域。应用”助推”在HSE中的主要目标之一是实现“'''<font color = 'ff8000'>零事故文化zero accident culture</font>'''” <ref>{{cite web|url=http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|title=Cast No Shadow|website= Rydermarsh.co.uk|url-status = dead|archiveurl = https://web.archive.org/web/20171010050856/http://www.rydermarsh.co.uk/pdfs/SHP.0112.pdf|archivedate =10 October 2017|last = Marsh|first = Tim|date = January 2012 }}</ref><br />
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Leading [[Silicon Valley]] companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Leading Silicon Valley companies are forerunners in applying nudge theory in a corporate setting. These companies are using nudges in various forms to increase the productivity and happiness of employees. Recently, further companies are gaining interest in using what is called "nudge management" to improve the productivity of their white-collar workers.<br />
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硅谷的各个企业巨头是”助推”理论应用方面的先锋。这些公司正在用各种方式的”助推”来提高员工的生产力和幸福感。最近,越来越多的公司开始研究如何利用“'''<font color = 'ff8000'>“助推”管理nudge management</font>'''”来提高白领工人的生产率<ref>{{Cite journal|last=Ebert|first=Philip|last2=Freibichler|first2=Wolfgang|year=2017|title=Nudge management: applying behavioural science to increase knowledge worker productivity|journal=Journal of Organization Design|volume=6:4|pages=|doi=10.1186/s41469-017-0014-1|hdl=1893/25187|hdl-access=free}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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Behavioral insights and nudges are currently used in many countries around the world.<br />
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目前世界上许多国家都在运用行为洞察力和“助推”力<ref>{{cite book|last=Carrasco-Villanueva|first=Marco|editor=上海社会科学院 [Shanghai Academy of Social Sciences]|title=2016上海青年汉学家研修计划论文集|language=zh|publisher=中国社会科学出版社 [China Social Sciences Press]|date=2016|pages=[https://archive.org/details/guidetolcshinfor00doej/page/368 368–392]|chapter=中国的环境公共政策:一个行为经济学的选择 [Environmental Public Policies in China: An Opportunity for Behavioral Economics]|isbn=978-1-234-56789-7|url=https://archive.org/details/guidetolcshinfor00doej/page/368}}</ref><br />
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==== Criticisms 批评====<br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation [[The King's Fund]], has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref><br />
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Nudging has also been criticised. Tammy Boyce, from public health foundation The King's Fund, has said: "We need to move away from short-term, politically motivated initiatives such as the 'nudging people' idea, which is not based on any good evidence and doesn't help people make long-term behaviour changes."<br />
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“助推”也受到了批评。来自公共卫生基金会“国王基金会The King's Fund”的塔米·博伊斯 Tammy Boyce说:“我们避免短期的、出于政治动机的行动,比如‘“助推”人们的想法——这种想法没有任何有力的证据支撑,也无助于人们做出长期的改变。<ref>{{cite news| url=https://www.independent.co.uk/life-style/health-and-wellbeing/health-news/unhealthy-lifestyles-here-to-stay-in-spite-of-costly-campaigns-1055693.html | work=The Independent | location=London | title=Unhealthy lifestyles here to stay, in spite of costly campaigns | first=Nina | last=Lakhani | date=December 7, 2008 | accessdate=April 28, 2010}}</ref>”<br />
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Cass Sunstein has responded to critiques at length in his ''The Ethics of Influence''<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref> making the case in favor of nudging against charges that nudges diminish autonomy,<ref>{{Cite journal|last=Schubert|first=Christian|date=2015-10-12|title=On the Ethics of Public Nudging: Autonomy and Agency|location=Rochester, NY|ssrn=2672970}}</ref> threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously.<ref>{{Cite journal|last=Barton|first=Adrien|last2=Grüne-Yanoff|first2=Till|date=2015-09-01|title=From Libertarian Paternalism to Nudging—and Beyond|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=341–359|doi=10.1007/s13164-015-0268-x|issn=1878-5158|doi-access=free}}</ref> These charges have been made by various participants in the debate from Bovens<ref>{{Cite book|title=Preference Change|last=Bovens|first=Luc|date=2009|publisher=Springer, Dordrecht|isbn=9789048125920|series=Theory and Decision Library|pages=207–219|language=en|doi=10.1007/978-90-481-2593-7_10|chapter = The Ethics of Nudge}}</ref> to Goodwin.<ref>{{Cite journal|last=Goodwin|first=Tom|date=2012-06-01|title=Why We Should Reject 'Nudge'|journal=Politics|language=en|volume=32|issue=2|pages=85–92|doi=10.1111/j.1467-9256.2012.01430.x|issn=0263-3957}}</ref> Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Cass Sunstein has responded to critiques at length in his The Ethics of Influence making the case in favor of nudging against charges that nudges diminish autonomy, threaten dignity, violate liberties, or reduce welfare. Ethicists have debated this rigorously. These charges have been made by various participants in the debate from Bovens to Goodwin. Wilkinson for example charges nudges for being manipulative, while others such as Yeung question their scientific credibility.<br />
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Sunstein在他的《'''<font color = 'ff8000'>影响力的道德The Ethics of Influence</font>'''》<ref>{{Cite book|url={{google books |plainurl=y |id=TlvWDAAAQBAJ|page=8}} |title=The Ethics of Influence: Government in the Age of Behavioral Science|last=Sunstein|first=Cass R.|date=2016-08-24|publisher=Cambridge University Press|isbn=9781107140707|language=en}}</ref>一书中对批评做出了详尽的回应,表示支持“助推”并反对那些认为“助推”会削弱自主权、威胁尊严、侵犯自由或减少福利的指控。伦理学家们对此展开了激烈的辩论。这些指控是由博芬申Bovens,古德温 Goodwin等辩论参与者提出的。例如,威尔金森 Wilkinson指责”助推”对会操纵个人行为,而杨 Yeung等人则质疑其科学可信度<ref>{{Cite journal|last=Yeung|first=Karen|date=2012-01-01|title=Nudge as Fudge|journal=The Modern Law Review|language=en|volume=75|issue=1|pages=122–148|doi=10.1111/j.1468-2230.2012.00893.x|issn=1468-2230}}</ref><br />
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Some, such as Hausman & Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref> have inquired whether nudging should be permissible on grounds of (distributive{{clarify|date=February 2018}}) justice; Lepenies & Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref> have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Some, such as Hausman & Welch have inquired whether nudging should be permissible on grounds of (distributive) justice; Lepenies & Malecka have questioned whether nudges are compatible with the rule of law. Similarly, legal scholars have discussed the role of nudges and the law.<br />
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豪斯曼 Hausman和韦尔奇 Welch<ref>{{Cite journal|last=Hausman|first=Daniel M.|last2=Welch|first2=Brynn|date=2010-03-01|title=Debate: To Nudge or Not to Nudge*|journal=Journal of Political Philosophy|language=en|volume=18|issue=1|pages=123–136|doi=10.1111/j.1467-9760.2009.00351.x|issn=1467-9760}}</ref>等人曾提出,在'''<font color = 'ff8000'>分配公平distributive justice</font>'''{{clarify|date=February 2018}}的基础上,“助推”是否应该被允许;勒皮尼 Lepenies和马莱卡 Malecka<ref>{{Cite journal|last=Lepenies|first=Robert|last2=Małecka|first2=Magdalena|date=2015-09-01|title=The Institutional Consequences of Nudging – Nudges, Politics, and the Law|journal=Review of Philosophy and Psychology|language=en|volume=6|issue=3|pages=427–437|doi=10.1007/s13164-015-0243-6|issn=1878-5158}}</ref>曾质疑”助推”是否符合法律规范。类似地,法律学者也讨论了“助推”和法律所扮演的角色<ref>{{Cite journal|last=Alemanno|first=A.|last2=Spina|first2=A.|date=2014-04-01|title=Nudging legally: On the checks and balances of behavioral regulation|journal=International Journal of Constitutional Law|language=en|volume=12|issue=2|pages=429–456|doi=10.1093/icon/mou033|issn=1474-2640|doi-access=free}}</ref><ref>{{Cite journal|last=Kemmerer|first=Alexandra|last2=Möllers|first2=Christoph|last3=Steinbeis|first3=Maximilian|last4=Wagner|first4=Gerhard|date=2016-07-15|title=Choice Architecture in Democracies: Exploring the Legitimacy of Nudging - Preface|location=Rochester, NY|ssrn=2810229}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still [[homo oeconomicus|homo economicus]], despite the proponents' claim to the contrary.<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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Behavioral economists such as Bob Sugden have pointed out that the underlying normative benchmark of nudging is still homo economicus, despite the proponents' claim to the contrary.<br />
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Bob Sugden等行为经济学家指出,”助推”的基准仍然是'''<font color = 'ff8000'>经济人homo economicus</font>'''——尽管该理论的支持者认为恰恰相反。<ref>{{Cite journal|last=Sugden|first=Robert|date=2017-06-01|title=Do people really want to be nudged towards healthy lifestyles?|journal=International Review of Economics|language=en|volume=64|issue=2|pages=113–123|doi=10.1007/s12232-016-0264-1|issn=1865-1704|doi-access=free}}</ref><br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) 增加“该理论的” 存疑。<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 认同增加“该理论的” 。<br />
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It has been remarked that nudging is also a [[euphemism]] for [[psychological manipulation]] as practiced in [[social engineering (political science)|social engineering]].<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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It has been remarked that nudging is also a euphemism for psychological manipulation as practiced in social engineering.<br />
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有人说,”助推”也是'''<font color = 'ff8000'>社会工程学social engineering</font>'''里对心理操纵的委婉说法<ref>{{cite web|url=http://www.law.harvard.edu/programs/olin_center/papers/pdf/Sunstein_809.pdf|title=NUDGING AND CHOICE ARCHITECTURE: ETHICAL CONSIDERATIONS|author=Cass R. Sunstein|website=Law.harvard.edu|accessdate=11 October 2017}}</ref><ref>{{cite web|url=http://www.abc.net.au/news/2015-12-01/berg-a-nudge-in-the-right-direction/6988786|title=A nudge in the right direction? How we can harness behavioural economics|date=1 December 2015|publisher=}}</ref><br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> and Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>).<br />
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There exists an anticipation and, simultaneously, implicit criticism of the nudge theory in works of Hungarian social psychologists who emphasize the active participation in the nudge of its target (Ferenc Merei and Laszlo Garai).<br />
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在强调积极参与“助推”的匈牙利社会心理学家(弗伦茨·梅雷 Ferenc Merei<ref>{{cite journal|last =MÉREI|first= Ferenc |date =1987|title = A perem-helyzet egyik változata: a szociálpszichológiai kontúr |trans-title=A variant of the edge-position: the contour social psychological |language = Hungarian|journal = Pszichológia |volume =1|pages = 1–5}}</ref> 和拉斯洛·加莱 Laszlo Garai<ref name = Garai>{{cite book|last =Garai|first = Laszlo|chapter= The Double-Storied Structure of Social Identity|title = Reconsidering Identity Economics|publisher = Palgrave Macmillan|location= New York|date = 2017|isbn = 978-1-137-52561-1}}</ref>))的著作中,对“助推”理论的预期和含蓄批评同时存在。<br />
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=== Behavioral finance 行为金融学<!--'Behavioral finance' redirects here--> ===<br />
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[[File:Robert J. Shiller 2017.jpg|thumb|left|140px|[[Robert J. Shiller]], winner of the 2013 Nobel Prize in economics]]<br />
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[[Robert J. Shiller, winner of the 2013 Nobel Prize in economics]]<br />
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罗伯特·希勒Robert J. Shiller,2013年诺贝尔经济学奖获得者<br />
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The central issue in '''behavioral finance'''<!--boldface per WP:R#PLA--> is explaining why market participants make irrational [[systematic errors]] contrary to assumption of rational market participants.<ref name="ssrn.com" /> Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage ([[arbitrage]]) of such errors and market inefficiencies.<br />
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The central issue in behavioral finance<!--boldface per WP:R#PLA--> is explaining why market participants make irrational systematic errors contrary to assumption of rational market participants. Such errors affect prices and returns, creating market inefficiencies. The study of behavioral finance also investigates how other participants take advantage (arbitrage) of such errors and market inefficiencies.<br />
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'''<font color = 'ff8000'>行为金融学behavioral finance</font>'''的核心问题是解释为什么市场参与者会犯与理性市场参与者假设相反的系统性非理性错误<ref name="ssrn.com" />。这些错误会影响价格和收益,造成'''<font color = 'ff8000'>市场失效market inefficiencies</font>'''。行为金融学也研究其他参与者如何利用这些错误和市场失效为自己牟利,也就是所谓的'''<font color = 'ff8000'>套利arbitrage</font>'''。<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of [[market trend]]s and, in extreme cases, of [[Economic bubble|bubbles]] and [[Stock market crash|crashes]]. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry ([[herding instinct]]) and [[noise trader|noise trading]]. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for [[technical analysis]].{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}<br />
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Behavioral finance highlights inefficiencies, such as under- or over-reactions to information, as causes of market trends and, in extreme cases, of bubbles and crashes. Such reactions have been attributed to limited investor attention, overconfidence, overoptimism, mimicry (herding instinct) and noise trading. Technical analysts consider behavioral finance to be behavioral economics' "academic cousin" and the theoretical basis for technical analysis.<br />
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行为金融学关注''<font color = 'ff8000'>低效率inefficiencies</font>''',例如'''<font color = 'ff8000'>对信息反应迟钝或过激under- or over-reactions to information</font>'''——它们引导着市场趋势,触发极端情况下的泡沫和崩溃。这被归因于'''<font color = 'ff8000'>投资者注意有限limited investor attention</font>'''、'''<font color = 'ff8000'>过度自信overconfidence</font>'''、'''<font color = 'ff8000'>过于乐观overoptimism</font>'''、'''<font color = 'ff8000'>模仿mimicry</font>'''('''<font color = 'ff8000'>集群本能herding instinct</font>''')和'''<font color = 'ff8000'>噪音交易noise trading</font>'''。技术分析家认为行为金融学是行为经济学的“'''<font color = 'ff8000'>学术表亲academic cousin</font>'''” ,是技术分析的理论基础{{sfn|Kirkpatrick|Dahlquist|2007|p=49}}。<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and [[loss aversion]], the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss.{{citation needed|date=October 2018}} It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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Other key observations include the asymmetry between decisions to acquire or keep resources, known as the "bird in the bush" paradox, and loss aversion, the unwillingness to let go of a valued possession. Loss aversion appears to manifest itself in investor behavior as a reluctance to sell shares or other equity if doing so would result in a nominal loss. It may also help explain why housing prices rarely/slowly decline to market clearing levels during periods of low demand.<br />
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其他关键的观察还包括获取和保留资源之间的不对称决策,即所谓的“'''<font color = 'ff8000'>林中之鸟 bird in the bush</font>'''(没把握的事)”悖论,以及损失厌恶——即不愿意放弃有价值的财产。损失厌恶可以表现为投资者在可能产生少量损失的条件下不愿出售股票或其他股权{{citation needed|date=October 2018}}。这可能也有助于解释为什么在需求低迷时期,会出现房价很少或者以极慢的速度下降到市场清算水平的现象。<br />
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Benartzi and Thaler, applying a version of [[prospect theory]], claim to have solved the [[equity premium puzzle]], something conventional finance models so far have been unable to do.{{sfn|Benartzi|Thaler|1995}} [[Experimental finance]] applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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Benartzi and Thaler, applying a version of prospect theory, claim to have solved the equity premium puzzle, something conventional finance models so far have been unable to do. Experimental finance applies the experimental method, e.g., creating an artificial market through some kind of simulation software to study people's decision-making process and behavior in financial markets.<br />
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通过使用前景理论的一个版本,贝纳奇 Benartzi 和泰勒 Thaler声称已经解决了'''<font color = 'ff8000'>股权溢价之谜equity premium puzzle</font>'''——一个传统金融模型迄今无法解决的问题。实验金融学在研究过程中会运用实验的方法,例如通过某种模拟软件人为创造一个市场来研究人们在金融市场中的决策过程和行为。<br />
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==== Quantitative behavioral finance 量化行为金融学====<br />
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[[Quantitative behavioral finance]] uses mathematical and statistical methodology to understand [[behavioral bias]]es. In marketing research, a study shows little evidence that escalating biases impact marketing decisions.<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref> Leading contributors include [[Gunduz Caginalp]] (Editor of the [[Journal of Behavioral Finance]] from 2001–04), and collaborators include 2002 Nobel Laureate [[Vernon L. Smith|Vernon Smith]], David Porter, Don Balenovich,<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref> Vladimira Ilieva and Ahmet Duran,<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref> and Ray Sturm.<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref><br />
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Quantitative behavioral finance uses mathematical and statistical methodology to understand behavioral biases. In marketing research, a study shows little evidence that escalating biases impact marketing decisions. Leading contributors include Gunduz Caginalp (Editor of the Journal of Behavioral Finance from 2001–04), and collaborators include 2002 Nobel Laureate Vernon Smith, David Porter, Don Balenovich, Vladimira Ilieva and Ahmet Duran, and Ray Sturm.<br />
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'''<font color = 'ff8000'>量化行为金融学Quantitative behavioral finance</font>'''使用数学和统计方法来研究行为偏差。在市场研究中,一项调查显示没有证据表明逐步升级的偏见会影响市场决策<ref>{{cite journal|url=http://www.forecastingprinciples.com/paperpdf/Escalation%20Bias.pdf|title=Escalation Bias: Does It Extend to Marketing?|author=J. Scott Armstrong, Nicole Coviello and Barbara Safranek|journal=Journal of the Academy of Marketing Science|volume=21|pages=247–352|year=1993|doi=10.1177/0092070393213008|issue=3|citeseerx=<!--10.1.1.335.5132-->}}</ref>。主要贡献者包括冈兹·卡基纳尔普 Gunduz Caginalp (2001-2004年《'''<font color = 'ff8000'>行为金融学期刊Journal of Behavioral Finance</font>'''》的编辑) ,合作者包括2002年诺贝尔奖获得者弗农·史密斯 Vernon Smith,戴维·波特 David Porter,唐·巴列诺维奇 Don Balenovich<ref name=porter>{{cite web|title=Dr. Donald A. Balenovich|publisher=Indiana University of Pennsylvania, Mathematics Department|url=http://www.ma.iup.edu/people/dabalen.html}}</ref>,弗拉基米尔·黎利耶夫 Vladimira Ilieva ,艾哈迈德·杜兰 Ahmet Duran<ref name=duran>{{cite web|title=Ahmet Duran|publisher=Department of Mathematics, [[University of Michigan]]-Ann Arbor|url=http://www.umich.edu/~durana}}</ref>以及雷·斯特姆 Ray Sturm<ref name=sturm>{{cite web|title=Dr Ray R. Sturm, CPA |publisher=College of Business Administration |url=http://www.bus.ucf.edu/rsturm |url-status=dead |archiveurl=https://web.archive.org/web/20060920114653/http://www.bus.ucf.edu/rsturm/ |archivedate=September 20, 2006 }}</ref>。<br />
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==== Financial models 金融模型====<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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Some financial models used in money management and asset valuation incorporate behavioral finance parameters. Examples:<br />
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一些用于货币管理和资产评估的金融模型与行为金融学参数相结合。例如:<br />
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* Thaler's model of price reactions to information, with three phases (underreaction, adjustment, and overreaction), creating a price [[market trend|trend]].<br />
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* Thaler制造过一个通过信息回馈来创造价格('''<font color = 'ff8000'>市场趋势market trend</font>''')。<br />
'''<font color = 'ff8000'>的价格反应模型model of price reactions to information</font>'''。该模型具有三个阶段('''<font color = 'ff8000'>反应不足underreaction</font>''','''<font color = 'ff8000'>调整adjustment</font>''',和'''<font color = 'ff8000'>反应过度overreaction</font>''')。<br />
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:One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing [[habit]]s.<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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One characteristic of overreaction is that average returns following announcements of good news is lower than following bad news. In other words, overreaction occurs if the market reacts too strongly or for too long to news, thus requiring an adjustment in the opposite direction. As a result, outperforming assets in one period is likely to underperform in the following period. This also applies to customers' irrational purchasing habits.<br />
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反应过度的一个特点是,宣布好消息后获得的平均收益低于宣布坏消息后获得的。换句话说,如果市场对新闻反应过强或过长就会出现反应过度现象,所以需要向反方向作出调整。因此,在一个时期超常表现的资产在下一个时期可能表现不佳。这也适用于解读消费者不理性的购买习惯<ref>{{cite web|url=http://flevy.com/blog/why-people-wont-buy-your-product-even-though-its-awesome/|title=Why People Won't Buy Your Product Even Though It's Awesome|last=Tang|first=David|date=6 May 2013|publisher=Flevy|accessdate=31 May 2013}}</ref><br />
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* The [[stock valuation|stock image]] coefficient.<br />
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* '''<font color = 'ff8000'>股票估价stock valuation</font>'''或'''<font color = 'ff8000'>股票图像stock image</font>'''系数<br />
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==== Criticisms 批评====<br />
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Critics such as [[Eugene Fama]] typically support the [[efficient-market hypothesis]]. They contend that behavioral finance is more a collection of [[Market anomaly|anomalies]] than a true branch of [[finance]] and that these anomalies are either quickly priced out of the market or explained by appealing to [[market microstructure]] arguments. However, individual [[cognitive bias]]es are distinct from social biases; the former can be averaged out by the market, while the other can create positive [[feedback loop]]s that drive the market further and further from a "[[fair price]]" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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Critics such as Eugene Fama typically support the efficient-market hypothesis. They contend that behavioral finance is more a collection of anomalies than a true branch of finance and that these anomalies are either quickly priced out of the market or explained by appealing to market microstructure arguments. However, individual cognitive biases are distinct from social biases; the former can be averaged out by the market, while the other can create positive feedback loops that drive the market further and further from a "fair price" equilibrium. Similarly, for an anomaly to violate market efficiency, an investor must be able to trade against it and earn abnormal profits; this is not the case for many anomalies.<br />
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像尤金·珐玛 Eugene Fama 一样,许多批评家通常支持'''<font color = 'ff8000'>市场有效性假说efficient-market hypothesis</font>'''。他们认为,与其说是一个真正的金融学分支,行为金融学更像是一个异常现象的集合——这些异常现象要么很快被排挤出市场,要么可以通过'''<font color = 'ff8000'>市场微观结构market microstructure</font>'''理论来解释。然而,'''<font color = 'ff8000'>个人认知偏差individual cognitive biases</font>'''不同于'''<font color = 'ff8000'>社会偏差social biases</font>''';前者可以被市场平均化,而后者可以创造正反馈循环从而使市场越来越偏离”'''<font color = 'ff8000'>公平价格fair price</font>'''”这一均衡状态。同样,对于违反市场有效性的异常现象,投资者必须有能力进行反向交易并获得异常利润。但事实上许多人难以做到<ref>{{Cite web|url=http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|archiveurl=https://web.archive.org/web/20100324015212/http://www.dimensional.com/famafrench/2009/08/fama-on-market-efficiency-in-a-volatile-market.html|url-status=dead|title=Fama on Market Efficiency in a Volatile Market|archivedate=March 24, 2010}}</ref><br />
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A specific example of this criticism appears in some explanations of the [[equity premium puzzle]]. It is argued that the cause is [[barriers to entry|entry barriers]] (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders.<ref>See Freeman, 2004 for a review</ref> In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers.{{citation needed|date=July 2016}} In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.{{citation needed|date=July 2016}}<br />
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A specific example of this criticism appears in some explanations of the equity premium puzzle. It is argued that the cause is entry barriers (both practical and psychological) and that returns between stocks and bonds should equalize as electronic resources open up the stock market to more traders. In response, others contend that most personal investment funds are managed through superannuation funds, minimizing the effect of these putative entry barriers. In addition, professional investors and fund managers seem to hold more bonds than one would expect given return differentials.<br />
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该批评的一个具体例子出现在对'''<font color = 'ff8000'>股票溢价之谜equity premium puzzle</font>'''的一些解释中。有人认为,股票溢价之谜的原因是'''<font color = 'ff8000'>壁垒entry barriers</font>'''(既是实际上的也是心理上的),并声称随着电子资源使股票市场向更多的交易者开放,股票和债券之间的回报应该相等<ref>See Freeman, 2004 for a review</ref>。作为回应,其他人认为,大多数个人投资基金是通过养老基金管理的,这最小化了这些假定壁垒的影响{{citation needed|date=July 2016}}。此外,考虑到'''<font color = 'ff8000'>回报率差异return differentials</font>''',专业投资者和基金经理持有的债券似乎超出了人们的预期{{citation needed|date=July 2016}}<br />
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=== Behavioral game theory 行为博弈论===<br />
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{{Main|Behavioral game theory}}<br />
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Behavioral game theory, invented by [[Colin Camerer]], analyzes interactive [[Strategy (game theory)|strategic]] decisions and behavior using the [[methodology|methods]] of [[game theory]],<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Experimental economics#Experimental topics|experimental economics]], and [[experimental psychology]]. Experiments include testing deviations from typical simplifications of economic theory such as the [[Independence of irrelevant alternatives|independence axiom]]<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref> and neglect of [[altruism]],<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref> [[Fair division|fairness]], <ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref><br />
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Behavioral game theory, invented by Colin Camerer, analyzes interactive strategic decisions and behavior using the methods of game theory, experimental economics, and experimental psychology. Experiments include testing deviations from typical simplifications of economic theory such as the independence axiom and neglect of altruism, fairness,<br />
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'''<font color = 'ff8000'>行为博弈论Behavioral game theory</font>'''由科林·卡梅勒 Colin Camerer发明,运用博弈论<ref>{{cite web |first=Robert |last=Auman |authorlink=Robert Aumann|title=Game Theory |url=http://www.dictionaryofeconomics.com/articleid=pde2008_G000007&q=game%20theory&topicid=&result_number=3}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、实验经济学和实验心理学的方法分析'''<font color = 'ff8000'>交互式战略决策interactive strategic decisions</font>'''和行为。实验包括检验典型的经济理论简化的偏差,如'''<font color = 'ff8000'>独立公理independence axiom</font>'''<ref>{{cite journal | last1 = Camerer | first1 = Colin | last2 = Ho | first2 = Teck-Hua | author-link1 = Colin Camerer | title = Violations of the betweenness axiom and nonlinearity in probability | journal = Journal of Risk and Uncertainty | volume = 8 | issue = 2 | pages = 167–96 | date = March 1994 | ref = harv | doi=10.1007/bf01065371}}</ref>和忽视'''<font color = 'ff8000'>利他主义altruism</font>'''<ref>{{cite web |first=James |last=Andreoni |title=Altruism in experiments |url=http://www.dictionaryofeconomics.com/article?id=pde008_A000240&edition=current&q=altruism%20game&topicid=&result_number=2 |display-authors=etal}} in {{harvnb|Palgrave|ref=Palgrave}}</ref>、'''<font color = 'ff8000'>公平公正fairness</font>'''<ref>{{cite web |first=H. Peyton |last=Young |authorlink=H. Peyton Young |title=Social norms|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref>,<br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and [[Framing effect (psychology)|framing effects]].<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref> On the [[positive economics|positive]] side, the method has been applied to interactive learning<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> and [[social preference]]s.<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref> As a research program, the subject is a development of the last three decades.<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref><br />
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|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} </ref> and framing effects. On the positive side, the method has been applied to interactive learning and social preferences. As a research program, the subject is a development of the last three decades.<br />
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和'''<font color = 'ff8000'>框架效应framing effects</font>'''<ref>{{cite journal | last = Camerer | first = Colin | author-link = Colin Camerer | title = Progress in behavioral game theory | journal = Journal of Economic Perspectives | volume = 11 | issue = 4 | page = 172 | date = 1997 | url = http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | ref = harv | doi = 10.1257/jep.11.4.167 | access-date = 2014-10-31 | archive-url = https://web.archive.org/web/20171223112437/http://www.hss.caltech.edu/content/progress-and-behavioral-game-theory | archive-date = 2017-12-23 | url-status = dead }} [http://authors.library.caltech.edu/22122/1/2138470%5B1%5D.pdf Pdf version.]</ref>。积极的一面是,这种方法已经应用于'''<font color = 'ff8000'>交互式学习interactive learning</font>'''<ref>{{cite web|first=Teck H. |last=Ho |year=2008 |title=Individual learning in games |url=http://www.dictionaryofeconomics.com/article?id=pde2008_L000055 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>和'''<font color = 'ff8000'>社会偏好social preferences</font>'''的研究<ref>{{cite journal |first1=Martin |last1=Dufwenberg |first2=Georg |last2=Kirchsteiger |year=2004 |title=A Theory of Sequential reciprocity |journal=Games and Economic Behavior |issue=2 |pages=268–98 |doi=10.1016/j.geb.2003.06.003 |volume=47|citeseerx=10.1.1.124.9311 }}</ref><ref>{{cite web |first=Faruk |last=Gul |authorlink=Faruk Gul |year=2008 |title=Behavioural economics and game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_G000210&edition=current&q=behavioural%20economics%20&topicid=&result_number=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><ref>{{cite web |first=Colin F. |last=Camerer |authorlink=Colin F. Camerer |year=2008 |title=Behavioral game theory |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000302&q=Behavioral%20economics%20&topicid=&result_number=13 }} in {{harvnb|Palgrave|ref=Palgrave}}</ref>。这是一门在近三十年的时间里发展起来的研究课题<ref>{{cite book | last = Camerer | first = Colin | author-link = Colin Camerer | title = Behavioral game theory: experiments in strategic interaction | publisher = Russell Sage Foundation Princeton University Press | location = New York, New York Princeton, New Jersey | year = 2003 | isbn = 978-0-691-09039-9 |url={{google books |plainurl=y |id=cr_Xg7cRvdcC}} }}</ref><ref>{{cite book |first1 = George |last1=Loewenstein |authorlink1 =George Loewenstein |first2=Matthew |last2=Rabin |authorlink2=Matthew Rabin |year=2003 |title=Advances in Behavioral Economics 1986–2003 papers |location=Princeton |url=http://press.princeton.edu/titles/8437.html }}</ref><ref>{{cite journal |last=Fudenberg |first=Drew |authorlink=Drew Fudenberg |year=2006 |title=Advancing Beyond Advances in Behavioral Economics |journal=Journal of Economic Literature |volume=44 |issue=3 | jstor=30032349 |pages= 694–711 |doi=10.1257/jel.44.3.694|citeseerx=10.1.1.1010.3674 }}</ref><ref>{{cite book |first=Vincent P. |last=Crawford |year=1997 |title=Theory and Experiment in the Analysis of Strategic Interaction |journal=Advances in Economics and Econometrics: Theory and Applications |pages=206–42 |url=http://weber.ucsd.edu/~vcrawfor/CrawfordThExp97.pdf |location =Cambridge|doi=10.1017/CCOL521580110.007 |citeseerx=10.1.1.298.3116 |isbn=9781139052009 |editor1-last=Kreps |editor1-first=David M |editor2-last=Wallis |editor2-first=Kenneth F }}</ref><ref>{{cite book |first=Martin |last=Shubik |authorlink=Martin Shubik |year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |publisher=Elsevier |volume= 3 |pages= 2327–51 |doi=10.1016/S1574-0005(02)03025-4|chapter=Chapter 62 Game theory and experimental gaming |series=Handbook of Game Theory with Economic Applications |isbn=9780444894281 }}</ref><ref>{{cite book |first1= Charles R.|last1=Plott |authorlink= | last2= Smith| first2 = Vernon l| year=2002 |title=Game Theory and Experimental Gaming |editor-first1=R. |editor-last1=Aumann and |editor-first2=S. |editor-last2=Hart |work=Handbook of Game Theory with Economic Applications |publisher=Elsevier |volume= 4 |pages= 387–615 | doi=10.1016/S1574-0722(07)00121-7 | chapter= 45–66 |series=Handbook of Experimental Economics Results |isbn=9780444826428 }}</ref><ref>''[[Games and Economic Behavior]]'' (journal), Elsevier. [http://www.journals.elsevier.com/games-and-economic-behavior Online]</ref>|url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000466&edition=current&q=fairness%20game%20&topicid=&result_number=1 }} in </ref><br />
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=== Economic reasoning in animals 动物的经济推理===<br />
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A handful of [[comparative psychology|comparative psychologists]] have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of [[laboratory rat|rats]] and [[rock pigeon|pigeons]]. These studies draw on the tenets of [[comparative psychology]], where the main goal is to discover analogs to human behavior in [[experiment]]ally-tractable non-human animals. They are also methodologically similar to the work of [[Charles Ferster|Ferster]] and [[B. F. Skinner|Skinner]].<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref> Methodological similarities aside, early researchers in non-human economics deviate from [[behaviorism]] in their [[terminology]]. Although such studies are set up primarily in an [[operant conditioning chamber]] using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of [[reinforcement]] and [[stimulus-response model|stimulus-response relationships]] but instead in terms of work, [[demand (economics)|demand]], [[budget]], and [[employment|labor]]. Recent studies have adopted a slightly different approach, taking a more [[evolution]]ary perspective, comparing economic behavior of humans to a species of non-human [[primate]], the [[capuchin monkey]].<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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A handful of comparative psychologists have attempted to demonstrate quasi-economic reasoning in non-human animals. Early attempts along these lines focus on the behavior of rats and pigeons. These studies draw on the tenets of comparative psychology, where the main goal is to discover analogs to human behavior in experimentally-tractable non-human animals. They are also methodologically similar to the work of Ferster and Skinner. Methodological similarities aside, early researchers in non-human economics deviate from behaviorism in their terminology. Although such studies are set up primarily in an operant conditioning chamber using food rewards for pecking/bar-pressing behavior, the researchers describe pecking and bar-pressing not in terms of reinforcement and stimulus-response relationships but instead in terms of work, demand, budget, and labor. Recent studies have adopted a slightly different approach, taking a more evolutionary perspective, comparing economic behavior of humans to a species of non-human primate, the capuchin monkey.<br />
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一些比较心理学家试图证明除了人,其他的动物也能够进行'''<font color = 'ff8000'>准经济推理quasi-economic reasoning</font>'''。早期尝试集中在大鼠和鸽子的行为研究上。这些研究运用了比较心理学的原则,其主要目标是在非人类动物实验体身上发现类人行为。它在研究方法上也与费斯特 Ferster和斯金纳 Skinner的工作相似<ref name="skin">{{cite book |last=Ferster |first=C. B. |year=1957 |title=Schedules of Reinforcement |url=https://archive.org/details/schedulesofreinf0000fers |url-access=registration |location=New York |publisher=Appleton-Century-Crofts |display-authors=etal}}</ref>。撇开这些不谈,'''<font color = 'ff8000'>非人类经济学non-human economics</font>'''的早期研究者所使用的术语偏离了'''<font color = 'ff8000'>行为主义behaviorism</font>'''的准则。尽管这些研究主要通过设置'''<font color = 'ff8000'>操作条件箱operant conditioning chamber</font>'''——用食物奖励啄食或按棒的行为——来获得,但研究人员并未从'''<font color = 'ff8000'>强化reinforcement</font>'''与'''<font color = 'ff8000'>刺激-反应stimulus-response</font>'''关系的角度来描述这些行为,而是从'''<font color = 'ff8000'>工作work</font>'''、'''<font color = 'ff8000'>需求demand</font>'''、'''<font color = 'ff8000'>预算budget</font>'''和'''<font color = 'ff8000'>劳动力labor</font>'''的角度进行阐释。最近的研究采用了稍微不同的方法,从人类进化的角度,将人类的经济行为与一种灵长类动物'''<font color = 'ff8000'>卷尾猴capuchin monkey</font>'''进行了比较<ref name="monkey">{{cite journal |last=Chen |first=M. K. |year=2006 |title=How Basic Are Behavioral Biases? Evidence from Capuchin Monkey Trading Behavior |journal=[[Journal of Political Economy]] |volume=114 |issue=3 |pages=517–37 |doi=10.1086/503550 |display-authors=etal|citeseerx=10.1.1.594.4936 }}</ref><br />
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==== Animal studies 动物研究====<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human [[labour supply|labor supply]].<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref> Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior.<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref> In a paper by Battalio, Green, and Kagel,<ref name="bat" /> they write,<br />
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Many early studies of non-human economic reasoning were performed on rats and pigeons in an operant conditioning chamber. These studies looked at things like peck rate (in the case of the pigeon) and bar-pressing rate (in the case of the rat) given certain conditions of reward. Early researchers claim, for example, that response pattern (pecking/bar-pressing rate) is an appropriate analogy to human labor supply. Researchers in this field advocate for the appropriateness of using animal economic behavior to understand the elementary components of human economic behavior. In a paper by Battalio, Green, and Kagel, they write,<br />
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许多关于非人类经济推理的早期研究都是在操作条件箱中的大鼠和鸽子身上进行的。这些研究记录了在一定奖励条件下的(鸽子)啄食率和(大鼠)压棒率。例如,早期的研究人员声称,反应模式(啄食或压棒速率)是'''<font color = 'ff8000'>劳动力供应human labor supply</font>'''的一个恰当类比<ref name="bat">{{cite journal |last=Battalio |first=R. C. |year=1981 |title=Income-Leisure Tradeoffs of Animal Workers |journal=[[American Economic Review]] |volume=71 |issue=4 |pages=621–32 |jstor=1806185 |doi= |display-authors=etal}}</ref>。这个领域的研究人员主张用动物的经济行为来理解基本的人类经济行为<ref name="kbook">{{cite book|first1=John H. |last1=Kagel|first2=Raymond C. |last2=Battalio|first3=Leonard |last3=Green|title=Economic Choice Theory: An Experimental Analysis of Animal Behavior|url={{google books |plainurl=y |id=s4zk69tXQs8C}}|year=1995|publisher=Cambridge University Press|isbn=978-0-521-45488-9}}</ref>。巴塔利奥 Battalio,格林 Green和凯格尔 Kagel<ref name="bat" />在他们的一篇论文中写道:<br />
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{{quote|Space considerations do not permit a detailed discussion of the reasons why economists should take seriously the investigation of economic theories using nonhuman subjects....[Studies of economic behavior in non-human animals] provide a laboratory for identifying, testing, and better understanding general laws of economic behavior. Use of this laboratory is predicated on the fact that behavior, as well as structure, vary continuously across species, and that principles of economic behavior would be unique among behavioral principles if they did not apply, with some variation, of course, to the behavior of nonhumans.}}<br />
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限于篇幅,研究者无法详细讨论为什么经济学家应该严肃对待使用非人类研究对象所进行的经济学理论研究(对动物的经济行为的研究)……因为这样的研究提供了一个用于识别、测试和深入理解经济行为一般规律的实验室。这个实验室的运行基于物种之间不同的行为和结构。经济行为原则如果不适用于非人类(当然也有一些变化),那么经济行为将是独一无二的。<br />
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--[[用户:嘉树|嘉树]]([[用户讨论:嘉树|讨论]]) Space considerations 译为篇幅?<br />
--[[用户:和光同尘|和光同尘]]([[用户讨论:和光同尘|讨论]]) 赞同<br />
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==== Labor supply 劳动供给====<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through [[Shaping (psychology)|orienting and exploring]] the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes [[reinforcement|reinforced]], as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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The typical laboratory environment to study labor supply in pigeons is set up as follows. Pigeons are first deprived of food. Since the animals become hungry, food becomes highly desired. The pigeons are then placed in an operant conditioning chamber and through orienting and exploring the environment of the chamber they discover that by pecking a small disk located on one side of the chamber, food is delivered to them. In effect, pecking behavior becomes reinforced, as it is associated with food. Before long, the pigeon pecks at the disk (or stimulus) regularly.<br />
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典型的鸽子劳动供给研究的实验环境是这样的:鸽子一开始就被剥夺食物。随着饥饿感的增强,它们变得渴望食物。然后鸽子被放在操作条件箱中,在定向和探索箱子环境的过程中,它们发现通过啄食房间一侧的小圆盘,可以获得被送来的食物。实际上,因为与食物有关,啄食行为得到了强化。不久之后,鸽子会定期啄食圆盘(或刺激物)。<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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In this circumstance, the pigeon is said to "work" for the food by pecking. The food, then, is thought of as the currency. The value of the currency can be adjusted in several ways, including the amount of food delivered, the rate of food delivery and the type of food delivered (some foods are more desirable than others).<br />
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在这种情况下,我们可以说鸽子为食物而“工作”:重复进行啄这一动作。因此,食物被认为是'''<font color = 'ff8000'>货币currency</font>'''。货币的价值可以通过几种方式进行调整,包括提供食物的数量、速度和类型(有些食物比其他食物更受欢迎)。<br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to [[labour supply|labor supply]] behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<ref name="bat" /><br />
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Economic behavior similar to that observed in humans is discovered when the hungry pigeons stop working/work less when the reward is reduced. Researchers argue that this is similar to labor supply behavior in humans. That is, like humans (who, even in need, will only work so much for a given wage), the pigeons demonstrate decreases in pecking (work) when the reward (value) is reduced.<br />
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当奖励减少时,饥饿的鸽子停止或减少工作,这和人类的经济行为相似。研究人员认为,这实际上与人类的劳动供给行为相似。也就是说,像人类一样(即使在需要食物的时候,面对既定工资也只会完成固定的工作量),当回报(价值)减少时,鸽子会表现出啄食行为(工作)的减少<ref name="bat" />。<br />
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==== Demand需求====<br />
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In human economics, a typical [[demand curve]] has [[slope|negative slope]]. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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In human economics, a typical demand curve has negative slope. This means that as the price of a certain good increase, the amount that consumers are willing and able to purchase decreases. Researchers studying the demand curves of non-human animals, such as rats, also find downward slopes.<br />
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在人类经济学中,典型的需求曲线具有'''<font color = 'ff8000'> 负斜率negative slope </font>'''。这意味着,随着某种商品价格的上涨,消费者愿意并且能够购买的数量会减少。研究人员在研究非人类动物(如大鼠)的需求曲线时,也发现了同样的情况。<br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as [[cherry cola]]. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
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Researchers have studied demand in rats in a manner distinct from studying labor supply in pigeons. Specifically, in an operant conditioning chamber containing rats as experimental subjects, we require them to press a bar, instead of pecking a small disk, to receive a reward. The reward can be food (reward pellets), water, or a commodity drink such as cherry cola. Unlike in previous pigeon studies, where the work analog was pecking and the monetary analog was a reward, the work analog in this experiment is bar-pressing. Under these circumstances, the researchers claim that changing the number of bar presses required to obtain a commodity item is analogous to changing the price of a commodity item in human economics.<br />
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研究人员用一种不同于研究鸽子劳动力供应关系的方式来研究大鼠的需求。具体就是,在一个以大鼠为实验对象的操作条件箱中,我们要求它们下压一个小杆而不是啄一个小圆盘以获得奖励。奖励可以是食物(奖励食丸)、水,或者像樱桃可乐这样的饮料。在以前的鸽子研究中,劳动的模拟行为是啄食,金钱的模拟物是奖励。大鼠的实验中工作的模拟行为则是压杆。在这种情况下,研究人员声称,改变能够获得商品的压杆次数标准类似于在人类经济学中改变商品的价格<ref name="kag">{{cite journal |last=Kagel |first=J. H. |year=1981 |title=Demand Curves for Animal Consumers |journal=[[Quarterly Journal of Economics]] |volume=96 |issue=1 |pages=1–16 |doi=10.2307/2936137|display-authors=etal |jstor=2936137}}</ref><br />
。<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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In effect, results of demand studies in non-human animals show that, as the bar-pressing requirement (cost) increase, the number of times an animal presses the bar equal to or greater than the bar-pressing requirement (payment) decreases.<br />
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实际上,对动物需求的研究结果表明,随着压杆要求(成本)的增加,动物压杆等于或大于压杆要求(回报)的次数在减少。<br />
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=== Evolutionary psychology 进化心理学===<br />
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{{Main|Evolutionary psychology}}<br />
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{{Further|Evolutionary economics}}<br />
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An [[evolutionary psychology]] perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological [[Fitness (biology)|fitness]] in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable [[reproductive success]] than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref><br />
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An evolutionary psychology perspective states that many of the perceived limitations in rational choice can be explained as being rational in the context of maximizing biological fitness in the ancestral environment, but not necessarily in the current one. Thus, when living at subsistence level where a reduction of resources may result in death, it may have been rational to place a greater value on preventing losses than on obtaining gains. It may also explain behavioral differences between groups, such as males being less risk-averse than females since males have more variable reproductive success than females. While unsuccessful risk-seeking may limit reproductive success for both sexes, males may potentially increase their reproductive success from successful risk-seeking much more than females can.<br />
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'''<font color = 'ff8000'> 进化心理学 evolutionary psychology</font>'''认为,我们可以这么解释理性选择中的许多局限性——在最大化生物适应性的祖传环境中的理性选择在当前环境中却不一定是。因此,当因资源减少而不得不生活在贫困线上,甚至可能面对死亡时,理性的做法是重视避免损失而不是获得收益。这也可以解释不同群体之间的行为差异,例如男性相对女性会更轻视风险规避,因为男性比女性有更大的'''<font color = 'ff8000'>繁殖成功率 reproductive success</font>'''。虽然失败的冒险行为可能会同时限制两性的繁殖成功率,但对男性而言,一旦冒险行为成功,其更有可能提高繁殖成功率<ref name=AEP>Paul H. Rubin and C. Monica Capra. The evolutionary psychology of economics. In {{Cite book | last1 = Roberts | first1 = S. C. | editor1-last = Roberts | doi = 10.1093/acprof:oso/9780199586073.001.0001 | editor1-first = S. Craig | title = Applied Evolutionary Psychology | year = 2011 | publisher = Oxford University Press| isbn = 9780199586073 | pmid = | pmc = |url={{google books |plainurl=y |id=I20uPfEjsNQC}}}}</ref>。<br />
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=== Artificial intelligence 人工智能===<br />
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{{Main|Artificial intelligence}}<br />
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Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. [[Tshilidzi Marwala]] and [[Evan Hurwitz]] in their book,<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref> studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of [[information asymmetry]] in the market, improve decision making and thus making markets more rational.<br />
<br />
Much of the decisions are more and more made either by human beings with the assistance of artificial intelligent machines or wholly made by these machines. Tshilidzi Marwala and Evan Hurwitz in their book, studied the utility of behavioral economics in such situations and concluded that these intelligent machines reduce the impact of bounded rational decision making. In particular, they observed that these intelligent machines reduce the degree of information asymmetry in the market, improve decision making and thus making markets more rational.<br />
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越来越多的决策开始由人工智能辅助下的人类做出,或者直接由人工智能做出。齐立兹·马尔瓦拉 Tshilidzi Marwala和埃文·赫维兹 Evan Hurwitz在他们的书中<ref name="ReferenceA">{{cite book |last1=Marwala |first1= Tshilidzi| last2=Hurwitz |first2= Evan |title=Artificial Intelligence and Economic Theory: Skynet in the Market |year=2017 |publisher=[[Springer Science+Business Media|Springer]] |location=London |isbn=978-3-319-66104-9}}</ref>研究了行为经济学在这种情况下的效用,并得出结论,称这些智能机器减少了有限理性决策的影响。特别是,他们观察到这些智能机器降低了市场的'''<font color = 'ff8000'>信息不对称information asymmetry</font>'''水平,促进决策改善,从而使市场更加理性。<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories.<ref name="ReferenceA"/> Other theories where AI has had impact include in [[rational choice]], [[rational expectations]], [[game theory]], [[Lewis turning point]], [[portfolio optimization]] and [[counterfactual thinking]].<br />
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The use of AI machines in the market in applications such as online trading and decision making has changed major economic theories. Other theories where AI has had impact include in rational choice, rational expectations, game theory, Lewis turning point, portfolio optimization and counterfactual thinking.<br />
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人工智能在市场上的应用(如在线交易和决策)已经改变了主流经济理论<ref name="ReferenceA"/>。受人工智能影响的理论还包括'''<font color = 'ff8000'>理性选择rational choice</font>'''、'''<font color = 'ff8000'>理性预期rational expectations</font>'''、'''<font color = 'ff8000'>博弈论game theory</font>'''、'''<font color = 'ff8000'>刘易斯转折点Lewis turning point</font>'''、'''<font color = 'ff8000'>投资组合优化portfolio optimization</font>'''和'''<font color = 'ff8000'>反事实思维counterfactual thinking</font>'''。<br />
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== Related fields 相关领域==<br />
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=== Experimental economics 实验经济学===<br />
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{{Main|Experimental economics}}<br />
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Experimental economics is the application of [[Experiment|experimental methods]], including [[statistical]], [[econometric]], and [[computational economics|computational]],<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref> to study economic questions. [[Economic data|Data]] collected in experiments are used to estimate [[effect size]], test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref><br />
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Experimental economics is the application of experimental methods, including statistical, econometric, and computational, to study economic questions. Data collected in experiments are used to estimate effect size, test the validity of economic theories, and illuminate market mechanisms. Economic experiments usually use cash to motivate subjects, in order to mimic real-world incentives. Experiments are used to help understand how and why markets and other exchange systems function as they do. Experimental economics have also expanded to understand institutions and the law (experimental law and economics).<br />
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实验经济学通过运用统计学、'''<font color = 'ff8000'>计量经济学econometric</font>'''和'''<font color = 'ff8000'>计算经济学computational</font>'''<ref>{{cite journal | last1 = Roth | first1 = Alvin E. | authorlink = Alvin E. Roth | year = 2002 | title = The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics | url = http://kuznets.fas.harvard.edu/~aroth/papers/engineer.pdf | format = PDF | journal = Econometrica | volume = 70 | issue = 4| pages = 1341–1378 | doi = 10.1111/1468-0262.00335 }}</ref>等实验方法来研究经济问题。实验中收集的数据被用于估计效果量,检验经济理论的有效性,以及阐明市场机制。经济实验通常使用现金来激励受试者,以模拟现实世界的激励。这些实验被用来解读市场和其他交易系统是如何以及为何这样运作的。实验经济学还被扩展到机构组织和法律('''<font color = 'ff8000'>实验法律experimental law</font>'''和经济学)的研究中去<ref>{{cite journal | last1 = See | first1 = | authorlink2 = Kristoffel Grechenig | last2 = Grechenig | first2 = K. | last3 = Nicklisch | first3 = A. | last4 = Thöni | first4 = C. | year = 2010 | title = Punishment despite reasonable doubt—a public goods experiment with sanctions under uncertainty | url = http://ssrn.com/abstract=1586775 | journal = Journal of Empirical Legal Studies | volume = 7 | issue = 4| pages = 847–867 }}</ref>。<br />
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A fundamental aspect of the subject is [[design of experiments]]. Experiments may be conducted in the [[Field experiments|field]] or in laboratory settings, whether of [[Experimental psychology|individual]] or [[Social psychology|group]] behavior.<br />
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A fundamental aspect of the subject is design of experiments. Experiments may be conducted in the field or in laboratory settings, whether of individual or group behavior.<br />
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这门学科的一个基本方面是实验设计。无论是个人行为还是群体行为,实验既可以在真实生活场景中(田野)进行,也可以在实验室环境中进行。<br />
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Variants of the subject outside such formal confines include [[natural experiment|natural]] and [[quasi-natural experiment]]s.<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref><br />
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Variants of the subject outside such formal confines include natural and quasi-natural experiments.<br />
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除了正式的标准实验,这里还有一些变体,包括'''<font color = 'ff8000'>自然实验natural experiments</font>'''和'''<font color = 'ff8000'>准自然实验quasi-natural experiments</font>'''<ref>J. DiNardo, 2008. "natural experiments and quasi-natural experiments," ''The New Palgrave Dictionary of Economics'', 2nd Edition. [http://www.dictionaryofeconomics.com/article?id=pde2008_N000142&edition=current&q Abstract.]</ref>。<br />
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=== Neuroeconomics 神经经济学===<br />
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{{Main|Neuroeconomics}}<br />
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Neuroeconomics is an [[Interdisciplinarity|interdisciplinary]] field that seeks to explain human [[decision making]], the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the [[brain]], and how neuroscientific discoveries can constrain and guide models of economics.<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
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Neuroeconomics is an interdisciplinary field that seeks to explain human decision making, the ability to process multiple alternatives and to follow a course of action. It studies how economic behavior can shape our understanding of the brain, and how neuroscientific discoveries can constrain and guide models of economics.<br />
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'''<font color = 'ff8000'>神经经济学 Neuroeconomics</font>'''是一个跨学科的领域,旨在探索研究人类决策机制以及人类处理多重选项的能力。该学科遵循一个行动方针。它研究经济行为如何影响我们对大脑的理解,以及神经科学的发现如何约束和指导经济学模型的建构与发展<ref name="neuroeconomics.duke.edu">{{cite web|url =https://dibs.duke.edu/centers/d-cides/about/research|title = Research|website = Duke Institute for Brain Sciences}}</ref><br />
。<br />
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It combines research methods from [[neuroscience]], [[Experimental economics|experimental]] and behavioral economics, and [[Cognitive psychology|cognitive]] and [[Social psychology|social]] psychology.<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref> As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from [[theoretical biology]], [[computer science]], and [[mathematics]]. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In [[mainstream economics]], [[Expected utility hypothesis|expected utility]] (EU) and the concept of [[rational agents]] are still being used. Many economic behaviors are not fully explained by these models, such as [[heuristics]] and [[Framing (social sciences)|framing]].<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
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It combines research methods from neuroscience, experimental and behavioral economics, and cognitive and social psychology. As research into decision-making behavior becomes increasingly computational, it has also incorporated new approaches from theoretical biology, computer science, and mathematics. Neuroeconomics studies decision making by using a combination of tools from these fields so as to avoid the shortcomings that arise from a single-perspective approach. In mainstream economics, expected utility (EU) and the concept of rational agents are still being used. Many economic behaviors are not fully explained by these models, such as heuristics and framing.<br />
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它综合运用了神经科学、实验和行为经济学以及认知和社会心理学的研究方法<ref name="LevalloisClithero2012">{{cite journal|last1=Levallois|first1=Clement|last2=Clithero|first2=John A.|last3=Wouters|first3=Paul|last4=Smidts|first4=Ale|last5=Huettel|first5=Scott A.|title=Translating upwards: linking the neural and social sciences via neuroeconomics|journal=Nature Reviews Neuroscience|volume=13|issue=11|year=2012|pages=789–797|issn=1471-003X|doi=10.1038/nrn3354|pmid=23034481}}</ref>。随着对决策行为的研究变得越来越与计算机相关,它也吸收了来自理论生物学、计算机科学和数学领域的新方法。神经经济学使用组合工具来研究决策,以避免出现因使用单一方法而产生的弊端。在主流经济学中,'''<font color = 'ff8000'>期望效用expected utility, EU</font>'''和理性主体这一概念仍被使用。不过这些模型无法充分解释某些经济行为,比如'''<font color = 'ff8000'>启发式heuristics</font>'''和'''<font color = 'ff8000'>框架效应framing</font>'''<ref name="annualreviews.org">{{cite journal | last1 = Loewenstein | first1 = G. | last2 = Rick | first2 = S. | last3 = Cohen | first3 = J. | year = 2008 | title = Neuroeconomics| url = | journal = Annual Reviews | volume = 59 | issue = | pages = 647–672 | doi = 10.1146/annurev.psych.59.103006.093710 | pmid = 17883335 }}</ref><br />
。<br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<ref name="neuroeconomics.duke.edu" /><br />
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Behavioral economics emerged to account for these anomalies by integrating social, cognitive, and emotional factors in understanding economic decisions. Neuroeconomics adds another layer by using neuroscientific methods in understanding the interplay between economic behavior and neural mechanisms. By using tools from various fields, some scholars claim that neuroeconomics offers a more integrative way of understanding decision making.<br />
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行为经济学在解读经济决策时,通过综合考虑社会、认知和情感因素来解释这些异常现象。神经经济学通过运用神经科学研究的方法为理解经济行为和神经机制之间的相互作用又增加了新的维度。通过使用来自不同领域的工具,一些学者声称神经经济学提供了一种更加综合的方式来帮助人理解决策机制<ref name="neuroeconomics.duke.edu" /><br />
。<br />
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<br />
== Notable people 著名人物==<br />
<br />
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<br />
=== Economics 经济学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Akerlof]]<br />
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* [[Werner De Bondt]]<br />
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* [[Paul De Grauwe]]<ref>{{Cite web|url=https://voxeu.org/article/behavioural-economics-also-useful-macroeconomics|title=Behavioural economics is also useful in macroeconomics|first1=Paul De|last1=Grauwe|first2=Yuemei|last2=Ji|date=November 1, 2017}}</ref><br />
<br />
* [[Linda C. Babcock]]<br />
<br />
* [[Douglas Bernheim]]<ref>{{cite web |ref=harv |last1=Bernheim| first1=Douglas |last2=Rangel |first2=Antonio |year=2008 |title=Behavioural public economics |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |issue=2}} in {{harvnb|Palgrave|ref=Palgrave}}</ref><br />
<br />
* [[Colin Camerer]]<br />
<br />
* [[Armin Falk]]<br />
<br />
* [[Urs Fischbacher]]<br />
<br />
*[[Tshilidzi Marwala]]<br />
<br />
*[[Susan E. Mayer]]<br />
<br />
* [[Ernst Fehr]]<br />
<br />
* [[Simon Gächter]]<br />
<br />
* [[Uri Gneezy]]<ref>{{cite web|url=http://rady.ucsd.edu/faculty/directory/gneezy/|title=Uri Gneezy|work=ucsd.edu}}</ref><br />
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* [[David Laibson]]<br />
<br />
* [[Louis Lévy-Garboua]]<br />
<br />
* [[John A. List]]<br />
<br />
* [[George Loewenstein]]<br />
<br />
* [[Sendhil Mullainathan]]<br />
<br />
* [[John Quiggin]]<br />
<br />
* [[Matthew Rabin]]<br />
<br />
* [[Reinhard Selten]]<br />
<br />
* [[Herbert A. Simon]]<br />
<br />
* [[Vernon L. Smith]]<br />
<br />
* [[Robert Sugden (economist)|Robert Sugden]]<ref>{{cite web|url =https://www.uea.ac.uk/economics/people/profile/r-sugden |title=Robert Sugden}}</ref><br />
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* [[Larry Summers]]<br />
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* [[Richard Thaler]]<br />
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{{div col end}}<br />
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<br />
<br />
=== Finance 金融学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[Malcolm Baker]]<br />
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* [[Nicholas Barberis]]<br />
<br />
* [[Gunduz Caginalp]]<br />
<br />
* [[David Hirshleifer]]<br />
<br />
* [[Andrew Lo]]<br />
<br />
* [[Michael Mauboussin]]<br />
<br />
* [[Terrance Odean]]<br />
<br />
* [[Richard L. Peterson]]<br />
<br />
* [[Charles Plott]]<br />
<br />
* [[Robert Prechter]]<br />
<br />
* [[Hersh Shefrin]]<br />
<br />
* [[Robert Shiller]]<br />
<br />
* [[Andrei Shleifer]]<br />
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* [[Robert Vishny]]<br />
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{{div col end}}<br />
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<br />
<br />
=== Psychology 心理学===<br />
<br />
{{div col|colwidth=20em}}<br />
<br />
* [[George Ainslie (psychologist)|George Ainslie]]<br />
<br />
* [[Dan Ariely]]<ref>{{cite web|title=Predictably Irrational|publisher=Dan Ariely|url=http://www.predictablyirrational.com/?page_id=5|accessdate=2008-04-25|archiveurl=https://web.archive.org/web/20080313201653/http://www.predictablyirrational.com/?page_id=5|archivedate=2008-03-13|url-status=dead}}</ref><br />
<br />
* [[Ed Diener]]<br />
<br />
* [[Ward Edwards]]<br />
<br />
* [[Laszlo Garai]]<br />
<br />
* [[Gerd Gigerenzer]] <br />
<br />
* [[Daniel Kahneman]] 丹尼尔·卡尼曼<br />
<br />
* [[Ariel Kalil]]<br />
<br />
* [[George Katona]]<br />
<br />
* [[Walter Mischel]]<br />
<br />
* [[Drazen Prelec]]<br />
<br />
* [[Eldar Shafir]]<br />
<br />
* [[Paul Slovic]]<br />
<br />
* [[John Staddon]]<ref>{{cite book|last=Staddon|first= John|date =2017|title= Scientific Method: How science works, fails to work or pretends to work |publisher = Routledge|chapter= 6: Behavioral Economics|chapter-url =https://books.google.com/books?id=TCBBDwAAQBAJ&lpg=PP1&pg=PT103}}</ref><br />
<br />
* [[Amos Tversky]]<br />
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{{div col end}}<br />
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== See also 参见==<br />
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{{Wikipedia books|Finance}} <br />
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{{div col|colwidth=30em}}<br />
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* [[Adaptive market hypothesis]] 适应性市场假设<br />
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* [[Animal Spirits (Keynes)]] 动物本能(凯恩斯)<br />
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* [[Behavioralism]] 行为主义<br />
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* [[Behavioral analysis of markets]] 市场的行为分析<br />
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* [[Behavioral operations research]] 行为运筹学<br />
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*[[Big Five personality traits]] 大五人格<br />
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* [[Confirmation bias]] 确认偏差<br />
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* [[Cultural economics]] 文化经济学<br />
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* [[Culture change]] 文化变迁<br />
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* [[Economic sociology]] 经济社会学<br />
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* [[Emotional bias]] 情绪偏差<br />
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* [[Fuzzy-trace theory]] 模糊痕迹理论<br />
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* [[Hindsight bias]] 后见之明偏差<br />
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* ''[[Homo reciprocans]]'' “人属”<br />
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* [[List of important publications in economics#Behavioral economics|Important publications in behavioral economics]] 经济学重要发表物列表 #行为经济学|行为经济学重要发表物<br />
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* [[List of cognitive biases]] 认知偏差列表<br />
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* [[Market sentiment]] 市场情绪<br />
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* [[Methodological individualism]] 方法论个人主义<br />
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* [[Nudge theory]] “助推”理论<br />
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* [[Observational techniques]] 可观察的技术<br />
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* [[Praxeology]] 人类行为学<br />
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* [[Priority heuristic]] 齐当别启发式<br />
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* [[Regret (decision theory)|Regret theory]] 后悔(决策理论)|后悔理论<br />
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* [[Repugnancy costs]] 厌恶成本<br />
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* [[Socioeconomics]] 社会经济学<br />
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* [[Socionomics]] (一种研究社会情绪和社会行为之间关系的学科,由Robert R. Prechter, Jr.创立。The study of the relationship between social mood and social behavior pioneered by Robert R. Prechter, Jr.)<br />
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{{div col end}}<br />
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== Citations ==<br />
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{{reflist|30em}}<br />
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== References ==<br />
<br />
* {{cite journal|doi=10.1037/h0076860|last=Ainslie|first=G.|year=1975|title=Specious Reward: A Behavioral /Theory of Impulsiveness and Impulse Control|journal=Psychological Bulletin|volume=82|issue=4|pages=463–96|pmid=1099599|ref=none|url=https://semanticscholar.org/paper/8cf0dba265275d8233b2d78c543269fedd6ff833}}<br />
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* {{cite journal|last1=Barberis|first1=N.|authorlink=Nicholas Barberis|authorlink2=Andrei Shleifer|last2=Shleifer|first2=A.|last3=Vishny|first3=R.|year=1998|title=A Model of Investor Sentiment|journal=Journal of Financial Economics|volume=49|issue=3|pages=307–43|doi=10.1016/S0304-405X(98)00027-0|url=http://jfe.rochester.edu/|accessdate=2008-04-25|ref=none|archiveurl=https://web.archive.org/web/20080420095719/http://jfe.rochester.edu/|archivedate=20 April 2008 |url-status=live}}<br />
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* {{cite journal|doi=10.1086/259394|last1=Becker |first1=Gary S.|authorlink1=Gary Becker|year=1968|title=Crime and Punishment: An Economic Approach| journal=The Journal of Political Economy|volume=76|issue=2| pages=169–217|url=http://www.nber.org/chapters/c3625.pdf }}<br />
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* {{cite journal|last1=Benartzi|first1=Shlomo|authorlink2=Richard Thaler|last2=Thaler|first2=Richard H.|year=1995|title=Myopic Loss Aversion and the Equity Premium Puzzle|journal=The Quarterly Journal of Economics|volume=110|issue=1|pages=73–92|doi=10.2307/2118511|ref=harv|jstor=2118511|url=http://www.nber.org/papers/w4369.pdf}}<br />
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* {{cite journal|last=Cunningham|first=Lawrence A.|year=2002|title=Behavioral Finance and Investor Governance|journal=Washington & Lee Law Review|volume=59|page=767|issn=1942-6658|doi=10.2139/ssrn.255778}}<br />
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* {{cite journal|last=Daniel|first=K.|authorlink2=David Hirshleifer|last2=Hirshleifer|first2=D.|last3=Subrahmanyam|first3=A.|year=1998|title=Investor Psychology and Security Market Under- and Overreactions|journal=Journal of Finance|volume=53|issue=6|pages=1839–85|doi=10.1111/0022-1082.00077|ref=none|url=https://deepblue.lib.umich.edu/bitstream/2027.42/73431/1/0022-1082.00077.pdf|hdl=2027.42/73431}}<br />
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* {{cite book|first1=Peter |last1=Diamond |author-link1=Peter A. Diamond|first2=Hannu |last2=Vartiainen|title=Behavioral Economics and Its Applications|url={{google books |plainurl=y |id=1-SVhlC9mVoC}}|year= 2012|publisher=Princeton University Press|isbn=978-1-4008-2914-9}} <br />
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* {{cite book|editor-first1=John |editor-last1=Eatwell|editor-first2=Murray |editor-last2=Milgate|editor-first3=Peter |editor-last3=Newman|title=The New Palgrave: A Dictionary of Economics|url={{google books |plainurl=y |id=9I2voAEACAAJ}}|year=1988|publisher=Macmillan|isbn=978-0-935859-10-2 |ref=Palgrave}}<br />
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** {{cite encyclopedia |last=Augier |first=Mie |url=http://www.dictionaryofeconomics.com/article?id=pde2008_S000455&q=behavioural&topicid=&result_number=8 |title=Simon, Herbert A. (1916–2001)}}<br />
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** {{cite encyclopedia|last1=Bernheim|first1=B. Douglas|first2=Antonio|last2=Rangel |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000331&q=public%20&topicid=&result_number=3 |title=Behavioral public economics}}<br />
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** {{cite encyclopedia|last1=Bloomfield|first1=Robert |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000339&q=Behavioral%20economics%20&topicid=&result_number=5 |title=Behavioral finance}}<br />
<br />
** {{cite encyclopedia|last=Simon|first=Herbert A |url=http://www.dictionaryofeconomics.com/article?id=pde2008_B000176&q=behavioural%20economics&topicid=&result_number=4 |title=Rationality, bounded}}<br />
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* {{cite journal |title=Loss Aversion and Seller Behavior: Evidence from the Housing Market |first1=David |last1=Genesove |first2=Christopher |last2=Mayer |date=March 2001 |journal=Quarterly Journal of Economics |volume=116 |issue=4 |pages=1233–1260 |doi=10.1162/003355301753265561 |ref=none|url=http://www.nber.org/papers/w8143.pdf }}<br />
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* {{cite encyclopedia|first1=S.|last1=Mullainathan|authorlink1=Sendhil Mullainathan|authorlink2=Richard Thaler|last2=Thaler|first2=R. H.|year=2001|chapter=Behavioral Economics|encyclopedia=[[International Encyclopedia of the Social & Behavioral Sciences]]|pages=1094–1100 |doi=10.1016/B0-08-043076-7/02247-6 |isbn=9780080430768}}<br />
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* {{Cite book |title=Reconsidering Identity Economics|last=Garai|first=Laszlo|authorlink=Garai Laszlo|date=2016-12-01|publisher=Palgrave Macmillan US|isbn=9781137525604|location=New York|pages=35–40|language=en|doi=10.1057/978-1-137-52561-1_3|chapter=Identity Economics: "An Alternative Economic Psychology"}}<br />
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* {{Cite web |ssrn=2435111 |url=http://papers.ssrn.com|access-date=2018-06-02|first=E. |last=McGaughey|title=Behavioural Economics and Labour Law|year=2014|number=LSE Legal Studies Working Paper No. 20/2014}}<br />
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* {{cite book|title=Behavioural Finance for Private Banking|last=Hens|first=Thorsten|author2=Bachmann, Kremena|year=2008|publisher=Wiley Finance Series|isbn=978-0-470-77999-6|url=http://www.bfpb.ch}}<br />
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* {{cite book|title=Rational Choice: The Contrast between Economics and Psychology|last=Hogarth|first=R. M.|last2=Reder|first2=M. W.|year=1987|publisher=University of Chicago Press|location=Chicago|isbn=978-0-226-34857-5|ref=harv|url-access=registration|url=https://archive.org/details/rationalchoice}}<br />
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* {{cite journal|last1=Kahneman|first1=Daniel|authorlink1=Daniel Kahneman|authorlink2=Amos Tversky|last2=Tversky|first2=Amos|year=1979|title=Prospect Theory: An Analysis of Decision under Risk|journal=Econometrica|volume=47|issue=2|pages=263–91|doi=10.2307/1914185|jstor=1914185|ref=none|citeseerx=10.1.1.407.1910}}<br />
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* {{cite book |last=Kahneman|first=Daniel|first2=Ed |last2=Diener|year=2003|title=Well-being: the foundations of hedonic psychology|publisher=[[Russell Sage Foundation]]|authorlink=Daniel Kahneman|ref=harv}}<br />
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* {{cite book|title=Technical Analysis: The Complete Resource for Financial Market Technicians|last1=Kirkpatrick|first1=Charles D.|last2=Dahlquist|first2=Julie R.|year=2007|publisher=Financial Times Press|location=Upper Saddle River, NJ|isbn=978-0-13-153113-0|ref=harv}}<br />
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* {{cite book|url={{google books |plainurl=y |id=HlKBaiCpSxYC|age=7}}|title=Private Truths, Public Lies: The Social Consequences of Preference Falsification|last=Kuran|first=Timur|authorlink=Timur Kuran|publisher=Harvard University Press|year=1997|isbn=978-0-674-70758-0|pages=7–}} [http://www.hup.harvard.edu/catalog.php?isbn=9780674707580 Description] <br />
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* {{cite book|last=Luce|first=R Duncan|title=Utility of Gains and Losses: Measurement-theoretical and Experimental Approaches|publisher=Lawrence Erlbaum Publishers|year=2000|location=Mahwah, New Jersey|authorlink=R. Duncan Luce|isbn=978-0-8058-3460-4|ref=harv}}<br />
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* {{cite book |first1=Charles R. |last1=Plott |authorlink1=Charles R. Plott |first2=Vernon L. |last2=Smith |editor-link2=Vernon L. Smith |year=2008 |title=Handbook of Experimental Economics Results |volume= 1 |publisher=Elsevier |url={{google books |plainurl=y |id=wAK_aKs3EPoC}} |ref=none}} Chapter-preview [http://www.sciencedirect.com/science?_ob=PublicationURL&_hubEid=1-s2.0-S1574072207X00015&_cid=277334&_pubType=HS&_auth=y&_acct=C000228598&_version=1&_urlVersion=0&_userid=10&md5=49f8b6d5e3024eac39ed5fad351fe568 links].<br />
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* {{cite journal|last=Rabin |first=Matthew |authorlink=Matthew Rabin |year=1998 |title=Psychology and Economics |journal=Journal of Economic Literature |volume=36 |issue=1 |pages=11–46 |url=http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |ref=harv |url-status=dead|archiveurl=https://web.archive.org/web/20110927133547/http://pages.towson.edu/jpomy/behavioralecon/PsychologyandEconomicsRabin98JEL.pdf |archivedate=September 27, 2011 }}<br />
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* {{cite journal|last=Shefrin |first=Hersh|url=http://forecastingprinciples.com/files/pdf/Shefrin%202002.pdf |title= Behavioral decision making, forecasting, game theory, and role-play |journal=International Journal of Forecasting |volume=18 |issue=3|pages=375–382|year=2002 |ref=harv|doi=10.1016/S0169-2070(02)00021-3}}<br />
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* {{cite book|first1=Thomas C. |last1=Schelling |author-link1=Thomas C. Schelling|title=Micromotives and Macrobehavior|url={{google books |plainurl=y |id=DenWKRgqzWMC}}|year= 2006|publisher=W. W. Norton|isbn=978-0-393-06977-8}} [https://web.archive.org/web/20171102093240/http://books.wwnorton.com/books/978-0-393-32946-9/ Description]<br />
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* {{cite book|title=Inefficient Markets: An Introduction to Behavioral Finance|last=Shleifer|first=Andrei|authorlink=Andrei Shleifer|year=1999|publisher=Oxford University Press|location=New York|isbn=978-0-19-829228-9|url=https://archive.org/details/inefficientmarke00andr}}<br />
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* {{cite encyclopedia|authorlink=Herbert A. Simon|last=Simon|first=Herbert A.|year=1987|title=Behavioral Economics|encyclopedia=[[The New Palgrave: A Dictionary of Economics]]|volume=1|pages=221–24}}<br />
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* {{cite journal | last1 = Thaler | first1 = Richard H | year = 2016 | title = Behavioral Economics: Past, Present, and Future | url = https://www.aeaweb.org/articles?id=10.1257/aer.106.7.1577 | journal = American Economic Review | volume = 106 | issue = 7| pages = 1577–1600 | doi = 10.1257/aer.106.7.1577 }}<br />
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*{{cite encyclopedia |last1=Thaler |first1=Richard H. |authorlink1= Richard Thaler |last2=Mullainathan |first2=Sendhil |editor= [[David R. Henderson]] |encyclopedia=[[Concise Encyclopedia of Economics]] |title=Behavioral Economics |url=http://www.econlib.org/library/Enc/BehavioralEconomics.html |year=2008 |edition= 2nd |publisher=[[Library of Economics and Liberty]] |location=Indianapolis |isbn=978-0-86597-665-8 |oclc=237794267}}<br />
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* {{cite encyclopedia |last1=Wheeler |first1=Gregory |authorlink1= Gregory Wheeler | editor= [[Edward Zalta]] |encyclopedia=[[Stanford Encyclopedia of Philosophy]] | title=Bounded Rationality |url=https://plato.stanford.edu/entries/bounded-rationality |year=2018 |location= Stanford, CA}}<br />
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*{{cite web|url=http://leconcurrentialiste.com/2014/04/23/behavioral-economics-in-u-s-antitrust-scholarly-papers/|title=Behavioral economics in U.S. (antitrust) scholarly papers|work=Le Concurrentialiste}}<br />
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== External links ==<!-- This section is linked from [[Behavioral finance]] --><br />
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== External links ==<!-- This section is linked from Behavioral finance --><br />
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外部链接! -- 这一部分链接来自行为金融学 -- <br />
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{{wikiquote}}<br />
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* [http://www.behavioraleconomics.com/ The Behavioral Economics Guide]<br />
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* [http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1488110 Overview of Behavioral Finance]<br />
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* [http://www.dremanbehavioralfinance.org/ The Institute of Behavioral Finance]<br />
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* [http://economicspsychologypolicy.blogspot.co.uk/ Stirling Behavioural Science Blog], of the Stirling Behavioural Science Centre at [[University of Stirling]]<br />
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* [https://web.archive.org/web/20120110110918/http://www.sabeonline.org/ Society for the Advancement of Behavioural Economics]<br />
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* [http://www.usapr.org/papers/paper.aspx?PaperID=30 Behavioral Economics: Past, Present, Future] – Colin F. Camerer and George Loewenstein<br />
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* [http://www.moneyscience.com/pg/blog/Admin/read/50567/a-history-of-behavioural-finance-in-published-research-1944-1988 A History of Behavioural Finance / Economics in Published Research: 1944–1988]<br />
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* [https://web.archive.org/web/20151017010637/http://www.essex.ac.uk/coursefinder/course_details.aspx?course=MSC+L11912 MSc Behavioural Economics], MSc in Behavioural Economics at the University of Essex<br />
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* [http://www.okanduru.com/becon.htm Behavioral Economics of Shipping Business]<br />
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{{Microeconomics}}<br />
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{{Instecon}}<br />
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{{Schools of economic thought}}<br />
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{{Authority control}}<br />
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[[Category:Behavioral economics| ]]<br />
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[[Category:Behavioral finance]]<br />
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Category:Behavioral finance<br />
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分类: 行为金融学<br />
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[[Category:Financial economics]]<br />
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Category:Financial economics<br />
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类别: 金融经济学<br />
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[[Category:Market trends]]<br />
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Category:Market trends<br />
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类别: 市场趋势<br />
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[[Category:Microeconomics]]<br />
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Category:Microeconomics<br />
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类别: 微观经济学<br />
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[[Category:Prospect theory]]<br />
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Category:Prospect theory<br />
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范畴: 展望理论<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Behavioral economics]]. Its edit history can be viewed at [[行为经济学/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E9%BA%A6%E5%85%8B%E6%96%AF%E9%9F%A6%E5%A6%96&diff=20941麦克斯韦妖2021-01-17T14:27:59Z<p>Vicky:/* 思想的起源和历史 */</p>
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<div>[[File:Maxwell's demon.svg|right|340px|thumb|Schematic figure of Maxwell's demon thought experiment.]]<br />
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Schematic figure of Maxwell's demon thought experiment.<br />
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麦克斯韦妖假想实验示意图。<br />
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'''Maxwell's demon''' is a [[thought experiment]] created by the physicist [[James Clerk Maxwell]] in 1867 in which he suggested how the [[second law of thermodynamics]] might hypothetically be violated.<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref> In the thought experiment, a [[Demon (thought experiment)|demon]] controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing [[entropy]] and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and [[information theory]] extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated. In the thought experiment, a demon controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and information theory extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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'''<font color="#ff8000"> 麦克斯韦妖 Maxwell's demon</font>'''是英国物理学家詹姆斯·克拉克·麦克斯韦 James Clerk Maxwell于1867年为了说明违反'''<font color="#ff8000"> 热力学第二定律 second law of thermodynamics</font>'''的可能性而设想的假想实验。在这个实验当中,一个妖怪控制着两个气体舱之间的一扇小门。当独立的气体分子接近门时,妖怪迅速的打开和关闭门,快速的分子进入其中的一个腔,慢速的分子进入另外一个腔。因为速度更快的分子温度更高,妖怪的动作导致一个腔室升温,另一个腔室降温,从而减少熵,违反了热力学第二定律。<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref>这个假想实验引起了关于热力学和信息论之间关系的争论和理论工作,并一直延续到今天,一些科学家认为理论上的考虑排除了任何以这种方式违反第二定律的实际装置。<br />
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== 思想的起源和历史 ==<br />
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The [[thought experiment]] first appeared in a letter [[James Clerk Maxwell|Maxwell]] wrote to [[Peter Guthrie Tait]] on 11 December 1867. It appeared again in a letter to [[John William Strutt]] in 1871, before it was presented to the public in Maxwell's 1872 book on [[thermodynamics]] titled ''Theory of Heat''.<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to John William Strutt in 1871, before it was presented to the public in Maxwell's 1872 book on thermodynamics titled Theory of Heat.<br />
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1867年12月11日,Maxwell在写给彼得·格思里·泰特 Peter Guthrie Tait的一封信中首次提出了这个假想实验。Maxwell在1871年写给约翰·威廉·斯特鲁特 John William Strutt 的信中再次提到该试验,后来在Maxwell 1872年出版的热力学书籍《热理论》(Theory of Heat)中公之于众。<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". [[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]] was the first to use the word "demon" for Maxwell's concept, in the journal ''[[Nature (journal)|Nature]]'' in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". William Thomson (Lord Kelvin) was the first to use the word "demon" for Maxwell's concept, in the journal Nature in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<br />
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在Maxwell的信件和书中,他将妖怪打开腔室的门描述为一个“有限的存在”。威廉·汤姆森 William Thomson (开尔文勋爵)在1874年的《自然》杂志上第一次用“妖”这个词来形容Maxwell的这一概念,并且表示他打算扩展这个词的含义,而不是恶意曲解。<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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== 最初的假想实验 ==<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different [[temperature]], when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature.<ref name="Bennett87">{{cite journal<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. The second law is also expressed as the assertion that in an isolated system, entropy never decreases.<br />
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热力学第二定律确保(通过统计概率)当两个不同温度的物体相互接触并与宇宙的其余部分隔离时,它们将演化为热力学平衡,最后两个物体的温度大致相同。第二定律也表示为这样的结论:在一个孤立的系统中,熵永远不会减少。<br />
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Maxwell构想了一个假想实验,作为进一步理解第二定律的方法。他对实验的描述如下:<br />
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....如果我们设想一种妖能力非常发达,以至于他能够跟踪每一个分子的运行轨迹,那么这种本质上和我们一样有限的存在,就能够做到我们不可能做到的事情。因为我们已经看到,在一个充满空气的容器中,在均匀的温度下,分子的运动速度决不是均匀的,尽管任意选择的大量分子的平均速度几乎是均匀的。假设我们有一箱气体被分成A和B两个区域,分割板上面有一个小洞。这个能够观察每一个分子的生灵,可以打开或关闭这个小洞,只允许速度快的分子从A飞向B,而速度慢的分子从B飞向A。如此一来,不需要任何外界做功,我们就可以升高B区的温度而降低A区的温度,从而打破热力学第二定律。<br />
<font color="#32cd32"> 这里多了一段非原文 </font> <br />
In other words, Maxwell imagines one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics. A heat engine operating between the thermal reservoirs A and B could extract useful work from this temperature difference.<br />
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换句话说,Maxwell假设一个容器被分成A和B两部分。两部分在相同的温度下装入相同的气体,并且相邻放置。通过观察两边的分子,一个假想中的妖怪守护着两部分之间的活动门。当一个来自A的比平均速度快的分子飞向活动门的时候,妖怪打开了这个活动门,这个分子就会从A飞向B。相对应的,当一个来自B的比平均速度慢的分子飞向活动门的时候,妖怪会让它从B飞向A。B中的分子的平均速度就会增加,而A中的分子的平均速度会减慢。由于平均分子速度与温度相对应,因此A中的温度降低,B中的温度升高,这与热力学第二定律相反。在热源A和热源B之间运行的热机可以从这种温度差中提取有用的功。<br />
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The demon must allow molecules to pass in both directions in order to produce only a temperature difference; one-way passage only of faster-than-average molecules from A to B will cause higher temperature and pressure to develop on the B side.<br />
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妖必须允许分子在两个方向上通过,以便只产生温度差; 只有比平均速度快的分子从A到B 单向通过才会使B部分产生更高的温度和压力。<br />
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== 批评与发展 ==<br />
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Several physicists have presented calculations that show that the second law of thermodynamics will not actually be violated, if a more complete analysis is made of the whole system including the demon. The essence of the physical argument is to show, by calculation, that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described. That is, it would take more thermodynamic work to gauge the speed of the molecules and selectively allow them to pass through the opening between A and B than the amount of energy gained by the difference of temperature caused by doing so.<br />
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一些物理学家展示的计算结果表明,如果对包括妖在内的整个系统进行更完整的分析,则实际上不会违反热力学第二定律。物理论证的精髓在于,通过计算来证明,任何妖都必须“产生”更多的熵来分离分子,这比描述的方法所消除的熵多。就是说,与通过这种方式引起的温度差所获得的能量相比,需要更多的热力学功来衡量分子的速度并选择性地使它们通过A和B之间的门。<br />
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One of the most famous responses to this question was suggested in 1929 by Leó Szilárd, and later by Léon Brillouin. He realized that some measuring processes need not increase thermodynamic entropy as long as they were thermodynamically reversible. He suggested these "reversible" measurements could be used to sort the molecules, violating the Second Law. However, due to the connection between thermodynamic entropy and information entropy, this also meant that the recorded measurement must not be erased. In other words, to determine whether to let a molecule through, the demon must acquire information about the state of the molecule and either discard it or store it. Discarding it leads to immediate increase in entropy but the demon cannot store it indefinitely. In 1982, Charles Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Although Bennett had reached the same conclusion as Szilard's 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons. Regarding Landauer's principle, the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz et al. in 2012. Furthermore, Lutz et al. confirmed that in order to approach the Landauer's limit, the system must asymptotically approach zero processing speed.<br />
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对这个问题最著名的回答之一是1929年由莱奥·西拉拉德Leó Szilárd和莱昂·布里渊 Léon Brillouin提出的。Szilárd指出,麦克斯韦妖需要一些方法来测量分子的速度,而获取信息的过程需要消耗能量。由于妖和气体是相互作用的,我们必须考虑气体和妖的总熵。妖的能量消耗将导致妖熵值的增加,这将大于气体熵值的降低。1960年,罗尔夫·兰道尔 Rolf Landauer提出了一个例外。他认识到,只要某些测量过程是热力学可逆的,就不需要增加熵。他认为这些“可逆”的测量可以用来分类分子,违反第二定律。但是,由于热力学熵和信息熵之间的联系,这还意味着不得删除已记录的测量。换句话说,为了决定是否让一个分子通过,妖必须获得关于分子状态的信息,要么丢弃它,要么存储它。丢弃它会立即导致熵的增加,但是妖不能无限期地储存它。1982年,查尔斯·本内特 Charles Bennett指出,无论准备得多么充分,妖最终都会耗尽信息存储空间,并且必须开始删除它先前收集的信息。擦除信息是一种热力学不可逆性过程,它增加了系统的熵。虽然Bennett得出了与Szilárd1929年的论文相同的结论,即麦克斯韦妖不能违反第二定律,因为会产生熵,而熵是由于不同的原因而达到的。根据Landauer原理,埃里克·卢兹 Eric Lutz等人在2012年通过实验测量了擦除信息所消耗的最小能量。此外,Lutz 等人证实,为了接近 Landauer 的极限,系统必须渐近接近零处理速度。<br />
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John Earman and John D. Norton have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the second law of thermodynamics cannot be violated by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc. It would therefore be circular to invoke these derived properties to defend the second law from the demonic argument. Bennett later acknowledged the validity of Earman and Norton's argument, while maintaining that Landauer's principle explains the mechanism by which real systems do not violate the second law of thermodynamics.<br />
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约翰·厄曼 John Earman和约翰 诺顿 John d. Norton 认为 Szilárd 和 Landauer 对麦克斯韦妖的解释是从假设热力学第二定律不会被妖侵犯开始的,并且从这个假设中得出妖的进一步属性,包括在擦除信息时消耗能量的必要性等等。因此援引这些派生属性来捍卫第二定律不受妖的影响是循环的。Bennett后来承认 Earman 和 Norton 的论点是正确的,同时坚持 Landauer 原理解释了真实系统不违反热力学第二定律的机制<br />
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== 近来的发展 ==<br />
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Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating systems has provided deeper insight on each information process with each subsystem. From this viewpoint, the measurement process is regarded as a process where the correlation (mutual information) between the engine and the demon increases, and the feedback process is regarded as a process where the correlation decreases. If the correlation changes, thermodynamic relations as the second law of thermodynamics and the fluctuation theorem for each subsystem should be modified, and for the case of external control a second-law like inequality and a generalized fluctuation theorem with mutual information are satisfied. These relations suggest that we need extra thermodynamic cost to increase correlation (measurement case), and in contrast we can apparently violate the second law up to the consumption of correlation (feedback case). For more general information processes including biological information processing, both inequality and equality with mutual information hold.<br />
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虽然 Landauer 和 Bennett 的论证只是回答了热力学第二定律和整个 Szilard 引擎系统的循环过程之间的一致性(引擎和妖的组合系统) ,但是最近一个基于非平衡态热力学的方法为小型波动系统提供了对每个子系统的信息处理的更深入的了解。从这个观点出发,将测量过程看作是引擎与妖之间相关性(互信息)增加的过程,而反馈过程看作是相关性减少的过程。如果相关性发生变化,则应修改作为热力学第二定律的热力学关系和每个子系统的波动定理,对于外部控制,则满足第二定律,如不等式和具有互信息的广义波动定理。这些关系表明,我们需要额外的热力学成本来增加相关性(测量案例) ,相比之下,我们可以明显地违反第二定律,直到消耗相关性(反馈案例)。对于包括生物信息处理在内的更一般的信息处理过程,互信息的不平等和平等都成立。<br />
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== 应用 ==<br />
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Real-life versions of Maxwellian demons occur, but all such "real demons" or molecular demons have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology. Single-atom traps used by particle physicists allow an experimenter to control the state of individual quanta in a way similar to Maxwell's demon.<br />
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现实版本的麦克斯韦妖也会出现,但是所有这些“真正的妖”或者分子妖都有其降低熵值的作用,并且在其他地方熵值的增加中得到适当的平衡。分子大小的机制不再只存在于生物学中; 它们也是纳米技术这一新兴领域的主题。粒子物理学家使用的单原子陷阱使得实验者可以像麦克斯韦妖那样控制单个量子的状态。<br />
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If hypothetical mirror matter exists, Zurab Silagadze proposes that demons can be envisaged, "which can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons."<br />
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如果假想的镜像物质存在,祖拉布·西拉加兹 Zurab Silagadze 提出妖可以被设想,“妖可以像第二类永久移动物一样: 只从一个蓄热池中提取热能,用它来做功,并与其他普通世界隔绝。然而,第二定律并没有被违反,因为妖通过发射镜像光子在世界的隐藏(镜像)区域付出了熵代价。<br />
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== 实验性工作 == <br />
In the February 2007 issue of Nature, David Leigh, a professor at the University of Edinburgh, announced the creation of a nano-device based on the Brownian ratchet popularized by Richard Feynman. Leigh's device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (light in this case) and therefore does not violate thermodynamics.<br />
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在2007年2月的《自然》杂志上,爱丁堡大学的戴维·利 David Leigh 教授宣布制造了一种基于理查德·费曼 Richard Feynman 推广的布朗棘轮的纳米装置。Leigh的设备能够使化学系统失衡,但它必须由外部源(在这种情况下是光)提供动力,因此不违反热力学。<br />
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Previously, researchers including Nobel Prize winner Fraser Stoddart, created ring-shaped molecules called rotaxanes which could be placed on an axle connecting two sites, A and B. Particles from either site would bump into the ring and move it from end to end. If a large collection of these devices were placed in a system, half of the devices had the ring at site A and half at B, at any given moment in time.<br />
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此前,包括诺贝尔奖获得者弗雷泽·斯托达特 Fraser Stoddart在内的研究人员创造了一种环状分子,称为轮烷,可以放置在连接两个位点A和B的轴上,任何一个位点的粒子都会撞到环上,从一端移动到另一端。如果将大量的这类设备放置在系统中,则在任何给定时间,一半的设备的环在站点A处,一半的站点在B处。<br />
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Leigh made a minor change to the axle so that if a light is shone on the device, the center of the axle will thicken, restricting the motion of the ring. It only keeps the ring from moving, however, if it is at A. Over time, therefore, the rings will be bumped from B to A and get stuck there, creating an imbalance in the system. In his experiments, Leigh was able to take a pot of "billions of these devices" from 50:50 equilibrium to a 70:30 imbalance within a few minutes.<br />
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Leigh对轮轴做了很小的改动,因此,如果在设备上照亮了灯,轮轴的中心将会变厚,从而限制了环的运动。但是,如果它位于A处,则只能阻止环移动。随着时间的推移,因此,环将从B碰撞到A并被困在那里,在系统中创建不平衡状态。在他的实验中,利 Leigh在几分钟之内就能从50:50的平衡状态变成70:30的不平衡状态,造就了“数十亿个此类设备”。<br />
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In 2009 Mark G. Raizen developed a laser atomic cooling technique which realizes the process Maxwell envisioned of sorting individual atoms in a gas into different containers based on their energy. The new concept is a one-way wall for atoms or molecules that allows them to move in one direction, but not go back. The operation of the one-way wall relies on an irreversible atomic and molecular process of absorption of a photon at a specific wavelength, followed by spontaneous emission to a different internal state. The irreversible process is coupled to a conservative force created by magnetic fields and/or light. Raizen and collaborators proposed using the one-way wall in order to reduce the entropy of an ensemble of atoms. In parallel, Gonzalo Muga and Andreas Ruschhaupt independently developed a similar concept. Their "atom diode" was not proposed for cooling, but rather for regulating the flow of atoms. The Raizen Group demonstrated significant cooling of atoms with the one-way wall in a series of experiments in 2008. Subsequently, the operation of a one-way wall for atoms was demonstrated by Daniel Steck and collaborators later in 2008. Their experiment was based on the 2005 scheme for the one-way wall, and was not used for cooling. The cooling method realized by the Raizen Group was called "single-photon cooling", because only one photon on average is required in order to bring an atom to near-rest. This is in contrast to other laser cooling techniques which use the momentum of the photon and require a two-level cycling transition.<br />
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2009年,马克 雷岑Mark g. Raizen开发了一种激光原子冷却技术,该技术实现了Maxwell设想的基于能量将气体中的单个原子分类放入不同容器的过程。这个新概念是原子或分子的单向墙,允许它们向一个方向运动,但不能向后移动。单向壁的操作依赖于一个不可逆的原子和分子过程,即吸收一个特定波长的光子,然后自发发射到另一个内部状态。不可逆性与磁场和/或光产生的保守力相耦合。Raizen 和他的合作者提出使用单向壁来减少原子团的熵。与此同时,贡萨洛·穆加 Gonzalo Muga 和安德烈亚斯 Andreas Ruschhaupt 独立地提出了一个类似的概念。他们的“原子二极管”不是用来冷却的,而是用来调节原子流。在2008年的一系列实验中,Raizen 团队证明了单向壁对原子的显著冷却作用。随后,丹尼尔·斯特克 Daniel Steck和合作者在2008年晚些时候演示了单向原子墙的操作。他们的实验是基于2005年的单向墙计划,并没有用于冷却。Raizen团队实现的冷却方法被称为“单光子冷却” ,因为平均只需要一个光子就可以使原子接近静止。这与其他激光冷却技术相反,后者使用光子的动量并需要两级循环过渡。<br />
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In 2006, Raizen, Muga, and Ruschhaupt showed in a theoretical paper that as each atom crosses the one-way wall, it scatters one photon, and information is provided about the turning point and hence the energy of that particle. The entropy increase of the radiation field scattered from a directional laser into a random direction is exactly balanced by the entropy reduction of the atoms as they are trapped by the one-way wall.<br />
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2006年,Raizen,Muga,和 Ruschhaupt 在一篇论文中指出,当每个原子穿过单向墙时,它散射一个光子,并提供了关于转折点的信息,因此也就提供了这个粒子的能量。定向激光向随机方向散射的辐射场的熵增与被单向壁俘获的原子的熵减完全平衡。<br />
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This technique is widely described as a "Maxwell's demon" because it realizes Maxwell's process of creating a temperature difference by sorting high and low energy atoms into different containers. However, scientists have pointed out that it is not a true Maxwell's demon in the sense that it does not violate the second law of thermodynamics; it does not result in a net decrease in entropy Only a year later and based on an earlier theoretical proposal, the same group presented the first experimental realization of an autonomous Maxwell's demon, which extracts microscopic information from a system and reduces its entropy by applying feedback. The demon is based on two capacitively coupled single-electron devices, both integrated on the same electronic circuit. The operation of the demon is directly observed as a temperature drop in the system, with a simultaneous temperature rise in the demon arising from the thermodynamic cost of generating the mutual information. In 2016, Pekola et al. demonstrated a proof-of-principle of an autonomous demon in coupled single-electron circuits, showing a way to cool critical elements in a circuit with information as a fuel. Pekola et al. have also proposed that a simple qubit circuit, e.g., made of a superconducting circuit, could provide a basis to study a quantum Szilard's engine.<br />
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这种技术被广泛地描述为“麦克斯韦妖”,因为它通过将高能和低能原子分类到不同的容器中产生温差实现了Maxwell的过程。然而,科学家已经指出,它不是一个真正的麦克斯韦妖,因为它没有违反热力学第二定律; 它不会导致熵减,也不能用来产生有用的能量。这是因为这个过程需要更多的能量从激光束比可能产生的温差。原子从激光束中吸收低熵的光子,并以随机方向发射它们,从而增加了环境的熵。<br />
<font color="#32cd32"> 可能缺失部分原文</font> <br />
2014年,佩科拉 Pekola 等人展示了 Szilárd 引擎实验的实现。仅仅一年之后,同一个研究小组根据早先的理论提议,第一次实验性地实现了自主的麦克斯韦妖,它从一个系统中提取微观信息,并通过反馈减少系统的熵。这个妖是基于集成在同一电路上的两个电容耦合的单电子器件。妖的运行直接表现为系统中的温度下降,同时由于产生互信息的热力学成本而引起的妖中的温度上升。2016年,Pekola 等人证明了单电子耦合电路中存在自主妖的原理,展示了一种以信息为燃料冷却电路中关键元件的方法。Pekola等人还提出,一个简单的量子比特电路,例如由超导电路构成的电路,可以为研究量子Szilárd引擎提供基础。<br />
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== 作为一种隐喻 ==<br />
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Daemons in computing, generally processes that run on servers to respond to users, are named for Maxwell's demon.<br />
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计算中的妖(通常是在服务器上运行以响应用户的进程)以麦克斯韦妖命名。<br />
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Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as a historical metaphor, though he misunderstood and misapplied the original principle. Adams interpreted history as a process moving towards "equilibrium", but he saw militaristic nations (he felt Germany pre-eminent in this class) as tending to reverse this process, a Maxwell's demon of history. Adams made many attempts to respond to the criticism of his formulation from his scientific colleagues, but the work remained incomplete at Adams' death in 1918. It was only published posthumously.<br />
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亨利·布鲁克斯·亚当斯 Henry Brooks Adams在他的手稿《应用于历史的阶段规则 》中试图用麦克斯韦妖作为历史隐喻,尽管他误解和误用了其原本的含义。Adams将历史解释为一个走向“均衡”的过程,但他认为军国主义国家(他认为德国在这一阶层中处于领先地位)倾向于扭转这一过程,这是历史的麦克斯韦妖。Adams曾多次尝试回应他的科学同事对他的公式的批评,但在1918年Adams去世时,这项工作仍未完成。这本书是死后才出版的。<br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E9%BA%A6%E5%85%8B%E6%96%AF%E9%9F%A6%E5%A6%96&diff=20940麦克斯韦妖2021-01-17T14:26:50Z<p>Vicky:</p>
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<div>[[File:Maxwell's demon.svg|right|340px|thumb|Schematic figure of Maxwell's demon thought experiment.]]<br />
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Schematic figure of Maxwell's demon thought experiment.<br />
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麦克斯韦妖假想实验示意图。<br />
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'''Maxwell's demon''' is a [[thought experiment]] created by the physicist [[James Clerk Maxwell]] in 1867 in which he suggested how the [[second law of thermodynamics]] might hypothetically be violated.<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref> In the thought experiment, a [[Demon (thought experiment)|demon]] controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing [[entropy]] and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and [[information theory]] extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated. In the thought experiment, a demon controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and information theory extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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'''<font color="#ff8000"> 麦克斯韦妖 Maxwell's demon</font>'''是英国物理学家詹姆斯·克拉克·麦克斯韦 James Clerk Maxwell于1867年为了说明违反'''<font color="#ff8000"> 热力学第二定律 second law of thermodynamics</font>'''的可能性而设想的假想实验。在这个实验当中,一个妖怪控制着两个气体舱之间的一扇小门。当独立的气体分子接近门时,妖怪迅速的打开和关闭门,快速的分子进入其中的一个腔,慢速的分子进入另外一个腔。因为速度更快的分子温度更高,妖怪的动作导致一个腔室升温,另一个腔室降温,从而减少熵,违反了热力学第二定律。<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref>这个假想实验引起了关于热力学和信息论之间关系的争论和理论工作,并一直延续到今天,一些科学家认为理论上的考虑排除了任何以这种方式违反第二定律的实际装置。<br />
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== 思想的起源和历史 ==<br />
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The [[thought experiment]] first appeared in a letter [[James Clerk Maxwell|Maxwell]] wrote to [[Peter Guthrie Tait]] on 11 December 1867. It appeared again in a letter to [[John William Strutt]] in 1871, before it was presented to the public in Maxwell's 1872 book on [[thermodynamics]] titled ''Theory of Heat''.<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to John William Strutt in 1871, before it was presented to the public in Maxwell's 1872 book on thermodynamics titled Theory of Heat.<br />
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1867年12月11日,Maxwell在写给彼得·格思里·泰特 Peter Guthrie Tait的一封信中首次提出了这个假想实验。Maxwell在1871年写给约翰·威廉·斯特鲁特 John William Strutt 的信中再次提到该试验,后来在Maxwell 1872年出版的热力学书籍《热理论》中公之于众。<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". [[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]] was the first to use the word "demon" for Maxwell's concept, in the journal ''[[Nature (journal)|Nature]]'' in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". William Thomson (Lord Kelvin) was the first to use the word "demon" for Maxwell's concept, in the journal Nature in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<br />
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在Maxwell的信件和书中,他将妖怪打开腔室的门描述为一个“有限的存在”。威廉·汤姆森 William Thomson (开尔文勋爵)在1874年的《自然》杂志上第一次用“妖”这个词来形容Maxwell的这一概念,并且表示他打算扩展这个词的含义,而不是恶意曲解。<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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== 最初的假想实验 ==<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different [[temperature]], when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature.<ref name="Bennett87">{{cite journal<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. The second law is also expressed as the assertion that in an isolated system, entropy never decreases.<br />
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热力学第二定律确保(通过统计概率)当两个不同温度的物体相互接触并与宇宙的其余部分隔离时,它们将演化为热力学平衡,最后两个物体的温度大致相同。第二定律也表示为这样的结论:在一个孤立的系统中,熵永远不会减少。<br />
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Maxwell构想了一个假想实验,作为进一步理解第二定律的方法。他对实验的描述如下:<br />
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....如果我们设想一种妖能力非常发达,以至于他能够跟踪每一个分子的运行轨迹,那么这种本质上和我们一样有限的存在,就能够做到我们不可能做到的事情。因为我们已经看到,在一个充满空气的容器中,在均匀的温度下,分子的运动速度决不是均匀的,尽管任意选择的大量分子的平均速度几乎是均匀的。假设我们有一箱气体被分成A和B两个区域,分割板上面有一个小洞。这个能够观察每一个分子的生灵,可以打开或关闭这个小洞,只允许速度快的分子从A飞向B,而速度慢的分子从B飞向A。如此一来,不需要任何外界做功,我们就可以升高B区的温度而降低A区的温度,从而打破热力学第二定律。<br />
<font color="#32cd32"> 这里多了一段非原文 </font> <br />
In other words, Maxwell imagines one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics. A heat engine operating between the thermal reservoirs A and B could extract useful work from this temperature difference.<br />
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换句话说,Maxwell假设一个容器被分成A和B两部分。两部分在相同的温度下装入相同的气体,并且相邻放置。通过观察两边的分子,一个假想中的妖怪守护着两部分之间的活动门。当一个来自A的比平均速度快的分子飞向活动门的时候,妖怪打开了这个活动门,这个分子就会从A飞向B。相对应的,当一个来自B的比平均速度慢的分子飞向活动门的时候,妖怪会让它从B飞向A。B中的分子的平均速度就会增加,而A中的分子的平均速度会减慢。由于平均分子速度与温度相对应,因此A中的温度降低,B中的温度升高,这与热力学第二定律相反。在热源A和热源B之间运行的热机可以从这种温度差中提取有用的功。<br />
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The demon must allow molecules to pass in both directions in order to produce only a temperature difference; one-way passage only of faster-than-average molecules from A to B will cause higher temperature and pressure to develop on the B side.<br />
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妖必须允许分子在两个方向上通过,以便只产生温度差; 只有比平均速度快的分子从A到B 单向通过才会使B部分产生更高的温度和压力。<br />
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== 批评与发展 ==<br />
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Several physicists have presented calculations that show that the second law of thermodynamics will not actually be violated, if a more complete analysis is made of the whole system including the demon. The essence of the physical argument is to show, by calculation, that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described. That is, it would take more thermodynamic work to gauge the speed of the molecules and selectively allow them to pass through the opening between A and B than the amount of energy gained by the difference of temperature caused by doing so.<br />
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一些物理学家展示的计算结果表明,如果对包括妖在内的整个系统进行更完整的分析,则实际上不会违反热力学第二定律。物理论证的精髓在于,通过计算来证明,任何妖都必须“产生”更多的熵来分离分子,这比描述的方法所消除的熵多。就是说,与通过这种方式引起的温度差所获得的能量相比,需要更多的热力学功来衡量分子的速度并选择性地使它们通过A和B之间的门。<br />
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One of the most famous responses to this question was suggested in 1929 by Leó Szilárd, and later by Léon Brillouin. He realized that some measuring processes need not increase thermodynamic entropy as long as they were thermodynamically reversible. He suggested these "reversible" measurements could be used to sort the molecules, violating the Second Law. However, due to the connection between thermodynamic entropy and information entropy, this also meant that the recorded measurement must not be erased. In other words, to determine whether to let a molecule through, the demon must acquire information about the state of the molecule and either discard it or store it. Discarding it leads to immediate increase in entropy but the demon cannot store it indefinitely. In 1982, Charles Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Although Bennett had reached the same conclusion as Szilard's 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons. Regarding Landauer's principle, the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz et al. in 2012. Furthermore, Lutz et al. confirmed that in order to approach the Landauer's limit, the system must asymptotically approach zero processing speed.<br />
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对这个问题最著名的回答之一是1929年由莱奥·西拉拉德Leó Szilárd和莱昂·布里渊 Léon Brillouin提出的。Szilárd指出,麦克斯韦妖需要一些方法来测量分子的速度,而获取信息的过程需要消耗能量。由于妖和气体是相互作用的,我们必须考虑气体和妖的总熵。妖的能量消耗将导致妖熵值的增加,这将大于气体熵值的降低。1960年,罗尔夫·兰道尔 Rolf Landauer提出了一个例外。他认识到,只要某些测量过程是热力学可逆的,就不需要增加熵。他认为这些“可逆”的测量可以用来分类分子,违反第二定律。但是,由于热力学熵和信息熵之间的联系,这还意味着不得删除已记录的测量。换句话说,为了决定是否让一个分子通过,妖必须获得关于分子状态的信息,要么丢弃它,要么存储它。丢弃它会立即导致熵的增加,但是妖不能无限期地储存它。1982年,查尔斯·本内特 Charles Bennett指出,无论准备得多么充分,妖最终都会耗尽信息存储空间,并且必须开始删除它先前收集的信息。擦除信息是一种热力学不可逆性过程,它增加了系统的熵。虽然Bennett得出了与Szilárd1929年的论文相同的结论,即麦克斯韦妖不能违反第二定律,因为会产生熵,而熵是由于不同的原因而达到的。根据Landauer原理,埃里克·卢兹 Eric Lutz等人在2012年通过实验测量了擦除信息所消耗的最小能量。此外,Lutz 等人证实,为了接近 Landauer 的极限,系统必须渐近接近零处理速度。<br />
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John Earman and John D. Norton have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the second law of thermodynamics cannot be violated by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc. It would therefore be circular to invoke these derived properties to defend the second law from the demonic argument. Bennett later acknowledged the validity of Earman and Norton's argument, while maintaining that Landauer's principle explains the mechanism by which real systems do not violate the second law of thermodynamics.<br />
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约翰·厄曼 John Earman和约翰 诺顿 John d. Norton 认为 Szilárd 和 Landauer 对麦克斯韦妖的解释是从假设热力学第二定律不会被妖侵犯开始的,并且从这个假设中得出妖的进一步属性,包括在擦除信息时消耗能量的必要性等等。因此援引这些派生属性来捍卫第二定律不受妖的影响是循环的。Bennett后来承认 Earman 和 Norton 的论点是正确的,同时坚持 Landauer 原理解释了真实系统不违反热力学第二定律的机制<br />
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== 近来的发展 ==<br />
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Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating systems has provided deeper insight on each information process with each subsystem. From this viewpoint, the measurement process is regarded as a process where the correlation (mutual information) between the engine and the demon increases, and the feedback process is regarded as a process where the correlation decreases. If the correlation changes, thermodynamic relations as the second law of thermodynamics and the fluctuation theorem for each subsystem should be modified, and for the case of external control a second-law like inequality and a generalized fluctuation theorem with mutual information are satisfied. These relations suggest that we need extra thermodynamic cost to increase correlation (measurement case), and in contrast we can apparently violate the second law up to the consumption of correlation (feedback case). For more general information processes including biological information processing, both inequality and equality with mutual information hold.<br />
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虽然 Landauer 和 Bennett 的论证只是回答了热力学第二定律和整个 Szilard 引擎系统的循环过程之间的一致性(引擎和妖的组合系统) ,但是最近一个基于非平衡态热力学的方法为小型波动系统提供了对每个子系统的信息处理的更深入的了解。从这个观点出发,将测量过程看作是引擎与妖之间相关性(互信息)增加的过程,而反馈过程看作是相关性减少的过程。如果相关性发生变化,则应修改作为热力学第二定律的热力学关系和每个子系统的波动定理,对于外部控制,则满足第二定律,如不等式和具有互信息的广义波动定理。这些关系表明,我们需要额外的热力学成本来增加相关性(测量案例) ,相比之下,我们可以明显地违反第二定律,直到消耗相关性(反馈案例)。对于包括生物信息处理在内的更一般的信息处理过程,互信息的不平等和平等都成立。<br />
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== 应用 ==<br />
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Real-life versions of Maxwellian demons occur, but all such "real demons" or molecular demons have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology. Single-atom traps used by particle physicists allow an experimenter to control the state of individual quanta in a way similar to Maxwell's demon.<br />
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现实版本的麦克斯韦妖也会出现,但是所有这些“真正的妖”或者分子妖都有其降低熵值的作用,并且在其他地方熵值的增加中得到适当的平衡。分子大小的机制不再只存在于生物学中; 它们也是纳米技术这一新兴领域的主题。粒子物理学家使用的单原子陷阱使得实验者可以像麦克斯韦妖那样控制单个量子的状态。<br />
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If hypothetical mirror matter exists, Zurab Silagadze proposes that demons can be envisaged, "which can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons."<br />
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如果假想的镜像物质存在,祖拉布·西拉加兹 Zurab Silagadze 提出妖可以被设想,“妖可以像第二类永久移动物一样: 只从一个蓄热池中提取热能,用它来做功,并与其他普通世界隔绝。然而,第二定律并没有被违反,因为妖通过发射镜像光子在世界的隐藏(镜像)区域付出了熵代价。<br />
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== 实验性工作 == <br />
In the February 2007 issue of Nature, David Leigh, a professor at the University of Edinburgh, announced the creation of a nano-device based on the Brownian ratchet popularized by Richard Feynman. Leigh's device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (light in this case) and therefore does not violate thermodynamics.<br />
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在2007年2月的《自然》杂志上,爱丁堡大学的戴维·利 David Leigh 教授宣布制造了一种基于理查德·费曼 Richard Feynman 推广的布朗棘轮的纳米装置。Leigh的设备能够使化学系统失衡,但它必须由外部源(在这种情况下是光)提供动力,因此不违反热力学。<br />
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Previously, researchers including Nobel Prize winner Fraser Stoddart, created ring-shaped molecules called rotaxanes which could be placed on an axle connecting two sites, A and B. Particles from either site would bump into the ring and move it from end to end. If a large collection of these devices were placed in a system, half of the devices had the ring at site A and half at B, at any given moment in time.<br />
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此前,包括诺贝尔奖获得者弗雷泽·斯托达特 Fraser Stoddart在内的研究人员创造了一种环状分子,称为轮烷,可以放置在连接两个位点A和B的轴上,任何一个位点的粒子都会撞到环上,从一端移动到另一端。如果将大量的这类设备放置在系统中,则在任何给定时间,一半的设备的环在站点A处,一半的站点在B处。<br />
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Leigh made a minor change to the axle so that if a light is shone on the device, the center of the axle will thicken, restricting the motion of the ring. It only keeps the ring from moving, however, if it is at A. Over time, therefore, the rings will be bumped from B to A and get stuck there, creating an imbalance in the system. In his experiments, Leigh was able to take a pot of "billions of these devices" from 50:50 equilibrium to a 70:30 imbalance within a few minutes.<br />
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Leigh对轮轴做了很小的改动,因此,如果在设备上照亮了灯,轮轴的中心将会变厚,从而限制了环的运动。但是,如果它位于A处,则只能阻止环移动。随着时间的推移,因此,环将从B碰撞到A并被困在那里,在系统中创建不平衡状态。在他的实验中,利 Leigh在几分钟之内就能从50:50的平衡状态变成70:30的不平衡状态,造就了“数十亿个此类设备”。<br />
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In 2009 Mark G. Raizen developed a laser atomic cooling technique which realizes the process Maxwell envisioned of sorting individual atoms in a gas into different containers based on their energy. The new concept is a one-way wall for atoms or molecules that allows them to move in one direction, but not go back. The operation of the one-way wall relies on an irreversible atomic and molecular process of absorption of a photon at a specific wavelength, followed by spontaneous emission to a different internal state. The irreversible process is coupled to a conservative force created by magnetic fields and/or light. Raizen and collaborators proposed using the one-way wall in order to reduce the entropy of an ensemble of atoms. In parallel, Gonzalo Muga and Andreas Ruschhaupt independently developed a similar concept. Their "atom diode" was not proposed for cooling, but rather for regulating the flow of atoms. The Raizen Group demonstrated significant cooling of atoms with the one-way wall in a series of experiments in 2008. Subsequently, the operation of a one-way wall for atoms was demonstrated by Daniel Steck and collaborators later in 2008. Their experiment was based on the 2005 scheme for the one-way wall, and was not used for cooling. The cooling method realized by the Raizen Group was called "single-photon cooling", because only one photon on average is required in order to bring an atom to near-rest. This is in contrast to other laser cooling techniques which use the momentum of the photon and require a two-level cycling transition.<br />
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2009年,马克 雷岑Mark g. Raizen开发了一种激光原子冷却技术,该技术实现了Maxwell设想的基于能量将气体中的单个原子分类放入不同容器的过程。这个新概念是原子或分子的单向墙,允许它们向一个方向运动,但不能向后移动。单向壁的操作依赖于一个不可逆的原子和分子过程,即吸收一个特定波长的光子,然后自发发射到另一个内部状态。不可逆性与磁场和/或光产生的保守力相耦合。Raizen 和他的合作者提出使用单向壁来减少原子团的熵。与此同时,贡萨洛·穆加 Gonzalo Muga 和安德烈亚斯 Andreas Ruschhaupt 独立地提出了一个类似的概念。他们的“原子二极管”不是用来冷却的,而是用来调节原子流。在2008年的一系列实验中,Raizen 团队证明了单向壁对原子的显著冷却作用。随后,丹尼尔·斯特克 Daniel Steck和合作者在2008年晚些时候演示了单向原子墙的操作。他们的实验是基于2005年的单向墙计划,并没有用于冷却。Raizen团队实现的冷却方法被称为“单光子冷却” ,因为平均只需要一个光子就可以使原子接近静止。这与其他激光冷却技术相反,后者使用光子的动量并需要两级循环过渡。<br />
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In 2006, Raizen, Muga, and Ruschhaupt showed in a theoretical paper that as each atom crosses the one-way wall, it scatters one photon, and information is provided about the turning point and hence the energy of that particle. The entropy increase of the radiation field scattered from a directional laser into a random direction is exactly balanced by the entropy reduction of the atoms as they are trapped by the one-way wall.<br />
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2006年,Raizen,Muga,和 Ruschhaupt 在一篇论文中指出,当每个原子穿过单向墙时,它散射一个光子,并提供了关于转折点的信息,因此也就提供了这个粒子的能量。定向激光向随机方向散射的辐射场的熵增与被单向壁俘获的原子的熵减完全平衡。<br />
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This technique is widely described as a "Maxwell's demon" because it realizes Maxwell's process of creating a temperature difference by sorting high and low energy atoms into different containers. However, scientists have pointed out that it is not a true Maxwell's demon in the sense that it does not violate the second law of thermodynamics; it does not result in a net decrease in entropy Only a year later and based on an earlier theoretical proposal, the same group presented the first experimental realization of an autonomous Maxwell's demon, which extracts microscopic information from a system and reduces its entropy by applying feedback. The demon is based on two capacitively coupled single-electron devices, both integrated on the same electronic circuit. The operation of the demon is directly observed as a temperature drop in the system, with a simultaneous temperature rise in the demon arising from the thermodynamic cost of generating the mutual information. In 2016, Pekola et al. demonstrated a proof-of-principle of an autonomous demon in coupled single-electron circuits, showing a way to cool critical elements in a circuit with information as a fuel. Pekola et al. have also proposed that a simple qubit circuit, e.g., made of a superconducting circuit, could provide a basis to study a quantum Szilard's engine.<br />
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这种技术被广泛地描述为“麦克斯韦妖”,因为它通过将高能和低能原子分类到不同的容器中产生温差实现了Maxwell的过程。然而,科学家已经指出,它不是一个真正的麦克斯韦妖,因为它没有违反热力学第二定律; 它不会导致熵减,也不能用来产生有用的能量。这是因为这个过程需要更多的能量从激光束比可能产生的温差。原子从激光束中吸收低熵的光子,并以随机方向发射它们,从而增加了环境的熵。<br />
<font color="#32cd32"> 可能缺失部分原文</font> <br />
2014年,佩科拉 Pekola 等人展示了 Szilárd 引擎实验的实现。仅仅一年之后,同一个研究小组根据早先的理论提议,第一次实验性地实现了自主的麦克斯韦妖,它从一个系统中提取微观信息,并通过反馈减少系统的熵。这个妖是基于集成在同一电路上的两个电容耦合的单电子器件。妖的运行直接表现为系统中的温度下降,同时由于产生互信息的热力学成本而引起的妖中的温度上升。2016年,Pekola 等人证明了单电子耦合电路中存在自主妖的原理,展示了一种以信息为燃料冷却电路中关键元件的方法。Pekola等人还提出,一个简单的量子比特电路,例如由超导电路构成的电路,可以为研究量子Szilárd引擎提供基础。<br />
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== 作为一种隐喻 ==<br />
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Daemons in computing, generally processes that run on servers to respond to users, are named for Maxwell's demon.<br />
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计算中的妖(通常是在服务器上运行以响应用户的进程)以麦克斯韦妖命名。<br />
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Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as a historical metaphor, though he misunderstood and misapplied the original principle. Adams interpreted history as a process moving towards "equilibrium", but he saw militaristic nations (he felt Germany pre-eminent in this class) as tending to reverse this process, a Maxwell's demon of history. Adams made many attempts to respond to the criticism of his formulation from his scientific colleagues, but the work remained incomplete at Adams' death in 1918. It was only published posthumously.<br />
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亨利·布鲁克斯·亚当斯 Henry Brooks Adams在他的手稿《应用于历史的阶段规则 》中试图用麦克斯韦妖作为历史隐喻,尽管他误解和误用了其原本的含义。Adams将历史解释为一个走向“均衡”的过程,但他认为军国主义国家(他认为德国在这一阶层中处于领先地位)倾向于扭转这一过程,这是历史的麦克斯韦妖。Adams曾多次尝试回应他的科学同事对他的公式的批评,但在1918年Adams去世时,这项工作仍未完成。这本书是死后才出版的。<br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E9%BA%A6%E5%85%8B%E6%96%AF%E9%9F%A6%E5%A6%96&diff=20673麦克斯韦妖2020-12-29T09:15:20Z<p>Vicky:</p>
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<div>[[File:Maxwell's demon.svg|right|340px|thumb|Schematic figure of Maxwell's demon thought experiment.]]<br />
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Schematic figure of Maxwell's demon thought experiment.<br />
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麦克斯韦妖假想实验示意图。<br />
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'''Maxwell's demon''' is a [[thought experiment]] created by the physicist [[James Clerk Maxwell]] in 1867 in which he suggested how the [[second law of thermodynamics]] might hypothetically be violated.<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref> In the thought experiment, a [[Demon (thought experiment)|demon]] controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing [[entropy]] and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and [[information theory]] extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell in 1867 in which he suggested how the second law of thermodynamics might hypothetically be violated. In the thought experiment, a demon controls a small door between two compartments of gas. As individual gas molecules approach the door, the demon quickly opens and shuts the door so that only fast molecules are passed into one of the chambers, while only slow molecules are passed into the other. Because faster molecules are hotter, the demon's behaviour causes one chamber to warm up and the other to cool down, thereby decreasing entropy and violating the second law of thermodynamics. This thought experiment has provoked debate and theoretical work on the relation between thermodynamics and information theory extending to the present day, with a number of scientists arguing that theoretical considerations rule out any practical device violating the second law in this way.<br />
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'''<font color="#ff8000"> 麦克斯韦妖 Maxwell's demon</font>'''是英国物理学家詹姆斯·克拉克·麦克斯韦 James Clerk Maxwell于1867年为了说明违反'''<font color="#ff8000"> 热力学第二定律 second law of thermodynamics</font>'''的可能性而设想的假想实验。在这个实验当中,一个妖怪控制着两个气体舱之间的一扇小门。当独立的气体分子接近门时,妖怪迅速的打开和关闭门,快速的分子进入其中的一个腔,慢速的分子进入另外一个腔。因为速度更快的分子温度更高,妖怪的动作导致一个腔室升温,另一个腔室降温,从而减少熵,违反了热力学第二定律。<ref>{{cite book |author=Cargill Gilston Knott |title=Life and Scientific Work of Peter Guthrie Tait |publisher=[[Cambridge University Press]] |year=1911 |pages=213–215 |chapter=Quote from undated letter from Maxwell to Tait | chapter-url=https://archive.org/stream/lifescientificwo00knotuoft#page/212/mode/2up}}</ref>这个假想实验引起了关于热力学和信息论之间关系的争论和理论工作,直至今天一些科学家认为理论上的考虑排除了任何以这种方式违反第二定律的实际装置。<br />
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== 思想的起源和历史 ==<br />
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The [[thought experiment]] first appeared in a letter [[James Clerk Maxwell|Maxwell]] wrote to [[Peter Guthrie Tait]] on 11 December 1867. It appeared again in a letter to [[John William Strutt]] in 1871, before it was presented to the public in Maxwell's 1872 book on [[thermodynamics]] titled ''Theory of Heat''.<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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The thought experiment first appeared in a letter Maxwell wrote to Peter Guthrie Tait on 11 December 1867. It appeared again in a letter to John William Strutt in 1871, before it was presented to the public in Maxwell's 1872 book on thermodynamics titled Theory of Heat.<br />
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1867年12月11日,Maxwell在写给彼得·格思里·泰特 Peter Guthrie Tait的一封信中首次提出了这个假想实验。Maxwell在1871年写给约翰·威廉·斯特鲁特 John William Strutt 的信中再次提到该试验,后来在Maxwell 1872年出版的热力学书籍《热理论》中公之于众。<ref name=Leff>[[#Leff Rex 02|Leff & Rex (2002)]], p. 370.</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". [[William Thomson, 1st Baron Kelvin|William Thomson (Lord Kelvin)]] was the first to use the word "demon" for Maxwell's concept, in the journal ''[[Nature (journal)|Nature]]'' in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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In his letters and books, Maxwell described the agent opening the door between the chambers as a "finite being". William Thomson (Lord Kelvin) was the first to use the word "demon" for Maxwell's concept, in the journal Nature in 1874, and implied that he intended the mediating, rather than malevolent, connotation of the word.<br />
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在Maxwell的信件和书中,他将妖怪打开腔室的门描述为一个“有限的存在”。威廉·汤姆森 William Thomson (开尔文勋爵)在1874年的《自然》杂志上第一次用“妖”这个词来形容Maxwell的这一概念,并且表示他打算扩展这个词的含义,而不是恶意曲解。<ref>{{cite journal |author=William Thomson |year=1874 |title=Kinetic theory of the dissipation of energy |journal=[[Nature (journal)|Nature]] |volume=9 |issue=232 |pages=441–444 |doi=10.1038/009441c0 |bibcode=1874Natur...9..441T|author-link=William Thomson, 1st Baron Kelvin |doi-access=free }}</ref><ref>{{cite journal |year=1879 |title=The sorting demon Of Maxwell |journal=Nature |volume=20 |issue=501 |pages=126 |bibcode=1879Natur..20Q.126. |doi=10.1038/020126a0 |doi-access=free }}</ref><ref name=Weber>{{cite book |author=Alan S. Weber |year=2000 |title=Nineteenth Century Science: a Selection of Original Texts |publisher=[[Broadview Press]] |page=300}}</ref><br />
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== 最初的假想实验 ==<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different [[temperature]], when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature.<ref name="Bennett87">{{cite journal<br />
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The second law of thermodynamics ensures (through statistical probability) that two bodies of different temperature, when brought into contact with each other and isolated from the rest of the Universe, will evolve to a thermodynamic equilibrium in which both bodies have approximately the same temperature. The second law is also expressed as the assertion that in an isolated system, entropy never decreases.<br />
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热力学第二定律确保(通过统计概率)当两个不同温度的物体相互接触并与宇宙的其余部分隔离时,它们将演化为热力学平衡,最后两个物体的温度大致相同。第二定律也表示为这样的结论:在一个孤立的系统中,熵永远不会减少。<br />
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Maxwell构想了一个假想实验,作为进一步理解第二定律的方法。他对实验的描述如下:<br />
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....如果我们设想一种妖能力非常发达,以至于他能够跟踪每一个分子的运行轨迹,那么这种本质上和我们一样有限的存在,就能够做到我们不可能做到的事情。因为我们已经看到,在一个充满空气的容器中,在均匀的温度下,分子的运动速度决不是均匀的,尽管任意选择的大量分子的平均速度几乎是均匀的。假设我们有一箱气体被分成A和B两个区域,分割板上面有一个小洞。这个能够观察每一个分子的生灵,可以打开或关闭这个小洞,只允许速度快的分子从A飞向B,而速度慢的分子从B飞向A。如此一来,不需要任何外界做功,我们就可以升高B区的温度而降低A区的温度,从而打破热力学第二定律。<br />
<font color="#32cd32"> 这里多了一段非原文 </font> <br />
In other words, Maxwell imagines one container divided into two parts, A and B. Both parts are filled with the same gas at equal temperatures and placed next to each other. Observing the molecules on both sides, an imaginary demon guards a trapdoor between the two parts. When a faster-than-average molecule from A flies towards the trapdoor, the demon opens it, and the molecule will fly from A to B. Likewise, when a slower-than-average molecule from B flies towards the trapdoor, the demon will let it pass from B to A. The average speed of the molecules in B will have increased while in A they will have slowed down on average. Since average molecular speed corresponds to temperature, the temperature decreases in A and increases in B, contrary to the second law of thermodynamics. A heat engine operating between the thermal reservoirs A and B could extract useful work from this temperature difference.<br />
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换句话说,Maxwell假设一个容器被分成A和B两部分。两部分在相同的温度下装入相同的气体,并且相邻放置。通过观察两边的分子,一个假想中的妖怪守护着两部分之间的活动门。当一个来自A的比平均速度快的分子飞向活动门的时候,妖怪打开了这个活动门,这个分子就会从A飞向B。相对应的,当一个来自B的比平均速度慢的分子飞向活动门的时候,妖怪会让它从B飞向A。B中的分子的平均速度就会增加,而A中的分子的平均速度会减慢。由于平均分子速度与温度相对应,因此A中的温度降低,B中的温度升高,这与热力学第二定律相反。在热源A和热源B之间运行的热机可以从这种温度差中提取有用的功。<br />
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The demon must allow molecules to pass in both directions in order to produce only a temperature difference; one-way passage only of faster-than-average molecules from A to B will cause higher temperature and pressure to develop on the B side.<br />
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妖必须允许分子在两个方向上通过,以便只产生温度差; 只有比平均速度快的分子从A到B 单向通过才会使B部分产生更高的温度和压力。<br />
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== 批评与发展 ==<br />
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Several physicists have presented calculations that show that the second law of thermodynamics will not actually be violated, if a more complete analysis is made of the whole system including the demon. The essence of the physical argument is to show, by calculation, that any demon must "generate" more entropy segregating the molecules than it could ever eliminate by the method described. That is, it would take more thermodynamic work to gauge the speed of the molecules and selectively allow them to pass through the opening between A and B than the amount of energy gained by the difference of temperature caused by doing so.<br />
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一些物理学家展示的计算结果表明,如果对包括妖在内的整个系统进行更完整的分析,则实际上不会违反热力学第二定律。物理论证的精髓在于,通过计算来证明,任何妖都必须“产生”更多的熵来分离分子,这比描述的方法所消除的熵多。就是说,与通过这种方式引起的温度差所获得的能量相比,需要更多的热力学功来衡量分子的速度并选择性地使它们通过A和B之间的门。<br />
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One of the most famous responses to this question was suggested in 1929 by Leó Szilárd, and later by Léon Brillouin. He realized that some measuring processes need not increase thermodynamic entropy as long as they were thermodynamically reversible. He suggested these "reversible" measurements could be used to sort the molecules, violating the Second Law. However, due to the connection between thermodynamic entropy and information entropy, this also meant that the recorded measurement must not be erased. In other words, to determine whether to let a molecule through, the demon must acquire information about the state of the molecule and either discard it or store it. Discarding it leads to immediate increase in entropy but the demon cannot store it indefinitely. In 1982, Charles Bennett showed that, however well prepared, eventually the demon will run out of information storage space and must begin to erase the information it has previously gathered. Erasing information is a thermodynamically irreversible process that increases the entropy of a system. Although Bennett had reached the same conclusion as Szilard's 1929 paper, that a Maxwellian demon could not violate the second law because entropy would be created, he had reached it for different reasons. Regarding Landauer's principle, the minimum energy dissipated by deleting information was experimentally measured by Eric Lutz et al. in 2012. Furthermore, Lutz et al. confirmed that in order to approach the Landauer's limit, the system must asymptotically approach zero processing speed.<br />
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对这个问题最著名的回答之一是1929年由莱奥·西拉拉德Leó Szilárd和莱昂·布里渊 Léon Brillouin提出的。Szilárd指出,麦克斯韦妖需要一些方法来测量分子的速度,而获取信息的过程需要消耗能量。由于妖和气体是相互作用的,我们必须考虑气体和妖的总熵。妖的能量消耗将导致妖熵值的增加,这将大于气体熵值的降低。1960年,罗尔夫·兰道尔 Rolf Landauer提出了一个例外。他认识到,只要某些测量过程是热力学可逆的,就不需要增加熵。他认为这些“可逆”的测量可以用来分类分子,违反第二定律。但是,由于热力学熵和信息熵之间的联系,这还意味着不得删除已记录的测量。换句话说,为了决定是否让一个分子通过,妖必须获得关于分子状态的信息,要么丢弃它,要么存储它。丢弃它会立即导致熵的增加,但是妖不能无限期地储存它。1982年,查尔斯·本内特 Charles Bennett指出,无论准备得多么充分,妖最终都会耗尽信息存储空间,并且必须开始删除它先前收集的信息。擦除信息是一种热力学不可逆性过程,它增加了系统的熵。虽然Bennett得出了与Szilárd1929年的论文相同的结论,即麦克斯韦妖不能违反第二定律,因为会产生熵,而熵是由于不同的原因而达到的。根据Landauer原理,埃里克·卢兹 Eric Lutz等人在2012年通过实验测量了擦除信息所消耗的最小能量。此外,Lutz 等人证实,为了接近 Landauer 的极限,系统必须渐近接近零处理速度。<br />
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John Earman and John D. Norton have argued that Szilárd and Landauer's explanations of Maxwell's demon begin by assuming that the second law of thermodynamics cannot be violated by the demon, and derive further properties of the demon from this assumption, including the necessity of consuming energy when erasing information, etc. It would therefore be circular to invoke these derived properties to defend the second law from the demonic argument. Bennett later acknowledged the validity of Earman and Norton's argument, while maintaining that Landauer's principle explains the mechanism by which real systems do not violate the second law of thermodynamics.<br />
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约翰·厄曼 John Earman和约翰 诺顿 John d. Norton 认为 Szilárd 和 Landauer 对麦克斯韦妖的解释是从假设热力学第二定律不会被妖侵犯开始的,并且从这个假设中得出妖的进一步属性,包括在擦除信息时消耗能量的必要性等等。因此援引这些派生属性来捍卫第二定律不受妖的影响是循环的。Bennett后来承认 Earman 和 Norton 的论点是正确的,同时坚持 Landauer 原理解释了真实系统不违反热力学第二定律的机制<br />
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== 近来的发展 ==<br />
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Although the argument by Landauer and Bennett only answers the consistency between the second law of thermodynamics and the whole cyclic process of the entire system of a Szilard engine (a composite system of the engine and the demon), a recent approach based on the non-equilibrium thermodynamics for small fluctuating systems has provided deeper insight on each information process with each subsystem. From this viewpoint, the measurement process is regarded as a process where the correlation (mutual information) between the engine and the demon increases, and the feedback process is regarded as a process where the correlation decreases. If the correlation changes, thermodynamic relations as the second law of thermodynamics and the fluctuation theorem for each subsystem should be modified, and for the case of external control a second-law like inequality and a generalized fluctuation theorem with mutual information are satisfied. These relations suggest that we need extra thermodynamic cost to increase correlation (measurement case), and in contrast we can apparently violate the second law up to the consumption of correlation (feedback case). For more general information processes including biological information processing, both inequality and equality with mutual information hold.<br />
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虽然 Landauer 和 Bennett 的论证只是回答了热力学第二定律和整个 Szilard 引擎系统的循环过程之间的一致性(引擎和妖的组合系统) ,但是最近一个基于非平衡态热力学的方法为小型波动系统提供了对每个子系统的信息处理的更深入的了解。从这个观点出发,将测量过程看作是引擎与妖之间相关性(互信息)增加的过程,而反馈过程看作是相关性减少的过程。如果相关性发生变化,则应修改作为热力学第二定律的热力学关系和每个子系统的波动定理,对于外部控制,则满足第二定律,如不等式和具有互信息的广义波动定理。这些关系表明,我们需要额外的热力学成本来增加相关性(测量案例) ,相比之下,我们可以明显地违反第二定律,直到消耗相关性(反馈案例)。对于包括生物信息处理在内的更一般的信息处理过程,互信息的不平等和平等都成立。<br />
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== 应用 ==<br />
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Real-life versions of Maxwellian demons occur, but all such "real demons" or molecular demons have their entropy-lowering effects duly balanced by increase of entropy elsewhere. Molecular-sized mechanisms are no longer found only in biology; they are also the subject of the emerging field of nanotechnology. Single-atom traps used by particle physicists allow an experimenter to control the state of individual quanta in a way similar to Maxwell's demon.<br />
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现实版本的麦克斯韦妖也会出现,但是所有这些“真正的妖”或者分子妖都有其降低熵值的作用,并且在其他地方熵值的增加中得到适当的平衡。分子大小的机制不再只存在于生物学中; 它们也是纳米技术这一新兴领域的主题。粒子物理学家使用的单原子陷阱使得实验者可以像麦克斯韦妖那样控制单个量子的状态。<br />
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If hypothetical mirror matter exists, Zurab Silagadze proposes that demons can be envisaged, "which can act like perpetuum mobiles of the second kind: extract heat energy from only one reservoir, use it to do work and be isolated from the rest of ordinary world. Yet the Second Law is not violated because the demons pay their entropy cost in the hidden (mirror) sector of the world by emitting mirror photons."<br />
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如果假想的镜像物质存在,祖拉布·西拉加兹 Zurab Silagadze 提出妖可以被设想,“妖可以像第二类永久移动物一样: 只从一个蓄热池中提取热能,用它来做功,并与其他普通世界隔绝。然而,第二定律并没有被违反,因为妖通过发射镜像光子在世界的隐藏(镜像)区域付出了熵代价。<br />
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== 实验性工作 == <br />
In the February 2007 issue of Nature, David Leigh, a professor at the University of Edinburgh, announced the creation of a nano-device based on the Brownian ratchet popularized by Richard Feynman. Leigh's device is able to drive a chemical system out of equilibrium, but it must be powered by an external source (light in this case) and therefore does not violate thermodynamics.<br />
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在2007年2月的《自然》杂志上,爱丁堡大学的戴维·利 David Leigh 教授宣布制造了一种基于理查德·费曼 Richard Feynman 推广的布朗棘轮的纳米装置。Leigh的设备能够使化学系统失衡,但它必须由外部源(在这种情况下是光)提供动力,因此不违反热力学。<br />
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Previously, researchers including Nobel Prize winner Fraser Stoddart, created ring-shaped molecules called rotaxanes which could be placed on an axle connecting two sites, A and B. Particles from either site would bump into the ring and move it from end to end. If a large collection of these devices were placed in a system, half of the devices had the ring at site A and half at B, at any given moment in time.<br />
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此前,包括诺贝尔奖获得者弗雷泽·斯托达特 Fraser Stoddart在内的研究人员创造了一种环状分子,称为轮烷,可以放置在连接两个位点A和B的轴上,任何一个位点的粒子都会撞到环上,从一端移动到另一端。如果将大量的这类设备放置在系统中,则在任何给定时间,一半的设备的环在站点A处,一半的站点在B处。<br />
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Leigh made a minor change to the axle so that if a light is shone on the device, the center of the axle will thicken, restricting the motion of the ring. It only keeps the ring from moving, however, if it is at A. Over time, therefore, the rings will be bumped from B to A and get stuck there, creating an imbalance in the system. In his experiments, Leigh was able to take a pot of "billions of these devices" from 50:50 equilibrium to a 70:30 imbalance within a few minutes.<br />
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Leigh对轮轴做了很小的改动,因此,如果在设备上照亮了灯,轮轴的中心将会变厚,从而限制了环的运动。但是,如果它位于A处,则只能阻止环移动。随着时间的推移,因此,环将从B碰撞到A并被困在那里,在系统中创建不平衡状态。在他的实验中,利 Leigh在几分钟之内就能从50:50的平衡状态变成70:30的不平衡状态,造就了“数十亿个此类设备”。<br />
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In 2009 Mark G. Raizen developed a laser atomic cooling technique which realizes the process Maxwell envisioned of sorting individual atoms in a gas into different containers based on their energy. The new concept is a one-way wall for atoms or molecules that allows them to move in one direction, but not go back. The operation of the one-way wall relies on an irreversible atomic and molecular process of absorption of a photon at a specific wavelength, followed by spontaneous emission to a different internal state. The irreversible process is coupled to a conservative force created by magnetic fields and/or light. Raizen and collaborators proposed using the one-way wall in order to reduce the entropy of an ensemble of atoms. In parallel, Gonzalo Muga and Andreas Ruschhaupt independently developed a similar concept. Their "atom diode" was not proposed for cooling, but rather for regulating the flow of atoms. The Raizen Group demonstrated significant cooling of atoms with the one-way wall in a series of experiments in 2008. Subsequently, the operation of a one-way wall for atoms was demonstrated by Daniel Steck and collaborators later in 2008. Their experiment was based on the 2005 scheme for the one-way wall, and was not used for cooling. The cooling method realized by the Raizen Group was called "single-photon cooling", because only one photon on average is required in order to bring an atom to near-rest. This is in contrast to other laser cooling techniques which use the momentum of the photon and require a two-level cycling transition.<br />
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2009年,马克 雷岑Mark g. Raizen开发了一种激光原子冷却技术,该技术实现了Maxwell设想的基于能量将气体中的单个原子分类放入不同容器的过程。这个新概念是原子或分子的单向墙,允许它们向一个方向运动,但不能向后移动。单向壁的操作依赖于一个不可逆的原子和分子过程,即吸收一个特定波长的光子,然后自发发射到另一个内部状态。不可逆性与磁场和/或光产生的保守力相耦合。Raizen 和他的合作者提出使用单向壁来减少原子团的熵。与此同时,贡萨洛·穆加 Gonzalo Muga 和安德烈亚斯 Andreas Ruschhaupt 独立地提出了一个类似的概念。他们的“原子二极管”不是用来冷却的,而是用来调节原子流。在2008年的一系列实验中,Raizen 团队证明了单向壁对原子的显著冷却作用。随后,丹尼尔·斯特克 Daniel Steck和合作者在2008年晚些时候演示了单向原子墙的操作。他们的实验是基于2005年的单向墙计划,并没有用于冷却。Raizen团队实现的冷却方法被称为“单光子冷却” ,因为平均只需要一个光子就可以使原子接近静止。这与其他激光冷却技术相反,后者使用光子的动量并需要两级循环过渡。<br />
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In 2006, Raizen, Muga, and Ruschhaupt showed in a theoretical paper that as each atom crosses the one-way wall, it scatters one photon, and information is provided about the turning point and hence the energy of that particle. The entropy increase of the radiation field scattered from a directional laser into a random direction is exactly balanced by the entropy reduction of the atoms as they are trapped by the one-way wall.<br />
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2006年,Raizen,Muga,和 Ruschhaupt 在一篇论文中指出,当每个原子穿过单向墙时,它散射一个光子,并提供了关于转折点的信息,因此也就提供了这个粒子的能量。定向激光向随机方向散射的辐射场的熵增与被单向壁俘获的原子的熵减完全平衡。<br />
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This technique is widely described as a "Maxwell's demon" because it realizes Maxwell's process of creating a temperature difference by sorting high and low energy atoms into different containers. However, scientists have pointed out that it is not a true Maxwell's demon in the sense that it does not violate the second law of thermodynamics; it does not result in a net decrease in entropy Only a year later and based on an earlier theoretical proposal, the same group presented the first experimental realization of an autonomous Maxwell's demon, which extracts microscopic information from a system and reduces its entropy by applying feedback. The demon is based on two capacitively coupled single-electron devices, both integrated on the same electronic circuit. The operation of the demon is directly observed as a temperature drop in the system, with a simultaneous temperature rise in the demon arising from the thermodynamic cost of generating the mutual information. In 2016, Pekola et al. demonstrated a proof-of-principle of an autonomous demon in coupled single-electron circuits, showing a way to cool critical elements in a circuit with information as a fuel. Pekola et al. have also proposed that a simple qubit circuit, e.g., made of a superconducting circuit, could provide a basis to study a quantum Szilard's engine.<br />
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这种技术被广泛地描述为“麦克斯韦妖”,因为它通过将高能和低能原子分类到不同的容器中产生温差实现了Maxwell的过程。然而,科学家已经指出,它不是一个真正的麦克斯韦妖,因为它没有违反热力学第二定律; 它不会导致熵减,也不能用来产生有用的能量。这是因为这个过程需要更多的能量从激光束比可能产生的温差。原子从激光束中吸收低熵的光子,并以随机方向发射它们,从而增加了环境的熵。<br />
<font color="#32cd32"> 可能缺失部分原文</font> <br />
2014年,佩科拉 Pekola 等人展示了 Szilárd 引擎实验的实现。仅仅一年之后,同一个研究小组根据早先的理论提议,第一次实验性地实现了自主的麦克斯韦妖,它从一个系统中提取微观信息,并通过反馈减少系统的熵。这个妖是基于集成在同一电路上的两个电容耦合的单电子器件。妖的运行直接表现为系统中的温度下降,同时由于产生互信息的热力学成本而引起的妖中的温度上升。2016年,Pekola 等人证明了单电子耦合电路中存在自主妖的原理,展示了一种以信息为燃料冷却电路中关键元件的方法。Pekola等人还提出,一个简单的量子比特电路,例如由超导电路构成的电路,可以为研究量子Szilárd引擎提供基础。<br />
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== 作为一种隐喻 ==<br />
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Daemons in computing, generally processes that run on servers to respond to users, are named for Maxwell's demon.<br />
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计算中的妖(通常是在服务器上运行以响应用户的进程)以麦克斯韦妖命名。<br />
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Historian Henry Brooks Adams in his manuscript The Rule of Phase Applied to History attempted to use Maxwell's demon as a historical metaphor, though he misunderstood and misapplied the original principle. Adams interpreted history as a process moving towards "equilibrium", but he saw militaristic nations (he felt Germany pre-eminent in this class) as tending to reverse this process, a Maxwell's demon of history. Adams made many attempts to respond to the criticism of his formulation from his scientific colleagues, but the work remained incomplete at Adams' death in 1918. It was only published posthumously.<br />
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亨利·布鲁克斯·亚当斯 Henry Brooks Adams在他的手稿《应用于历史的阶段规则 》中试图用麦克斯韦妖作为历史隐喻,尽管他误解和误用了其原本的含义。Adams将历史解释为一个走向“均衡”的过程,但他认为军国主义国家(他认为德国在这一阶层中处于领先地位)倾向于扭转这一过程,这是历史的麦克斯韦妖。Adams曾多次尝试回应他的科学同事对他的公式的批评,但在1918年Adams去世时,这项工作仍未完成。这本书是死后才出版的。<br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%90%B8%E5%BC%95%E5%AD%90&diff=20376吸引子2020-12-21T09:18:50Z<p>Vicky:</p>
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<div>此词条暂由水流心不竞初译,翻译字数共,未经审校,带来阅读不便,请见谅。<br />
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{{short description|Concept in dynamical systems}}<br />
{{简介|动力系统中的概念}}<br />
{{other uses}}<br />
{{其他用途}}<br />
{{redirect|Strange attractor|other uses|Strange Attractor (disambiguation)}}<br />
{{redirect |奇怪吸引子|其他用途|奇怪吸引子(释疑)}}<br />
{{Use dmy dates|date=May 2013}}<br />
{{使用dmy日期|日期=2013年5月}}<br />
{{more footnotes|date=March 2013}}<br />
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[[File:Attractor Poisson Saturne.jpg|right|333px|thumb|Visual representation of a [[#Strange_attractor|strange attractor]]<ref>The figure shows the attractor of a second order 3-D Sprott-type polynomial, originally computed by Nicholas Desprez using the Chaoscope freeware (cf. http://www.chaoscope.org/gallery.htm and the linked project files for parameters).</ref>.]]<br />
[[File:Attractor Poisson Saturne.jpg|right|333px|thumb|奇异吸引子<ref>The figure shows the attractor of a second order 3-D Sprott-type polynomial, originally computed by Nicholas Desprez using the Chaoscope freeware (cf. http://www.chaoscope.org/gallery.htm and the linked project files for parameters).</ref>的可视化]]<br />
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[[strange attractor.]]<br />
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[[奇异吸引子]]<br />
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In the [[mathematics|mathematical]] field of [[dynamical system]]s, an '''attractor''' is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.<br />
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In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.<br />
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在动力系统的数学领域中,<font color="#ff8000">吸引子 Attractor</font>是系统在各种初始条件下演化趋向于的一组数值。即使稍微受到干扰,与吸引子的值足够接近的系统值仍然保持足够接近吸引子。<br />
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In finite-dimensional systems, the evolving variable may be represented [[algebra]]ically as an ''n''-dimensional [[Coordinate vector|vector]]. The attractor is a region in [[space (mathematics)|''n''-dimensional space]]. In [[Physics|physical systems]], the ''n'' dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in [[Economics|economic systems]], they may be separate variables such as the [[inflation rate]] and the [[unemployment rate]].<br />
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In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.<br />
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在有限维系统中,演化变量可用代数表示为 n 维向量。吸引子是 n 维空间中的一个区域。在物理系统中,n 维可以是,例如,一个或多个物理实体的两个或三个位置坐标; 在经济系统中,它们可以是单独的变量,如通货膨胀率和失业率。<br />
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If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented [[Geometry|geometrically]] in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a [[point (geometry)|point]], a finite set of points, a [[curve]], a [[manifold]], or even a complicated set with a [[fractal]] structure known as a ''strange attractor'' (see [[Attractor#Strange attractor|strange attractor]] below). If the variable is a [[scalar (mathematics)|scalar]], the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of [[chaos theory]].<br />
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If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor (see strange attractor below). If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.<br />
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如果演化变量是二维或三维的,则动态过程的吸引子可以几何地表示为二维或三维(例如右图所示的三维情况)。一个吸引子可以是一个点,一个有限的点集,一条曲线,一个流形,甚至是一个复杂的集合,具有一个分形结构称为奇异吸引子(见下面的奇异吸引子)。如果变量是标量,那么吸引子就是实数线的子集。描述<font color="#ff8000"> 混沌动力学系统Chaotic dynamical systems</font>的吸引子是混沌理论的重要成果之一。<br />
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A [[trajectory]] of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be [[Periodic function|periodic]] or [[Chaos theory|chaotic]]. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a '''repeller''' (or ''repellor'').<br />
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A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a repeller (or repellor).<br />
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动力系统在吸引子中的[[轨迹]]除了保持在吸引子上的时间向前外,不必满足任何特殊的约束条件。轨迹可能是周期性的,也可能是混沌的。如果一组点是周期性的或混沌的,但其附近的流远离该集合,则该集合不是吸引子,而是称为<font color="#ff8000"> 排斥点(或斥点)Repeller (or repellor)</font><br />
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== Motivation of attractors 吸引子的动力机制==<br />
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A [[dynamical system]] is generally described by one or more [[differential equations|differential]] or [[difference equations]]. The equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is often necessary to [[Integral|integrate]] the equations, either through analytical means or through [[iteration]], often with the aid of computers.<br />
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A dynamical system is generally described by one or more differential or difference equations. The equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is often necessary to integrate the equations, either through analytical means or through iteration, often with the aid of computers.<br />
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动力系统通常由一个或多个微分方程或差分方程描述。一个给定动力系统的方程表明了它在任何给定的短时间内的行为。为了确定系统在较长时间内的行为,往往需要通过分析手段或通过<font color="#ff8000"> 迭代Iteration</font>(通常借助于计算机)对方程进行积分。<br />
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Dynamical systems in the physical world tend to arise from [[dissipative system|dissipative systems]]: if it were not for some driving force, the motion would cease. (Dissipation may come from [[friction|internal friction]], [[thermodynamics|thermodynamic losses]], or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the [[phase space]] of the dynamical system corresponding to the typical behavior is the '''attractor''', also known as the attracting section or attractee.<br />
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Dynamical systems in the physical world tend to arise from dissipative systems: if it were not for some driving force, the motion would cease. (Dissipation may come from internal friction, thermodynamic losses, or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the phase space of the dynamical system corresponding to the typical behavior is the attractor, also known as the attracting section or attractee.<br />
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物理世界中的动力系统往往产生于<font color="#ff8000">耗散系统Dissipative system</font>: 如果没有某种驱动力,运动就会停止。(耗散可能来自内部摩擦,热力学损失,或材料损失等许多原因。)耗散和驱动力趋于平衡,消除<font color="#ff8000">初始瞬态Initial transients</font>,使系统进入其典型状态。与典型行为相对应的动力系统相空间的子集是吸引子,也称为吸引部分或吸引子。<br />
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Invariant sets and [[limit set]]s are similar to the attractor concept. An ''invariant set'' is a set that evolves to itself under the dynamics.<ref>{{cite book|author1=Carvalho, A.|author2=Langa, J.A.|author3=Robinson, J.|year=2012|title=Attractors for infinite-dimensional non-autonomous dynamical systems|volume=182|publisher=Springer|p=109}}</ref> Attractors may contain invariant sets. A ''limit set'' is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set (i.e. to each point of the set) as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed slightly off the limit set may get knocked off and never return to the vicinity of the limit set.<br />
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Invariant sets and limit sets are similar to the attractor concept. An invariant set is a set that evolves to itself under the dynamics. Attractors may contain invariant sets. A limit set is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set (i.e. to each point of the set) as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed slightly off the limit set may get knocked off and never return to the vicinity of the limit set.<br />
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不变集和极限集是类似于吸引子的概念。不变集是在动力学作用下向自身演化的集合。<ref>{{cite book|author1=Carvalho, A.|author2=Langa, J.A.|author3=Robinson, J.|year=2012|title=Attractors for infinite-dimensional non-autonomous dynamical systems|volume=182|publisher=Springer|p=109}}</ref> 不变集可能包含于吸引子。极限集是一组点,这些点存在一些初始状态,这些初始状态随着时间的推移到无穷远时最终将任意接近极限集(即收敛到集合的每个点)。吸引子是极限集,但不是所有的极限集都是吸引子: 系统的某些点可能会收敛到极限集,但是稍微偏离极限集的不同点可能会被敲掉,永远不会回到极限集附近。<br />
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For example, the [[damping ratio|damped]] [[pendulum]] has two invariant points: the point {{math|x<sub>0</sub>}} of minimum height and the point {{math|x<sub>1</sub>}} of maximum height. The point {{math|x<sub>0</sub>}} is also a limit set, as trajectories converge to it; the point {{math|x<sub>1</sub>}} is not a limit set. Because of the dissipation due to air resistance, the point {{math|x<sub>0</sub>}} is also an attractor. If there was no dissipation, {{math|x<sub>0</sub>}} would not be an attractor. Aristotle believed that objects moved only as long as they were pushed, which is an early formulation of a dissipative attractor.<br />
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For example, the damped pendulum has two invariant points: the point of minimum height and the point of maximum height. The point is also a limit set, as trajectories converge to it; the point is not a limit set. Because of the dissipation due to air resistance, the point is also an attractor. If there was no dissipation, would not be an attractor. Aristotle believed that objects moved only as long as they were pushed, which is an early formulation of a dissipative attractor.<br />
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例如,<font color="#ff8000">阻尼摆Damping ratio|damped</font>有两个不变点: 最小高度点{{math|x<sub>0</sub>}}和最大高度点{{math|x<sub>1</sub>}}。点{{math|x<sub>0</sub>}}也是一个极限集,因为轨迹向它收敛;点 {{math|x<sub>1</sub>}}不是一个极限集。由于空气阻力的耗散,点{{math|x<sub>0</sub>}}也是吸引子。如果没有耗散,{{math|x<sub>0</sub>}}就不会是吸引子。亚里士多德认为物体只有在被推动时才会移动,这是<font color="#ff8000">耗散吸引子 dissipative attractor</font>的早期表述。<br />
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Some attractors are known to be chaotic (see [[#Strange attractor]]), in which case the evolution of any two distinct points of the attractor result in exponentially [[chaos theory|diverging trajectories]], which complicates prediction when even the smallest noise is present in the system.<ref>{{cite book|author1=Kantz, H.|author2=Schreiber, T.|year=2004|title=Nonlinear time series analysis|publisher=Cambridge university press}}</ref><br />
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Some attractors are known to be chaotic (see #Strange attractor), in which case the evolution of any two distinct points of the attractor result in exponentially diverging trajectories, which complicates prediction when even the smallest noise is present in the system.<br />
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有些吸引子是混沌的(参见#奇异吸引子),在这种情况下,吸引子的任意两个不同点的演化都会导致指数发散轨迹,即使系统中存在最小的噪声,预测也会变得复杂。<ref>{{cite book|author1=Kantz, H.|author2=Schreiber, T.|year=2004|title=Nonlinear time series analysis|publisher=Cambridge university press}}</ref><br />
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== Mathematical definition数学定义 ==<br />
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Let ''t'' represent time and let ''f''(''t'', •) be a function which specifies the dynamics of the system. That is, if ''a'' is a point in an ''n''-dimensional phase space, representing the initial state of the system, then ''f''(0, ''a'') = ''a'' and, for a positive value of ''t'', ''f''(''t'', ''a'') is the result of the evolution of this state after ''t'' units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane '''R'''<sup>2</sup> with coordinates (''x'',''v''), where ''x'' is the position of the particle, ''v'' is its velocity, ''a''&nbsp;=&nbsp;(''x'',''v''), and the evolution is given by<br />
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Let t represent time and let f(t, •) be a function which specifies the dynamics of the system. That is, if a is a point in an n-dimensional phase space, representing the initial state of the system, then f(0, a) = a and, for a positive value of t, f(t, a) is the result of the evolution of this state after t units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane R<sup>2</sup> with coordinates (x,v), where x is the position of the particle, v is its velocity, a&nbsp;=&nbsp;(x,v), and the evolution is given by<br />
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设 t 表示时间,设 f (t,•)是指定系统动力学的函数。也就是说,如果 a 是 n 维相空间中的一个点,表示系统的初始状态,那么 f (0,a) = a,以及对于 t 的正值,f (t,a)是该状态在 t 个时间单位之后演化的结果。例如,如果系统描述了自由粒子在一维空间中的演化,那么相空间是坐标为(x,v)的平面 '''R'''<sup>2</sup> ,,其中 x 是粒子的位置,v 是粒子的速度,a&nbsp;=&nbsp;(x,v),由以下给出<br />
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[[File:Julia immediate basin 1 3.png|right|thumb|Attracting period-3 cycle and its immediate basin of attraction for a certain parametrization of ''f''(''z'')&nbsp;=&nbsp;''z''<sup>2</sup>&nbsp;+&nbsp;''c''. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.]]<br />
[[资料图:茱莉亚立即盆地1 3.png |右|拇指|吸引周期-3旋回及其对“f”(“z”)参数化的直接吸引域。三个最暗的点是3循环的点,它们按顺序相互连接,从吸引域中的任何点迭代会导致(通常是渐进的)收敛到这三个点的序列。]]<br />
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Attracting period-3 cycle and its immediate basin of attraction for a certain parametrization of f(z)&nbsp;=&nbsp;z<sup>2</sup>&nbsp;+&nbsp;c. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.<br />
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f(z)&nbsp;=&nbsp;z<sup>2</sup>&nbsp;+&nbsp;c的某一特定参数的吸引3-周期循环及其直接吸引池。最暗的三个点是3-周期循环的点,它们依次相向,从吸引域中的任何一点迭代都会导致(通常是渐近的)收敛到这三个点的序列。<br />
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: <math> f(t,(x,v))=(x+tv,v).\ </math><br />
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<math> f(t,(x,v))=(x+tv,v).\ </math><br />
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F (t,(x,v)) = (x + tv,v)<br />
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An '''attractor''' is a [[subset]] ''A'' of the [[phase space]] characterized by the following three conditions:<br />
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An attractor is a subset A of the phase space characterized by the following three conditions:<br />
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吸引子是<font color="#ff8000">相空间 phase space </font>的<font color="#ff8000">子集 subset </font>A,具有以下三个条件:<br />
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* ''A'' is ''forward invariant'' under ''f'': if ''a'' is an element of ''A'' then so is ''f''(''t'',''a''), for all&nbsp;''t''&nbsp;>&nbsp;0.<br />
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*“A”是“f”下的“前向不变”:如果“A”是“A”的元素,则对于所有“t”>0,“f”(“t”,“A”)也是。<br />
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* There exists a [[Neighbourhood (mathematics)|neighborhood]] of ''A'', called the '''basin of attraction''' for ''A'' and denoted ''B''(''A''), which consists of all points ''b'' that "enter ''A'' in the limit ''t''&nbsp;→&nbsp;∞". More formally, ''B''(''A'') is the set of all points ''b'' in the phase space with the following property:<br />
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*存在一个“A”的[[邻域(数学)|邻域]],称为“A”的“吸引域”,表示为“B”(“A”),它由所有“B”点组成,这些点“B”在极限''t''&nbsp;→&nbsp;∞"时“进入”A“。更正式地说,“B”(“A”)是相空间中所有点“B”的集合,具有以下特性:<br />
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:: For any open neighborhood ''N'' of ''A'', there is a positive constant ''T'' such that ''f''(''t'',''b'') ∈ ''N'' for all real ''t'' > ''T''.<br />
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For any open neighborhood N of A, there is a positive constant T such that f(t,b) ∈ N for all real t > T.<br />
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●对于“A”的任何开邻域“N”,存在一个正常数“T”,使得对所有实数“T”>“T”,有''f''(''t'',''b'') ∈ ''N'',。<br />
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* There is no proper (non-empty) subset of ''A'' having the first two properties.<br />
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*“A”中不存在具有前两个属性的正确(非空)子集。<br />
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Since the basin of attraction contains an [[open set]] containing ''A'', every point that is sufficiently close to ''A'' is attracted to ''A''. The definition of an attractor uses a [[metric space|metric]] on the phase space, but the resulting notion usually depends only on the topology of the phase space. In the case of '''R'''<sup>''n''</sup>, the Euclidean norm is typically used.<br />
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Since the basin of attraction contains an open set containing A, every point that is sufficiently close to A is attracted to A. The definition of an attractor uses a metric on the phase space, but the resulting notion usually depends only on the topology of the phase space. In the case of R<sup>n</sup>, the Euclidean norm is typically used.<br />
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由于吸引域包含一个含有 a 的开集合,所以每一个足够接近 a 的点都会被 a 吸引。吸引子的定义使用了相空间上的一个度量,但得到的结果通常只依赖于相空间的拓扑结构。在R<sup>n</sup>的情况下,通常使用<font color="#ff8000">欧氏范数Euclidean norm</font>。<br />
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Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive [[measure (mathematics)|measure]] (preventing a point from being an attractor), others relax the requirement that ''B''(''A'') be a neighborhood. <ref>{{cite journal | author=John Milnor | author-link=John Milnor | title= On the concept of attractor | journal=Communications in Mathematical Physics | year=1985 | volume=99 | pages=177–195| doi= 10.1007/BF01212280 | issue=2}}</ref><br />
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Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive measure (preventing a point from being an attractor), others relax the requirement that B(A) be a neighborhood. <br />
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在文献中有吸引子的许多其他定义出现。例如,一些作者要求吸引子具有正测度(防止一个点成为吸引子) ,另一些作者放松了 B(A)是一个邻域的要求。<ref>{{cite journal | author=John Milnor | author-link=John Milnor | title= On the concept of attractor | journal=Communications in Mathematical Physics | year=1985 | volume=99 | pages=177–195| doi= 10.1007/BF01212280 | issue=2}}</ref><br />
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== Types of attractors 吸引子的类型==<br />
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Attractors are portions or [[subset]]s of the [[Configuration space (physics)|phase space]] of a [[dynamical system]]. Until the 1960s, attractors were thought of as being [[Geometric primitive|simple geometric subsets]] of the phase space, like [[Point (geometry)|points]], [[Line (mathematics)|lines]], [[Surface (topology)|surface]]s, and simple regions of [[three-dimensional space]]. More complex attractors that cannot be categorized as simple geometric subsets, such as [[topology|topologically]] wild sets, were known of at the time but were thought to be fragile anomalies. [[Stephen Smale]] was able to show that his [[horseshoe map]] was [[structural stability|robust]] and that its attractor had the structure of a [[Cantor set]].<br />
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Attractors are portions or subsets of the phase space of a dynamical system. Until the 1960s, attractors were thought of as being simple geometric subsets of the phase space, like points, lines, surfaces, and simple regions of three-dimensional space. More complex attractors that cannot be categorized as simple geometric subsets, such as topologically wild sets, were known of at the time but were thought to be fragile anomalies. Stephen Smale was able to show that his horseshoe map was robust and that its attractor had the structure of a Cantor set.<br />
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吸引子是动力系统的相空间的一部分或子集。直到20世纪60年代,吸引子被认为是相空间的简单几何子集,像点、线、面和简单的三维空间。更复杂的吸引子,不能被归类为简单的几何子集,如<font color="#ff8000"> 拓扑野生集Topologically wild sets,</font>,在当时是已知的,但被认为是脆弱的异常。斯蒂芬 · 斯梅尔Stephen Smale能够证明他的马蹄地图是健壮的,它的吸引子具有<font color="#ff8000">康托集Cantor set</font>的结构。<br />
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Two simple attractors are a [[Fixed point (mathematics)|fixed point]] and the [[limit cycle]]. Attractors can take on many other geometric shapes (phase space subsets). But when these sets (or the motions within them) cannot be easily described as simple combinations (e.g. [[intersection (set theory)|intersection]] and [[union (set theory)|union]]) of [[Geometric primitive|fundamental geometric objects]] (e.g. [[Line (mathematics)|lines]], [[Surface (topology)|surface]]s, [[sphere]]s, [[toroid]]s, [[manifold]]s), then the attractor is called a ''[[attractor#Strange attractor|strange attractor]]''.<br />
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Two simple attractors are a fixed point and the limit cycle. Attractors can take on many other geometric shapes (phase space subsets). But when these sets (or the motions within them) cannot be easily described as simple combinations (e.g. intersection and union) of fundamental geometric objects (e.g. lines, surfaces, spheres, toroids, manifolds), then the attractor is called a strange attractor.<br />
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两个简单的吸引子是一个<font color="#ff8000">不动点fixed point </font>和一个<font color="#ff8000">极限环 limit cycle </font>。吸引子可以呈现许多其他几何形状(相空间子集)。但当这些集合(或其中的运动)不能简单地描述为[[几何本原|基本几何对象]](例如,[直线(数学)|直线]],[[曲面(拓扑)|曲面]]s,[[球体]]s,[[环面]]s,[[环面]]s,[[流形]]s的简单组合(例如,[交集(集合论)|交集]]和[[并集理论)|并集]],则这个吸引子被称为“[[奇怪吸引子]]”。<br />
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=== Fixed point驻点 ===<br />
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[[File:Critical orbit 3d.png|right|thumb|Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial]]. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.]]<br />
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[[文件:临界轨道3d.png |右|拇指|根据[[复二次多项式]]演化的复数的弱吸引不动点。相空间是水平复平面;纵轴测量访问复平面中的点的频率。复平面中峰值频率正下方的点是不动点吸引子。]]<br />
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Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.]]<br />
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根据[[复二次多项式演化的复数的弱吸引不动点。相空间是水平复平面;纵轴测量访问复平面中的点的频率。复平面中峰值频率正下方的点是不动点吸引子。]]<br />
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A [[Fixed point (mathematics)|fixed point]] of a function or transformation is a point that is mapped to itself by the function or transformation. If we regard the evolution of a dynamical system as a series of transformations, then there may or may not be a point which remains fixed under each transformation. The final state that a dynamical system evolves towards corresponds to an attracting fixed point of the evolution function for that system, such as the center bottom position of a [[damping ratio|damped]] [[pendulum]], the level and flat water line of sloshing water in a glass, or the bottom center of a bowl contain a rolling marble. But the fixed point(s) of a dynamic system is not necessarily an attractor of the system. For example, if the bowl containing a rolling marble was inverted and the marble was balanced on top of the bowl, the center bottom (now top) of the bowl is a fixed state, but not an attractor. This is equivalent to the difference between [[Stability theory#Stability of fixed points|stable and unstable equilibria]]. In the case of a marble on top of an inverted bowl (a hill), that point at the top of the bowl (hill) is a fixed point (equilibrium), but not an attractor (stable equilibrium).<br />
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A fixed point of a function or transformation is a point that is mapped to itself by the function or transformation. If we regard the evolution of a dynamical system as a series of transformations, then there may or may not be a point which remains fixed under each transformation. The final state that a dynamical system evolves towards corresponds to an attracting fixed point of the evolution function for that system, such as the center bottom position of a damped pendulum, the level and flat water line of sloshing water in a glass, or the bottom center of a bowl contain a rolling marble. But the fixed point(s) of a dynamic system is not necessarily an attractor of the system. For example, if the bowl containing a rolling marble was inverted and the marble was balanced on top of the bowl, the center bottom (now top) of the bowl is a fixed state, but not an attractor. This is equivalent to the difference between stable and unstable equilibria. In the case of a marble on top of an inverted bowl (a hill), that point at the top of the bowl (hill) is a fixed point (equilibrium), but not an attractor (stable equilibrium).<br />
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函数或变换的不动点是通过函数或变换映射到自身的点。如果我们把动力系统的演化看作是一系列的转变,那么在每一个转变下,可能会有一个点是固定的,也可能没有。动力系统的最终状态对应于该系统演化函数的吸引固定点,例如阻尼摆的中心底部位置,玻璃杯中晃动水的水平线和平坦线,或碗的底部中心含有滚动的大理石。但是动态系统的不动点不一定是系统的吸引子。例如,如果装有滚动大理石的碗被倒置,大理石平衡在碗的顶部,碗的中心底部(现在是顶部)是一个固定的状态,但不是一个吸引子。这等价于稳定平衡点和不稳定平衡点之差。如果一个大理石在一个倒碗(山)的顶部,这个点在碗(山)的顶部是一个固定点(平衡) ,但不是一个吸引子(稳定的平衡)。<br />
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In addition, physical dynamic systems with at least one fixed point invariably have multiple fixed points and attractors due to the reality of dynamics in the physical world, including the [[nonlinear dynamics]] of [[stiction]], [[friction]], [[surface roughness]], [[Deformation (engineering)|deformation]] (both [[Elastic deformation|elastic]] and [[plastic]]ity), and even [[quantum mechanics]].<ref name="Contact of Nominally Flat Surfaces">{{cite journal|last=Greenwood|first=J. A.|author2=J. B. P. Williamson|title=Contact of Nominally Flat Surfaces|journal=Proceedings of the Royal Society|date=6 December 1966|volume=295|issue=1442|pages=300–319|doi=10.1098/rspa.1966.0242}}</ref> In the case of a marble on top of an inverted bowl, even if the bowl seems perfectly [[Sphere#Hemisphere|hemispherical]], and the marble's [[sphere|spherical]] shape, are both much more complex surfaces when examined under a microscope, and their [[Contact mechanics#History|shapes change]] or [[deformation (mechanics)|deform]] during contact. Any physical surface can be seen to have a rough terrain of multiple peaks, valleys, saddle points, ridges, ravines, and plains.<ref name="NISTIR 89-4088">{{cite book|last=Vorberger|first=T. V.|title=Surface Finish Metrology Tutorial|year=1990|publisher=U.S. Department of Commerce, National Institute of Standards (NIST)|page=5|url=https://www.nist.gov/calibrations/upload/89-4088.pdf}}</ref> There are many points in this surface terrain (and the dynamic system of a similarly rough marble rolling around on this microscopic terrain) that are considered [[Critical point (mathematics)|stationary]] or fixed points, some of which are categorized as attractors.<br />
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In addition, physical dynamic systems with at least one fixed point invariably have multiple fixed points and attractors due to the reality of dynamics in the physical world, including the nonlinear dynamics of stiction, friction, surface roughness, deformation (both elastic and plasticity), and even quantum mechanics. In the case of a marble on top of an inverted bowl, even if the bowl seems perfectly hemispherical, and the marble's spherical shape, are both much more complex surfaces when examined under a microscope, and their shapes change or deform during contact. Any physical surface can be seen to have a rough terrain of multiple peaks, valleys, saddle points, ridges, ravines, and plains. There are many points in this surface terrain (and the dynamic system of a similarly rough marble rolling around on this microscopic terrain) that are considered stationary or fixed points, some of which are categorized as attractors.<br />
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此外,至少有一个固定点的物理动力系统,由于物理世界动力学的现实性,包括非线性动力学的粘滞,摩擦,表面粗糙度,变形(弹性和塑性) ,甚至量子力学,总是有多个固定点和吸引子。在倒置碗顶的大理石上,即使碗看起来完美的半球形,和大理石的球形,在显微镜下观察时都是更复杂的表面,它们的形状在接触过程中改变或变形。任何物理表面都可以看到一个由多个山峰、山谷、鞍点、山脊、峡谷和平原组成的崎岖地形。在这个表面地形中有许多点(以及在这个微观地形上滚动的同样粗糙的大理石的动力系统)被认为是静止的或不动的点,其中一些被归类为吸引子。<br />
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===Finite number of points有限点数===<br />
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In a [[Discrete time and continuous time|discrete-time]] system, an attractor can take the form of a finite number of points that are visited in sequence. Each of these points is called a [[periodic point]]. This is illustrated by the [[logistic map]], which depending on its specific parameter value can have an attractor consisting of 2<sup>''n''</sup> points, 3×2<sup>''n''</sup> points, etc., for any value of ''n''.<br />
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In a discrete-time system, an attractor can take the form of a finite number of points that are visited in sequence. Each of these points is called a periodic point. This is illustrated by the logistic map, which depending on its specific parameter value can have an attractor consisting of 2<sup>n</sup> points, 3×2<sup>n</sup> points, etc., for any value of n.<br />
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在一个[[离散和连续时间|离散时间]]系统中,吸引子可以以有限数量的点的形式依次访问。每个点都称为[[周期点]]。[[逻辑图]]说明了这一点,根据其特定参数值,对于任何“n”值,可以有由2<sup>''n''</sup>点、3×2<sup>''n''</sup>点等组成的吸引子。<br />
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=== Limit cycle 极限环===<br />
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{{main|Limit cycle}}<br />
{{main |极限环}}<br />
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A [[limit cycle]] is a periodic orbit of a continuous dynamical system that is [[isolated point|isolated]]. Examples include the swings of a [[pendulum clock]], and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).<br />
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A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. Examples include the swings of a pendulum clock, and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).<br />
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[[极限环]]是连续动力系统的周期轨道,它是[[孤立点|孤立]]。例如[[钟摆时钟]]的摆动,以及休息时的心跳。(理想摆的极限环不是极限环吸引子的一个例子,因为它的轨道不是孤立的:在理想摆的相空间中,在一个周期轨道的任何一个点附近都有另一个点属于不同周期轨道,因此前一个轨道不具有吸引力)。<br />
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[[File:VanDerPolPhaseSpace.png|center|250px|thumb|<center>[[Van der Pol oscillator|Van der Pol]] [[phase portrait]]: an attracting limit cycle</center>]]<br />
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[[文件:VanDerPolPhaseSpace.png|center| 250px |拇指|<center>[[Van der Pol振荡器| Van der Pol]][[相位肖像]]:吸引极限环</center>]]<br />
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Van der Pol phase portrait: an attracting limit cycle</center>]]<br />
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范德波尔相图: 一个吸引极限环 </center>]]<br />
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=== Limit torus 极限环===<br />
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There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an [[irrational number|irrational fraction]] (i.e. they are [[commensurability (mathematics)|incommensurate]]), the trajectory is no longer closed, and the limit cycle becomes a limit [[torus]]. This kind of attractor is called an {{math|''N''<sub>''t''</sub>}} -torus if there are {{math|N<sub>t</sub>}} incommensurate frequencies. For example, here is a 2-torus:<br />
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There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an irrational fraction (i.e. they are incommensurate), the trajectory is no longer closed, and the limit cycle becomes a limit torus. This kind of attractor is called an -torus if there are incommensurate frequencies. For example, here is a 2-torus:<br />
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在系统通过极限循环状态的周期轨迹中,可能存在多个频率。例如,在物理学中,一个频率可以决定一颗行星围绕恒星运行的速率,而第二个频率则描述了两个天体之间距离的振荡。如果其中两个频率形成[[无理数|无理分数]](即它们是[[可公度(数学)|不公度]]),则轨迹不再闭合,极限循环变成极限环。如果存在 {{math|N<sub>t</sub>}}非公度频率,这种吸引子被称为{{math|''N''<sub>''t''</sub>}} 环面。例如,这个2环面体:<br />
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[[File:torus.png|300px]]<br />
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A time series corresponding to this attractor is a [[quasiperiodic]] series: A discretely sampled sum of {{math|N<sub>t</sub>}} periodic functions (not necessarily [[sine]] waves) with incommensurate frequencies. Such a time series does not have a strict periodicity, but its [[power spectrum]] still consists only of sharp lines.<br />
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A time series corresponding to this attractor is a quasiperiodic series: A discretely sampled sum of periodic functions (not necessarily sine waves) with incommensurate frequencies. Such a time series does not have a strict periodicity, but its power spectrum still consists only of sharp lines.<br />
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与这个吸引子对应的时间序列是一个准周期序列: 具有非公度频率的周期函数(不一定是正弦波)的离散采样和。这样的时间序列不具有严格的周期性,但其功率谱仍然只包含锐线。<br />
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=== Strange attractor 奇异吸引子===<!-- This section is linked from [[Lorenz attractor]] 本节链接自[[洛伦兹吸引子]]--><br />
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[[File:Lorenz attractor yb.svg|thumb|200px|right|A plot of Lorenz's strange attractor for values&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3]]<br />
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[[文件:洛伦兹吸引子yb.svg公司|thumb | 200px | right | 洛伦兹奇异吸引子的图,&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3]]<br />
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A plot of Lorenz's strange attractor for values&nbsp;ρ&nbsp;=&nbsp;28,&nbsp;σ&nbsp;=&nbsp;10,&nbsp;β&nbsp;=&nbsp;8/3<br />
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关于洛伦兹奇怪吸引子 ρ = 28,σ = 10,β = 8/3的图<br />
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An attractor is called '''strange''' if it has a [[fractal]] structure. This is often the case when the dynamics on it are [[chaos theory|chaotic]], but [[strange nonchaotic attractor]]s also exist. If a strange attractor is chaotic, exhibiting [[sensitive dependence on initial conditions]], then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.<ref>{{cite journal | author = Grebogi Celso, Ott Edward, Yorke James A | year = 1987 | title = Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics | url = | journal = Science | volume = 238 | issue = 4827| pages = 632–638 | doi = 10.1126/science.238.4827.632 | pmid = 17816542 | bibcode = 1987Sci...238..632G }}</ref><br />
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An attractor is called strange if it has a fractal structure. This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist. If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.<br />
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如果吸引子具有[[分形]]结构,则称为“奇异”。当它的动力学是[[混沌理论|混沌]]时,通常会出现这种情况,但是[[奇异的非混沌吸引子]]也存在。如果一个奇异吸引子是混沌的,表现出[[对初始条件的敏感依赖性]],那么在吸引子上两个任意接近的备选初始点,经过任意多次迭代后,都会导致任意相距很远的点(受吸引子的限制),而在其他次数的迭代之后,都会导致任意接近的点。因此,具有混沌吸引子的动态系统是局部不稳定的但全局稳定的:一旦一些序列进入吸引子,附近的点就会彼此发散,但不会离开吸引子。<ref>{{cite journal | author = Grebogi Celso, Ott Edward, Yorke James A | year = 1987 | title = Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics | url = | journal = Science | volume = 238 | issue = 4827| pages = 632–638 | doi = 10.1126/science.238.4827.632 | pmid = 17816542 | bibcode = 1987Sci...238..632G }}</ref><br />
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The term '''strange attractor''' was coined by [[David Ruelle]] and [[Floris Takens]] to describe the attractor resulting from a series of [[bifurcation theory|bifurcations]] of a system describing fluid flow.<ref>{{cite journal |last=Ruelle |first=David |last2=Takens |first2=Floris |date=1971 |title=On the nature of turbulence |url=http://projecteuclid.org/euclid.cmp/1103857186 |journal=Communications in Mathematical Physics |volume=20 |issue=3 |pages=167–192 |doi=10.1007/bf01646553}}</ref> Strange attractors are often [[Differentiable function|differentiable]] in a few directions, but some are [[homeomorphic|like]] a [[Cantor dust]], and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.<ref name="Stochastic climate dynamics: Random attractors and time-dependent invariant measures">{{cite journal|author1=Chekroun M. D. |author2=Simonnet E. |author3=Ghil M. |author-link3=Michael Ghil |name-list-style=amp|<br />
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The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.<br />
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术语“奇异吸引子”是由[[David Ruelle]]和[[Floris Takens]]提出,用来描述一个描述流体流动的系统的一系列[[分岔理论|分叉]]所产生的吸引子。<ref>{{cite journal |last=Ruelle |first=David |last2=Takens |first2=Floris |date=1971 |title=On the nature of turbulence |url=http://projecteuclid.org/euclid.cmp/1103857186 |journal=Communications in Mathematical Physics |volume=20 |issue=3 |pages=167–192 |doi=10.1007/bf01646553}}</ref>奇异吸引子通常在几个方向上[[可微函数|可微]],但有些吸引子是[[同胚|类似]]的一个[[康托尘埃]],因此不可微。在存在噪声的情况下,也可以发现奇异的吸引子,它们可以证明支持Sinai-Ruelle-Bowen型的不变随机概率测度。<ref name="Stochastic climate dynamics: Random attractors and time-dependent invariant measures">{{cite journal|author1=Chekroun M. D. |author2=Simonnet E. |author3=Ghil M. |author-link3=Michael Ghil |name-list-style=amp|<br />
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year = 2011 |<br />
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title = Stochastic climate dynamics: Random attractors and time-dependent invariant measures |<br />
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Examples of strange attractors include the double-scroll attractor, Hénon attractor, Rössler attractor, and Lorenz attractor.<br />
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奇异吸引子的例子包括<font color="#ff8000">双涡卷吸引子double-scroll attractor</font>、<font color="#ff8000">埃农吸引子Hénon attractor</font>、<font color="#ff8000">若斯叻吸引子Rössler attractor</font>和<font color="#ff8000">洛伦兹吸引子Lorenz attractor</font>。<br />
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journal = Physica D |<br />
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volume = 240 |<br />
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issue = 21 |<br />
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pages = 1685–1700 |<br />
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Bifurcation diagram of the [[logistic map. The attractor(s) for any value of the parameter r are shown on the ordinate in the domain <math>0<x<1</math>. The colour of a point indicates how often the point <math>(r, x)</math> is visited over the course of 10<sup>6</sup> iterations: frequently encountered values are coloured in blue, less frequently encountered values are yellow. A bifurcation appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).]]<br />
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[[逻辑映射的分岔图。参数r的任何值的吸引子显示在区间<math>0<x<1</math>的纵坐标上。点的颜色表示在10<sup>6</sup>次迭代过程中访问点<math>(r, x)</math>的频率:经常遇到的值用蓝色表示,不太常见的值用黄色表示。在<math>r\approx3.0</math>附近出现分叉,在<math>r\approx3.5</math>附近出现第二个分叉(导致四个吸引子值)。当<math>r>3.6</math>时,行为变得越来越复杂,中间穿插着行为更简单的区域(白色条纹)。]]<br />
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doi = 10.1016/j.physd.2011.06.005|citeseerx=10.1.1.156.5891 }}</ref><br />
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The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map, <math>x_{n+1}=rx_n(1-x_n)</math>, whose basins of attraction for various values of the parameter r are shown in the figure. If <math>r=2.6</math>, all starting x values of <math>x<0</math> will rapidly lead to function values that go to negative infinity; starting x values of <math>x>0</math> will go to infinity. But for <math>0<x<1</math> the x values rapidly converge to <math>x\approx0.615</math>, i.e. at this value of r, a single value of x is an attractor for the function's behaviour. For other values of r, more than one value of x may be visited: if r is 3.2, starting values of <math>0<x<1</math> will lead to function values that alternate between <math>x\approx0.513</math> and <math>x\approx0.799</math>. At some values of r, the attractor is a single point (a "fixed point"), at other values of r two values of x are visited in turn (a period-doubling bifurcation); at yet other values of r, any given number of values of x are visited in turn; finally, for some values of r, an infinitude of points are visited. Thus one and the same dynamic equation can have various types of attractors, depending on its starting parameters.<br />
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动力学方程的参数随着方程的迭代而变化,具体值可能取决于初始参数。一个例子是研究得很好的logistic地图,<math>x{n+1}=rx}n(1-xun)</math>,图中显示了参数r的各种值的吸引域。如果<math>r=2.6</math>,则<math>x<0</math>的所有起始x值将迅速导致函数值变为负无穷大;<math>x>0</math>的起始x值将变为无穷大。但是对于<math>0<x<1</math>,x值迅速收敛到<math>x\approx0.615</math>,也就是说,在这个r值下,x的单个值是函数行为的吸引子。对于r的其他值,可以访问x的多个值:如果r为3.2,<math>0<x<1</math>的起始值将导致函数值在<math>x\approx0.513</math>和<math>x\approx0.799</math>之间交替。在r的某些值处,吸引子是一个单点(“不动点”),在r的其他值处,依次访问x的两个值(倍周期分岔);在r的其他值处,依次访问任意数量的x值;最后,对于r的某些值,访问无穷多个点。因此,同一个动力学方程可以有不同类型的吸引子,这取决于它的起始参数。<br />
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Examples of strange attractors include the [[Double scroll attractor|double-scroll attractor]], [[Hénon map|Hénon attractor]], [[Rössler attractor]], and [[Lorenz attractor]].<br />
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奇异吸引子的例子包括[[双涡旋吸引子|双涡旋吸引子]]、[[Hénon-map | Hénon吸引子]]、[[Rössler吸引子]]和[[Lorenz吸引子]]。<br />
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==Attractors characterize the evolution of a system吸引子表征系统的演化==<br />
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An attractor's basin of attraction is the region of the phase space, over which iterations are defined, such that any point (any initial condition) in that region will asymptotically be iterated into the attractor. For a stable linear system, every point in the phase space is in the basin of attraction. However, in nonlinear systems, some points may map directly or asymptotically to infinity, while other points may lie in a different basin of attraction and map asymptotically into a different attractor; other initial conditions may be in or map directly into a non-attracting point or cycle.<br />
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吸引子的吸引域是相空间的区域,在这个区域上定义了迭代,使得该区域中的任何点(任何初始条件)都将渐近地迭代到吸引子中。对于一个稳定的线性系统,相空间中的每一点都在吸引域中。然而,在非线性系统中,有些点可能直接或渐近地映射到无穷大,而另一些点可能位于不同的吸引域中并渐近映射到不同的吸引子;其他初始条件可能位于或直接映射到非吸引点或循环中。<br />
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[[File:Logistic Map Bifurcation Diagram, Matplotlib.svg|350px|thumb|right|Bifurcation diagram of the [[logistic map]]. The attractor(s) for any value of the parameter ''r'' are shown on the ordinate in the domain <math>0<x<1</math>. The colour of a point indicates how often the point <math>(r, x)</math> is visited over the course of 10<sup>6</sup> iterations: frequently encountered values are coloured in blue, less frequently encountered values are yellow. A [[period-doubling bifurcation|bifurcation]] appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).]]<br />
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[[文件:逻辑图分岔图,Matplotlib.svg|350px |拇指|右|分岔图[[逻辑图]]。参数“r”的任何值的吸引子显示在域<math>0<x<1</math>的纵坐标上。点的颜色表示在10次<sup>6次迭代过程中访问点<math>(r,x)</math>的频率:经常遇到的值用蓝色表示,不太常见的值用黄色表示。在<math>r\approx3.0</math>附近出现[[倍周期分岔|分岔]],在<math>r\approx3.5</math>附近出现第二个分岔(导致四个吸引子值)。当<math>r>3.6<math>时,行为变得越来越复杂,中间穿插着行为更简单的区域(白色条纹)。]]<br />
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The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied [[logistic map]], <math>x_{n+1}=rx_n(1-x_n)</math>, whose basins of attraction for various values of the parameter ''r'' are shown in the figure. If <math>r=2.6</math>, all starting ''x'' values of <math>x<0</math> will rapidly lead to function values that go to negative infinity; starting ''x'' values of <math>x>0</math> will go to infinity. But for <math>0<x<1</math> the ''x'' values rapidly converge to <math>x\approx0.615</math>, i.e. at this value of ''r'', a single value of ''x'' is an attractor for the function's behaviour. For other values of ''r'', more than one value of x may be visited: if ''r'' is 3.2, starting values of <math>0<x<1</math> will lead to function values that alternate between <math>x\approx0.513</math> and <math>x\approx0.799</math>. At some values of ''r'', the attractor is a single point (a [[#Fixed_point|"fixed point"]]), at other values of ''r'' two values of ''x'' are visited in turn (a [[period-doubling bifurcation]]); at yet other values of r, any given number of values of ''x'' are visited in turn; finally, for some values of ''r'', an infinitude of points are visited. Thus one and the same dynamic equation can have various types of attractors, depending on its starting parameters.<br />
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动力学方程的参数随着方程的迭代而变化,具体值可能取决于初始参数。一个例子是经过充分研究的[[logistic map]],<math>x{n+1}=rx\u n(1-xün)</math>,其对参数“r”的各种值的吸引范围如图所示。如果<math>r=2.6</math>,所有开始的<math>x<0</math>的“x”值将迅速导致函数值变为负无穷大;<math>x>0开始的“x”值将变为无穷大。但对于<math>0<x<1</math>“x”值迅速收敛到<math>x\approx0.615</math>,即在“r”值处,单个值“x”是函数行为的吸引子。对于“r”的其他值,可以访问x的多个值:如果“r”为3.2,<math>0<x<1</math>的起始值将导致函数值在<math>x\approx0.513</math>和<math>x\approx0.799</math>之间交替。在“r”的某些值处,吸引子是一个单点(a[[#不动点|“不动点”]]),在“r”的其他值处,依次访问“x”的两个值(a[[倍周期分岔]]);在r的其他值处,依次访问任意给定数量的“x”值;最后,对于“r”的某些值,访问无穷多个点。因此,同一个动力学方程可以有不同类型的吸引子,这取决于它的起始参数。<br />
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A single-variable (univariate) linear difference equation of the homogeneous form <math>x_t=ax_{t-1}</math> diverges to infinity if |a| > 1 from all initial points except 0; there is no attractor and therefore no basin of attraction. But if |a| < 1 all points on the number line map asymptotically (or directly in the case of 0) to 0; 0 is the attractor, and the entire number line is the basin of attraction.<br />
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齐次形式的单变量(单变量)线性差分方程<math>x_t=ax{t-1}</math>从除0以外的所有初始点| A>1发散到无穷大;没有吸引子,因此没有吸引池。但是如果| a |<1,则数线图上的所有点渐进地(或在0的情况下直接)到0;0是吸引子,整个数线是吸引域。<br />
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==Basins of attraction吸引池==<br />
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Likewise, a linear matrix difference equation in a dynamic vector X, of the homogeneous form <math>X_t=AX_{t-1}</math> in terms of square matrix A will have all elements of the dynamic vector diverge to infinity if the largest eigenvalue of A is greater than 1 in absolute value; there is no attractor and no basin of attraction. But if the largest eigenvalue is less than 1 in magnitude, all initial vectors will asymptotically converge to the zero vector, which is the attractor; the entire n-dimensional space of potential initial vectors is the basin of attraction.<br />
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同样地,动态向量X中的线性矩阵差分方程,如果a的最大特征值绝对值大于1,则动态向量X中的所有元素<math>X_t=AX_{t-1}</math> 都将发散到无穷大;不存在吸引子和吸引池。但如果最大特征值小于1,则所有初始向量将渐近收敛于零向量,即零为吸引子;潜在初始向量的整个n维空间就是<font color="#ff8000">吸引池 basin of attraction </font>。<br />
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An attractor's '''basin of attraction''' is the region of the [[phase space]], over which iterations are defined, such that any point (any [[initial condition]]) in that region will [[asymptotic behavior|asymptotically]] be iterated into the attractor. For a [[stability (mathematics)|stable]] [[linear system]], every point in the phase space is in the basin of attraction. However, in [[nonlinear system]]s, some points may map directly or asymptotically to infinity, while other points may lie in a different basin of attraction and map asymptotically into a different attractor; other initial conditions may be in or map directly into a non-attracting point or cycle.<ref>{{cite journal|last1=Strelioff|first1=C.|last2=Hübler|first2=A.|title=Medium-Term Prediction of Chaos|journal=Phys. Rev. Lett.|date=2006|volume=96|issue=4|doi=10.1103/PhysRevLett.96.044101|pmid=16486826|page=044101}}</ref><br />
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吸引子的“吸引池”是[[相空间]]的区域,在该区域上定义迭代,因此该区域中的任何点(任何[[初始条件]])将[[渐近行为|渐进]]迭代到吸引子中。对于一个[[稳定性(数学)|稳定]][[线性系统]],相空间中的每一点都在吸引池中。然而,在[[非线性系统]]s中,有些点可能直接或渐近地映射到无穷大,而另一些点可能位于不同的吸引池中并渐进地映射到不同的吸引子;其他初始条件可能位于或直接映射到一个非吸引点或循环中。<ref>{{cite journal|last1=Strelioff|first1=C.|last2=Hübler|first2=A.|title=Medium-Term Prediction of Chaos|journal=Phys. Rev. Lett.|date=2006|volume=96|issue=4|doi=10.1103/PhysRevLett.96.044101|pmid=16486826|page=044101}}</ref><br />
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Similar features apply to linear differential equations. The scalar equation <math> dx/dt =ax</math> causes all initial values of x except zero to diverge to infinity if a > 0 but to converge to an attractor at the value 0 if a < 0, making the entire number line the basin of attraction for 0. And the matrix system <math>dX/dt=AX</math> gives divergence from all initial points except the vector of zeroes if any eigenvalue of the matrix A is positive; but if all the eigenvalues are negative the vector of zeroes is an attractor whose basin of attraction is the entire phase space.<br />
<br />
类似的特征也适用于线性微分方程。标量方程<math> dx/dt =ax</math> 导致除0以外的所有 x 的初始值在 a > 0时发散到无穷大,但在 a < 0时收敛到吸引子,使整条数线成为0的吸引池。矩阵系统 <math>dX/dt=AX</math>如果矩阵 A 的任何特征值是正的,则该矩阵系统从除零向量以外的所有初始点发散; 但如果所有特征值都是负的,则零向量是吸引池为整个相空间的吸引子。<br />
<br />
===Linear equation or system线性方程或系统===<br />
<br />
<br />
<br />
A single-variable (univariate) linear [[difference equation]] of the [[homogeneous equation|homogeneous form]] <math>x_t=ax_{t-1}</math> diverges to infinity if |''a''| > 1 from all initial points except 0; there is no attractor and therefore no basin of attraction. But if |''a''| < 1 all points on the number line map asymptotically (or directly in the case of 0) to 0; 0 is the attractor, and the entire number line is the basin of attraction.<br />
<br />
[[齐次方程|齐次形式]]<math>x|t=ax{t-1}</math>的单变量(单变量)线性[[差分方程]]发散到无穷大,如果除了0以外的所有初始点|“A”>>1;没有吸引子,因此没有吸引池。但如果 |''a''| < 1,则数线图上的所有点渐进地(或在0的情况下直接映射)到0;0是吸引子,整个数线是吸引池。<br />
<br />
Equations or systems that are nonlinear can give rise to a richer variety of behavior than can linear systems. One example is Newton's method of iterating to a root of a nonlinear expression. If the expression has more than one real root, some starting points for the iterative algorithm will lead to one of the roots asymptotically, and other starting points will lead to another. The basins of attraction for the expression's roots are generally not simple&mdash;it is not simply that the points nearest one root all map there, giving a basin of attraction consisting of nearby points. The basins of attraction can be infinite in number and arbitrarily small. For example, for the function <math>f(x)=x^3-2x^2-11x+12</math>, the following initial conditions are in successive basins of attraction:<br />
<br />
与线性系统相比,非线性方程或系统可以产生更多种类的行为。一个例子是非线性表达式根的牛顿迭代法。如果表达式有多个实根,则迭代算法的某些起始点会渐近地得出其中一个根,而其他起始点会得出另一个根。表达式根的吸引池通常并不简单,最接近一个根的点都映射到那里,从而形成由附近点组成的吸引区。吸引的区域在数值上可以是无限的,可以任意小。例如,对于函数<math>f(x)=x^3-2x^2-11x+12</math>,以下初始条件在连续的吸引池中:<br />
<br />
Likewise, a linear [[matrix difference equation]] in a dynamic [[coordinate vector|vector]] ''X'', of the homogeneous form <math>X_t=AX_{t-1}</math> in terms of [[square matrix]] ''A'' will have all elements of the dynamic vector diverge to infinity if the largest [[eigenvalue]] of ''A'' is greater than 1 in absolute value; there is no attractor and no basin of attraction. But if the largest eigenvalue is less than 1 in magnitude, all initial vectors will asymptotically converge to the zero vector, which is the attractor; the entire ''n''-dimensional space of potential initial vectors is the basin of attraction.<br />
<br />
同样地,在动态[[坐标向量|向量]''X''中的线性[[矩阵差分方程]]在[[平方矩阵]]''a'中的齐次形式<math>X|t=AX{t-1}</math>中,如果“a”的最大[[特征值]]在绝对值上大于1,则动态向量的所有元素将发散到无穷大;没有吸引子,也没有吸引池。但如果最大特征值小于1,则所有初始向量将渐近收敛于零向量,即零为吸引子;潜在初始向量的整个n维空间就是吸引池。<br />
<br />
Basins of attraction in the complex plane for using Newton's method to solve x<sup>5</sup>&nbsp;−&nbsp;1&nbsp;=&nbsp;0. Points in like-colored regions map to the same root; darker means more iterations are needed to converge.<br />
<br />
用牛顿法求解 x<sup>5</sup>&nbsp;−&nbsp;1&nbsp;=&nbsp;0。相似颜色区域中的点映射到同一个根; 颜色较深意味着需要更多的迭代来收敛。<br />
<br />
Similar features apply to linear [[differential equation]]s. The scalar equation <math> dx/dt =ax</math> causes all initial values of ''x'' except zero to diverge to infinity if ''a'' > 0 but to converge to an attractor at the value 0 if ''a'' < 0, making the entire number line the basin of attraction for 0. And the matrix system <math>dX/dt=AX</math> gives divergence from all initial points except the vector of zeroes if any eigenvalue of the matrix ''A'' is positive; but if all the eigenvalues are negative the vector of zeroes is an attractor whose basin of attraction is the entire phase space.<br />
<br />
类似的特征也适用于线性[[微分方程]]s。标量方程<math>dx/dt=ax</math>会导致“x”的所有初始值(除了0)发散到无穷大,如果“a”<0,则收敛到值为0的吸引子,使整条数线成为0的吸引域。如果矩阵“A”的任何特征值为正,则矩阵系统的dX/dt=AX除了零向量外,会从所有初始点发散;但如果所有特征值都为负,则零点向量是一个吸引子,其吸引域是整个相空间。<br />
<br />
2.35287527 converges to 4;<br />
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2.35287527汇聚到4;<br />
<br />
===Nonlinear equation or system非线性方程或系统===<br />
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2.35284172 converges to −3;<br />
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2.35284172 收敛到 −3;<br />
<br />
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2.35283735 converges to 4;<br />
<br />
2.35283735收敛到4;<br />
<br />
Equations or systems that are [[nonlinear system|nonlinear]] can give rise to a richer variety of behavior than can linear systems. One example is [[Newton's method]] of iterating to a root of a nonlinear expression. If the expression has more than one [[real number|real]] root, some starting points for the iterative algorithm will lead to one of the roots asymptotically, and other starting points will lead to another. The basins of attraction for the expression's roots are generally not simple&mdash;it is not simply that the points nearest one root all map there, giving a basin of attraction consisting of nearby points. The basins of attraction can be infinite in number and arbitrarily small. For example,<ref>Dence, Thomas, "Cubics, chaos and Newton's method", ''[[Mathematical Gazette]]'' 81, November 1997, 403–408.</ref> for the function <math>f(x)=x^3-2x^2-11x+12</math>, the following initial conditions are in successive basins of attraction:<br />
<br />
与线性系统相比,[[非线性系统|非线性]]的方程或系统可以产生更丰富的行为。一个例子是迭代到非线性表达式根的[[牛顿方法]]。如果表达式有多个[[实数|实]]根,则迭代算法的某些起始点将渐近地导致其中一个根,而其他起点将导致另一个根。表达式根的吸引域通常并不简单,最接近一个根的点都映射到那里,从而形成由附近点组成的吸引区。吸引的盆地可以是无限的,可以任意小。例如,<ref>dance,Thomas,“Cubics,chaos and Newton's method”,“[[mathematic Gazette]]”811997年11月,403–408。</ref>对于函数<math>f(x)=x^3-2x^2-11x+12</math>,以下初始条件在连续的吸引域中:<br />
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2.352836327 converges to −3;<br />
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2.352836327 converges to −3;<br />
<br />
<br />
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2.352836323 converges to 1.<br />
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2.352836323汇聚为1。<br />
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[[File:newtroot 1 0 0 0 0 m1.png|thumb|Basins of attraction in the complex plane for using Newton's method to solve ''x''<sup>5</sup>&nbsp;−&nbsp;1&nbsp;=&nbsp;0. Points in like-colored regions map to the same root; darker means more iterations are needed to converge.]]<br />
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[[文件:newtroot 10 0 0 0 m1.png |拇指|复杂平面中的吸引盆地,用于使用牛顿法求解“x”<sup>5</sup>—1&nbsp;=0。相同颜色区域中的点映射到同一根;较暗表示需要更多迭代才能收敛。]]<br />
<br />
Newton's method can also be applied to complex functions to find their roots. Each root has a basin of attraction in the complex plane; these basins can be mapped as in the image shown. As can be seen, the combined basin of attraction for a particular root can have many disconnected regions. For many complex functions, the boundaries of the basins of attraction are fractals.<br />
<br />
牛顿法也可以应用于求复变函数的根。在复杂的平面上,每个根部都有一个吸引池; 这些区域可以如图所示绘制出来。可以看出,组合区域的吸引力为一个特定的根可以有许多不相连的地区。对于许多复杂的函数,吸引池的边界是分形。<br />
<br />
:2.35287527 converges to 4;<br />
<br />
:2.35284172 converges to −3;<br />
<br />
:2.35283735 converges to 4;<br />
<br />
Parabolic partial differential equations may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The Ginzburg–Landau, the Kuramoto–Sivashinsky, and the two-dimensional, forced Navier–Stokes equations are all known to have global attractors of finite dimension.<br />
<br />
抛物型偏微分方程可能具有有限维吸引子。方程的扩散部分阻尼更高的频率,在某些情况下导致一个全局吸引子。<font color="#ff8000">金兹堡-朗道方程 Ginzburg-Landau equations </font>、 <font color="#ff8000">K-S方程 Kuramoto-Sivashinsky equations </font>和二维<font color="#ff8000">强迫纳维-斯托克斯方程forced Navier–Stokes equation</font>都具有有限维的全局吸引子。<br />
<br />
:2.352836327 converges to −3;<br />
<br />
:2.352836323 converges to 1.<br />
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For the three-dimensional, incompressible Navier–Stokes equation with periodic boundary conditions, if it has a global attractor, then this attractor will be of finite dimensions.<br />
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对于具有周期边界条件的三维不可压 Navier-Stokes 方程,如果它有一个全局吸引子,那么这个吸引子将是有限维的。<br />
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Newton's method can also be applied to [[complex analysis|complex functions]] to find their roots. Each root has a basin of attraction in the [[complex plane]]; these basins can be mapped as in the image shown. As can be seen, the combined basin of attraction for a particular root can have many disconnected regions. For many complex functions, the boundaries of the basins of attraction are [[fractal]]s.<br />
<br />
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< ! -- 一旦隐藏吸引子中的 < nowiki > </nowiki > 得到解决,应该取消评论。更多信息请参见演讲页面。<br />
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== Partial differential equations偏微分方程 ==<br />
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[[File:Chua-chaotic-hidden-attractor.jpg|thumb|<br />
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[文件: Chua-chaotic-hidden-attractor. jpg | thumb | <br />
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[[Parabolic partial differential equation]]s may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The ''Ginzburg–Landau'', the ''Kuramoto–Sivashinsky'', and the two-dimensional, forced [[Navier–Stokes equation]]s are all known to have global attractors of finite dimension.<br />
<br />
[[抛物型偏微分方程]]可能具有有限维吸引子。方程的扩散部分会阻尼更高的频率,在某些情况下会导致全局吸引子。<font color="#ff8000"> “金茨堡-兰道”、“库拉莫托-西瓦辛斯基”和二维受迫[[纳维-斯托克斯方程]]</font>都具有有限维的全局吸引子。<br />
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Chaotic hidden attractor (green domain) in Chua's system.<br />
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蔡氏系统中的混沌隐藏吸引子(绿域)。<br />
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Trajectories with initial data in a neighborhood of two saddle points (blue) tend (red arrow) to infinity or tend (black arrow) to stable zero equilibrium point (orange).<br />
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带有初始数据的一个邻近鞍点(蓝色)的轨迹趋向(红色箭头)至无穷大或趋向(黑色箭头)至稳定的零平衡点(橙色)。<br />
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For the three-dimensional, incompressible Navier–Stokes equation with periodic [[boundary condition]]s, if it has a global attractor, then this attractor will be of finite dimensions.<ref>[[Geneviève Raugel]], Global Attractors in Partial Differential Equations, ''Handbook of Dynamical Systems'', Elsevier, 2002, pp. 885–982.</ref><br />
对于具有周期[[边界条件]]s的三维不可压缩Navier–Stokes方程,如果它有一个全局吸引子,那么这个吸引子将是有限维的。<ref>[[Geneviève Raugel]], Global Attractors in Partial Differential Equations, ''Handbook of Dynamical Systems'', Elsevier, 2002, pp. 885–982.</ref><br />
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]]<br />
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<!-- This should be uncommented once the <nowiki>{{Notability}}</nowiki> in [[hidden attractor]] is solved. See the talk page for more information.<br />
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From a computational point of view, attractors can be naturally regarded as self-excited attractors or<br />
<br />
从计算的角度来看,吸引子可以自然地被看作自激吸引子或<br />
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== Numerical localization (visualization) of attractors: self-excited and hidden attractors 吸引子的数值局部化(可视化):自激吸引子和隐吸引子==<br />
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hidden attractors. Self-excited attractors can be localized numerically by standard computational procedures, in which after a transient sequence, a trajectory starting from a point on an unstable manifold in a small neighborhood of an unstable equilibrium reaches an attractor, such as the classical attractors in the Van der Pol, Belousov–Zhabotinsky, Lorenz, and many other dynamical systems. In contrast, the basin of attraction of a hidden attractor does not contain neighborhoods of equilibria, so the hidden attractor cannot be localized by standard computational procedures.<br />
<br />
隐藏吸引子。<font color="#ff8000">自激吸引子 Self-excited attractors</font>可以用标准的计算程序进行数值局部化,在一个瞬态序列之后,从不稳定平衡点的小邻域的不稳定流形上的一个点出发的轨迹将到达一个吸引子,如 Van der Pol、 Belousov-Zhabotinsky、 Lorenz 等许多其他动力系统中的经典吸引子。相反,一个隐藏吸引子的吸引池不包含平衡邻域,因此隐藏吸引子不能被标准的计算程序局部化。<br />
<br />
[[File:Chua-chaotic-hidden-attractor.jpg|thumb|<br />
<br />
--><br />
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--><br />
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Chaotic [[hidden attractor]] (green domain) in [[Chua's circuit|Chua's system]].<br />
[[蔡氏电路|蔡氏系统]]中的混沌[[隐藏吸引子]](绿域)。<br />
<br />
Trajectories with initial data in a neighborhood of two saddle points (blue) tend (red arrow) to infinity or tend (black arrow) to stable zero equilibrium point (orange).<br />
<br />
初始数据位于两个鞍点附近(蓝色)的轨迹趋向于无穷大(红色箭头)或趋向于(黑色箭头)稳定的零平衡点(橙色)。<br />
<br />
]]<br />
<br />
<br />
<br />
From a computational point of view, attractors can be naturally regarded as ''self-excited attractors'' or<br />
<br />
''[[hidden attractor]]s''.<ref name="2011-PLA-Hidden-Chua-attractor">{{cite journal |author1=Leonov G.A. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |<br />
<br />
从计算的角度来看,吸引子可以自然地看作是“自激吸引子”或''[[隐藏吸引子]]s''<ref name="2011-PLA-Hidden-Chua-attractor">{{cite journal |author1=Leonov G.A. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |<br />
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year = 2011 |<br />
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title = Localization of hidden Chua's attractors |<br />
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journal = Physics Letters A |<br />
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volume = 375 |<br />
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issue = 23 |<br />
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pages = 2230–2233 |<br />
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url = http://www.math.spbu.ru/user/nk/PDF/2011-PhysLetA-Hidden-Attractor-Chua.pdf |<br />
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doi = 10.1016/j.physleta.2011.04.037}}<br />
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</ref><ref>{{cite journal<br />
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|author1=Bragin V.O. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |author4=Leonov G.A. | year = 2011<br />
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| title = Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits<br />
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| journal = Journal of Computer and Systems Sciences International<br />
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| volume = 50<br />
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| number = 5<br />
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| pages = 511–543<br />
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| last = Ruelle<br />
<br />
| last = Ruelle<br />
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| url = http://www.math.spbu.ru/user/nk/PDF/2011-TiSU-Hidden-oscillations-attractors-Aizerman-Kalman-conjectures.pdf<br />
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| first = David<br />
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第一名: David<br />
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| doi = 10.1134/S106423071104006X}}<br />
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| authorlink = David Ruelle<br />
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| authorlink = David Ruelle<br />
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</ref><ref name="2012-Physica-D-Hidden-attractor-Chua-circuit-smooth">{{cite journal |author1=Leonov G.A. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |<br />
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| title = What is...a Strange Attractor?<br />
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| title = 什么是... 奇异吸引子?<br />
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year = 2012 |<br />
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| journal = Notices of the American Mathematical Society<br />
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| journal = 美国数学学会公告<br />
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title = Hidden attractor in smooth Chua systems |<br />
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|date=August 2006<br />
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| date = August 2006<br />
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journal = Physica D |<br />
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| volume = 53<br />
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53<br />
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volume = 241 |<br />
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| issue = 7<br />
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第7期<br />
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issue = 18 |<br />
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| pages = 764–765<br />
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| 页 = 764-765<br />
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pages = 1482–1486 |<br />
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| url = http://www.ams.org/notices/200607/what-is-ruelle.pdf<br />
<br />
Http://www.ams.org/notices/200607/what-is-ruelle.pdf<br />
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url = http://www.math.spbu.ru/user/nk/PDF/2012-Physica-D-Hidden-attractor-Chua-circuit-smooth.pdf |<br />
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| accessdate = 16 January 2008 }}<br />
<br />
16 January 2008}}<br />
<br />
doi = 10.1016/j.physd.2012.05.016}}<br />
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</ref><ref name="2013-IJBC-Hidden-attractors">{{cite journal |author1=Leonov G.A. |author2=Kuznetsov N.V. |<br />
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year = 2013 |<br />
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title = Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits |<br />
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journal = International Journal of Bifurcation and Chaos |<br />
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volume = 23 |<br />
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issue = 1 |<br />
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pages = art. no. 1330002|<br />
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doi = 10.1142/S0218127413300024|<br />
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doi-access = free }}<br />
<br />
</ref> Self-excited attractors can be localized numerically by standard computational procedures, in which after a transient sequence, a trajectory starting from a point on an unstable manifold in a small neighborhood of an unstable equilibrium reaches an attractor, such as the classical attractors in the [[Van der Pol oscillator|Van der Pol]], [[Belousov–Zhabotinsky reaction|Belousov–Zhabotinsky]], [[Lorenz attractor|Lorenz]], and many other dynamical systems. In contrast, the basin of attraction of a [[hidden attractor]] does not contain neighborhoods of equilibria, so the [[hidden attractor]] cannot be localized by standard computational procedures.<br />
<br />
自激吸引子可以用标准的计算程序进行数值定域,在一个瞬态序列之后,从不稳定平衡小邻域中不稳定流形上的点开始的轨迹到达吸引子,例如[[Van der Pol振荡器| Van der Pol]]中的经典吸引子,[[Belousov–Zhabotinsky reaction | Belousov–Zhabotinsky]],[[Lorenz吸引子| Lorenz]],以及许多其他动力系统。相比之下,[[隐藏吸引子]]的吸引域不包含平衡邻域,因此[[隐藏吸引子]]不能用标准的计算程序进行局部化。<br />
--><br />
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== See also 请参阅==<br />
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{{commons|Attractor}}<br />
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* [[Cycle detection]]<br />
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* [[Hyperbolic set]]<br />
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* [[Stable manifold]]<br />
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* [[Steady state]]<br />
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{{常见 |吸引子}}<br />
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*[[循环检测]]<br />
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*[双曲线集][]<br />
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*[[稳定流形]]<br />
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*[[稳态]]<br />
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Category:Limit sets<br />
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类别: 极限集<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Attractor]]. Its edit history can be viewed at [[吸引子/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E5%90%B8%E5%BC%95%E5%AD%90&diff=20371吸引子2020-12-21T08:41:05Z<p>Vicky:</p>
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<div>此词条暂由水流心不竞初译,翻译字数共,未经审校,带来阅读不便,请见谅。<br />
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{{short description|Concept in dynamical systems}}<br />
{{简介|动力系统中的概念}}<br />
{{other uses}}<br />
{{其他用途}}<br />
{{redirect|Strange attractor|other uses|Strange Attractor (disambiguation)}}<br />
{{redirect |奇怪吸引子|其他用途|奇怪吸引子(释疑)}}<br />
{{Use dmy dates|date=May 2013}}<br />
{{使用dmy日期|日期=2013年5月}}<br />
{{more footnotes|date=March 2013}}<br />
{{更多脚注{日期=2013年3月}}<br />
[[File:Attractor Poisson Saturne.jpg|right|333px|thumb|Visual representation of a [[#Strange_attractor|strange attractor]]<ref>The figure shows the attractor of a second order 3-D Sprott-type polynomial, originally computed by Nicholas Desprez using the Chaoscope freeware (cf. http://www.chaoscope.org/gallery.htm and the linked project files for parameters).</ref>.]]<br />
[[File:Attractor Poisson Saturne.jpg|right|333px|thumb|奇异吸引子<ref>The figure shows the attractor of a second order 3-D Sprott-type polynomial, originally computed by Nicholas Desprez using the Chaoscope freeware (cf. http://www.chaoscope.org/gallery.htm and the linked project files for parameters).</ref>.的可视化图]]<br />
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[[strange attractor.]]<br />
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[[奇异吸引子]]<br />
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In the [[mathematics|mathematical]] field of [[dynamical system]]s, an '''attractor''' is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.<br />
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In the mathematical field of dynamical systems, an attractor is a set of numerical values toward which a system tends to evolve, for a wide variety of starting conditions of the system. System values that get close enough to the attractor values remain close even if slightly disturbed.<br />
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在动力系统的数学领域中,<font color="#ff8000"> 吸引子Attractor</font>是系统在各种初始条件下演化趋向于的一组数值。即使稍微受到干扰,与吸引子的值足够接近的系统值仍然保持足够接近<font color="#ff8000"> 吸引子</font>。<br />
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In finite-dimensional systems, the evolving variable may be represented [[algebra]]ically as an ''n''-dimensional [[Coordinate vector|vector]]. The attractor is a region in [[space (mathematics)|''n''-dimensional space]]. In [[Physics|physical systems]], the ''n'' dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in [[Economics|economic systems]], they may be separate variables such as the [[inflation rate]] and the [[unemployment rate]].<br />
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In finite-dimensional systems, the evolving variable may be represented algebraically as an n-dimensional vector. The attractor is a region in n-dimensional space. In physical systems, the n dimensions may be, for example, two or three positional coordinates for each of one or more physical entities; in economic systems, they may be separate variables such as the inflation rate and the unemployment rate.<br />
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在有限维系统中,演化变量可用代数表示为 n 维向量。<font color="#ff8000"> 吸引子</font>是 n 维空间中的一个区域。在物理系统中,n 维可以是,例如,一个或多个物理实体的两个或三个位置坐标; 在经济系统中,它们可以是单独的变量,如通货膨胀率和失业率。<br />
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If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented [[Geometry|geometrically]] in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a [[point (geometry)|point]], a finite set of points, a [[curve]], a [[manifold]], or even a complicated set with a [[fractal]] structure known as a ''strange attractor'' (see [[Attractor#Strange attractor|strange attractor]] below). If the variable is a [[scalar (mathematics)|scalar]], the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of [[chaos theory]].<br />
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If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor (see strange attractor below). If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.<br />
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如果演化变量是二维或三维的,则动态过程的<font color="#ff8000"> 吸引子</font>可以几何地表示为二维或三维(例如右图所示的三维情况)。一个<font color="#ff8000"> 吸引子</font>可以是一个点,一个有限的点集,一条曲线,一个流形,甚至是一个复杂的集合,具有一个分形结构称为<font color="#ff8000"> 奇异吸引子Strange attractor</font>(见下面的奇异吸引子)。如果变量是标量,那么吸引子就是实数线的子集。描述<font color="#ff8000"> 混沌动力学系统Chaotic dynamical systems</font>的吸引子是混沌理论的重要成果之一。<br />
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A [[trajectory]] of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be [[Periodic function|periodic]] or [[Chaos theory|chaotic]]. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a '''repeller''' (or ''repellor'').<br />
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A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor, forward in time. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighborhood is away from the set, the set is not an attractor, but instead is called a repeller (or repellor).<br />
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动力系统在吸引子中的[[轨迹]]除了保持在<font color="#ff8000"> 吸引子</font>上的时间向前外,不必满足任何特殊的约束条件。轨迹可能是周期性的,也可能是混沌的。如果一组点是周期性的或混沌的,但其附近的流远离该集合,则该集合不是吸引子,而是称为<font color="#ff8000"> 排斥点(或斥点)Repeller (or repellor)</font><br />
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== Motivation of attractors 吸引子的动力机制==<br />
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A [[dynamical system]] is generally described by one or more [[differential equations|differential]] or [[difference equations]]. The equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is often necessary to [[Integral|integrate]] the equations, either through analytical means or through [[iteration]], often with the aid of computers.<br />
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A dynamical system is generally described by one or more differential or difference equations. The equations of a given dynamical system specify its behavior over any given short period of time. To determine the system's behavior for a longer period, it is often necessary to integrate the equations, either through analytical means or through iteration, often with the aid of computers.<br />
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<font color="#ff8000"> 动力系统</font>通常由一个或多个<font color="#ff8000"> 微分方程</font>或<font color="#ff8000"> 差分方程</font>描述。一个给定动力系统的方程表明了它在任何给定的短时间内的行为。为了确定系统在较长时间内的行为,往往需要通过分析手段或通过<font color="#ff8000"> 迭代Iteration</font>(通常借助于计算机)对方程进行积分。<br />
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Dynamical systems in the physical world tend to arise from [[dissipative system|dissipative systems]]: if it were not for some driving force, the motion would cease. (Dissipation may come from [[friction|internal friction]], [[thermodynamics|thermodynamic losses]], or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the [[phase space]] of the dynamical system corresponding to the typical behavior is the '''attractor''', also known as the attracting section or attractee.<br />
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Dynamical systems in the physical world tend to arise from dissipative systems: if it were not for some driving force, the motion would cease. (Dissipation may come from internal friction, thermodynamic losses, or loss of material, among many causes.) The dissipation and the driving force tend to balance, killing off initial transients and settle the system into its typical behavior. The subset of the phase space of the dynamical system corresponding to the typical behavior is the attractor, also known as the attracting section or attractee.<br />
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物理世界中的动力系统往往产生于<font color="#ff8000"> 耗散系统Dissipative system</font>: 如果没有某种驱动力,运动就会停止。(耗散可能来自内部摩擦,热力学损失,或材料损失等许多原因。)耗散和驱动力趋于平衡,消除<font color="#ff8000">初始瞬态Initial transients</font>,使系统进入其典型状态。与典型行为相对应的动力系统相空间的子集是<font color="#ff8000"> 吸引子</font>,也称为吸引部分或<font color="#ff8000"> 吸引子</font>。<br />
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Invariant sets and [[limit set]]s are similar to the attractor concept. An ''invariant set'' is a set that evolves to itself under the dynamics.<ref>{{cite book|author1=Carvalho, A.|author2=Langa, J.A.|author3=Robinson, J.|year=2012|title=Attractors for infinite-dimensional non-autonomous dynamical systems|volume=182|publisher=Springer|p=109}}</ref> Attractors may contain invariant sets. A ''limit set'' is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set (i.e. to each point of the set) as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed slightly off the limit set may get knocked off and never return to the vicinity of the limit set.<br />
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Invariant sets and limit sets are similar to the attractor concept. An invariant set is a set that evolves to itself under the dynamics. Attractors may contain invariant sets. A limit set is a set of points such that there exists some initial state that ends up arbitrarily close to the limit set (i.e. to each point of the set) as time goes to infinity. Attractors are limit sets, but not all limit sets are attractors: It is possible to have some points of a system converge to a limit set, but different points when perturbed slightly off the limit set may get knocked off and never return to the vicinity of the limit set.<br />
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<font color="#ff8000"> 不变集</font>和<font color="#ff8000"> 极限集</font>是类似于吸引子的概念。<font color="#ff8000"> 不变集</font>是在动力学作用下向自身演化的集合。<font color="#ff8000"> 不变集</font>可能包含于<font color="#ff8000"> 吸引子</font>。<font color="#ff8000"> 极限集</font>是一组点,这些点存在一些初始状态,这些初始状态随着时间的推移到无穷远时最终将任意接近极限集(即收敛到集合的每个点)。<font color="#ff8000"> 吸引子</font>是<font color="#ff8000"> 极限集</font>,但不是所有的<font color="#ff8000"> 极限集</font>都是<font color="#ff8000"> 吸引子</font>: 系统的某些点可能会收敛到极限集,但是稍微偏离极限集的不同点可能会被敲掉,永远不会回到极限集附近。<br />
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For example, the [[damping ratio|damped]] [[pendulum]] has two invariant points: the point {{math|x<sub>0</sub>}} of minimum height and the point {{math|x<sub>1</sub>}} of maximum height. The point {{math|x<sub>0</sub>}} is also a limit set, as trajectories converge to it; the point {{math|x<sub>1</sub>}} is not a limit set. Because of the dissipation due to air resistance, the point {{math|x<sub>0</sub>}} is also an attractor. If there was no dissipation, {{math|x<sub>0</sub>}} would not be an attractor. Aristotle believed that objects moved only as long as they were pushed, which is an early formulation of a dissipative attractor.<br />
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For example, the damped pendulum has two invariant points: the point of minimum height and the point of maximum height. The point is also a limit set, as trajectories converge to it; the point is not a limit set. Because of the dissipation due to air resistance, the point is also an attractor. If there was no dissipation, would not be an attractor. Aristotle believed that objects moved only as long as they were pushed, which is an early formulation of a dissipative attractor.<br />
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例如,<font color="#ff8000"> 阻尼摆Damping ratio|damped</font>有两个不变点: 最小高度点{{math|x<sub>0</sub>}}和最大高度点{{math|x<sub>1</sub>}}。点{{math|x<sub>0</sub>}}也是一个极限集,因为轨迹向它收敛;点 {{math|x<sub>1</sub>}}不是一个极限集。由于空气阻力的耗散,点{{math|x<sub>0</sub>}}也是吸引子。如果没有耗散,{{math|x<sub>0</sub>}}就不会是<font color="#ff8000"> 吸引子</font>。亚里士多德认为物体只有在被推动时才会移动,这是<font color="#ff8000"> 耗散吸引子</font>的早期表述。<br />
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Some attractors are known to be chaotic (see [[#Strange attractor]]), in which case the evolution of any two distinct points of the attractor result in exponentially [[chaos theory|diverging trajectories]], which complicates prediction when even the smallest noise is present in the system.<ref>{{cite book|author1=Kantz, H.|author2=Schreiber, T.|year=2004|title=Nonlinear time series analysis|publisher=Cambridge university press}}</ref><br />
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Some attractors are known to be chaotic (see #Strange attractor), in which case the evolution of any two distinct points of the attractor result in exponentially diverging trajectories, which complicates prediction when even the smallest noise is present in the system.<br />
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有些<font color="#ff8000"> 吸引子</font>是混沌的(参见#奇异吸引子),在这种情况下,吸引子的任意两个不同点的演化都会导致指数发散轨迹,即使系统中存在最小的<font color="#ff8000"> 噪声</font>,预测也会变得复杂。<br />
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== Mathematical definition数学定义 ==<br />
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Let ''t'' represent time and let ''f''(''t'', •) be a function which specifies the dynamics of the system. That is, if ''a'' is a point in an ''n''-dimensional phase space, representing the initial state of the system, then ''f''(0, ''a'') = ''a'' and, for a positive value of ''t'', ''f''(''t'', ''a'') is the result of the evolution of this state after ''t'' units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane '''R'''<sup>2</sup> with coordinates (''x'',''v''), where ''x'' is the position of the particle, ''v'' is its velocity, ''a''&nbsp;=&nbsp;(''x'',''v''), and the evolution is given by<br />
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Let t represent time and let f(t, •) be a function which specifies the dynamics of the system. That is, if a is a point in an n-dimensional phase space, representing the initial state of the system, then f(0, a) = a and, for a positive value of t, f(t, a) is the result of the evolution of this state after t units of time. For example, if the system describes the evolution of a free particle in one dimension then the phase space is the plane R<sup>2</sup> with coordinates (x,v), where x is the position of the particle, v is its velocity, a&nbsp;=&nbsp;(x,v), and the evolution is given by<br />
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设 t 表示时间,设 f (t,•)是指定系统动力学的函数。也就是说,如果 a 是 n 维相空间中的一个点,表示系统的初始状态,那么 f (0,a) = a,以及对于 t 的正值,f (t,a)是该状态在 t 个时间单位之后演化的结果。例如,如果系统描述了自由粒子在一维空间中的演化,那么相空间是坐标为(x,v)的平面 '''R'''<sup>2</sup> ,,其中 x 是粒子的位置,v 是粒子的速度,a&nbsp;=&nbsp;(x,v),由以下给出<br />
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[[File:Julia immediate basin 1 3.png|right|thumb|Attracting period-3 cycle and its immediate basin of attraction for a certain parametrization of ''f''(''z'')&nbsp;=&nbsp;''z''<sup>2</sup>&nbsp;+&nbsp;''c''. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.]]<br />
[[资料图:茱莉亚立即盆地1 3.png |右|拇指|吸引周期-3旋回及其对“f”(“z”)参数化的直接吸引域。三个最暗的点是3循环的点,它们按顺序相互连接,从吸引域中的任何点迭代会导致(通常是渐进的)收敛到这三个点的序列。]]<br />
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Attracting period-3 cycle and its immediate basin of attraction for a certain parametrization of f(z)&nbsp;=&nbsp;z<sup>2</sup>&nbsp;+&nbsp;c. The three darkest points are the points of the 3-cycle, which lead to each other in sequence, and iteration from any point in the basin of attraction leads to (usually asymptotic) convergence to this sequence of three points.<br />
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f(z)&nbsp;=&nbsp;z<sup>2</sup>&nbsp;+&nbsp;c的某一特定参数的吸引3-周期循环及其直接吸引池。最暗的三个点是3-周期循环的点,它们依次相向,从吸引域中的任何一点迭代都会导致(通常是渐近的)收敛到这三个点的序列。<br />
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: <math> f(t,(x,v))=(x+tv,v).\ </math><br />
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<math> f(t,(x,v))=(x+tv,v).\ </math><br />
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F (t,(x,v)) = (x + tv,v)<br />
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An '''attractor''' is a [[subset]] ''A'' of the [[phase space]] characterized by the following three conditions:<br />
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An attractor is a subset A of the phase space characterized by the following three conditions:<br />
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<font color="#ff8000"> 吸引子</font>是<font color="#ff8000"> 相空间</font>的<font color="#ff8000"> 子集</font>A,具有以下三个条件:<br />
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* ''A'' is ''forward invariant'' under ''f'': if ''a'' is an element of ''A'' then so is ''f''(''t'',''a''), for all&nbsp;''t''&nbsp;>&nbsp;0.<br />
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*“A”是“f”下的“前向不变”:如果“A”是“A”的元素,则对于所有“t”>0,“f”(“t”,“A”)也是。<br />
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* There exists a [[Neighbourhood (mathematics)|neighborhood]] of ''A'', called the '''basin of attraction''' for ''A'' and denoted ''B''(''A''), which consists of all points ''b'' that "enter ''A'' in the limit ''t''&nbsp;→&nbsp;∞". More formally, ''B''(''A'') is the set of all points ''b'' in the phase space with the following property:<br />
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*存在一个“A”的[[邻域(数学)|邻域]],称为“A”的“吸引域”,表示为“B”(“A”),它由所有“B”点组成,这些点“B”在极限''t''&nbsp;→&nbsp;∞"时“进入”A“。更正式地说,“B”(“A”)是相空间中所有点“B”的集合,具有以下特性:<br />
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:: For any open neighborhood ''N'' of ''A'', there is a positive constant ''T'' such that ''f''(''t'',''b'') ∈ ''N'' for all real ''t'' > ''T''.<br />
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For any open neighborhood N of A, there is a positive constant T such that f(t,b) ∈ N for all real t > T.<br />
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●对于“A”的任何开邻域“N”,存在一个正常数“T”,使得对所有实数“T”>“T”,有''f''(''t'',''b'') ∈ ''N'',。<br />
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* There is no proper (non-empty) subset of ''A'' having the first two properties.<br />
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*“A”中不存在具有前两个属性的正确(非空)子集。<br />
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Since the basin of attraction contains an [[open set]] containing ''A'', every point that is sufficiently close to ''A'' is attracted to ''A''. The definition of an attractor uses a [[metric space|metric]] on the phase space, but the resulting notion usually depends only on the topology of the phase space. In the case of '''R'''<sup>''n''</sup>, the Euclidean norm is typically used.<br />
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Since the basin of attraction contains an open set containing A, every point that is sufficiently close to A is attracted to A. The definition of an attractor uses a metric on the phase space, but the resulting notion usually depends only on the topology of the phase space. In the case of R<sup>n</sup>, the Euclidean norm is typically used.<br />
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由于吸引域包含一个含有 a 的开集合,所以每一个足够接近 a 的点都会被 a 吸引。吸引子的定义使用了相空间上的一个度量,但得到的结果通常只依赖于相空间的拓扑结构。在R<sup>n</sup>的情况下,通常使用<font color="#ff8000"> 欧氏范数Euclidean norm</font>。<br />
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Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive [[measure (mathematics)|measure]] (preventing a point from being an attractor), others relax the requirement that ''B''(''A'') be a neighborhood. <ref>{{cite journal | author=John Milnor | author-link=John Milnor | title= On the concept of attractor | journal=Communications in Mathematical Physics | year=1985 | volume=99 | pages=177–195| doi= 10.1007/BF01212280 | issue=2}}</ref><br />
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Many other definitions of attractor occur in the literature. For example, some authors require that an attractor have positive measure (preventing a point from being an attractor), others relax the requirement that B(A) be a neighborhood. <br />
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在文献中有<font color="#ff8000"> 吸引子</font>的许多其他定义出现。例如,一些作者要求<font color="#ff8000"> 吸引子</font>具有正测度(防止一个点成为吸引子) ,另一些作者放松了 B(A)是一个邻域的要求。<br />
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== Types of attractors 吸引子的类型==<br />
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Attractors are portions or [[subset]]s of the [[Configuration space (physics)|phase space]] of a [[dynamical system]]. Until the 1960s, attractors were thought of as being [[Geometric primitive|simple geometric subsets]] of the phase space, like [[Point (geometry)|points]], [[Line (mathematics)|lines]], [[Surface (topology)|surface]]s, and simple regions of [[three-dimensional space]]. More complex attractors that cannot be categorized as simple geometric subsets, such as [[topology|topologically]] wild sets, were known of at the time but were thought to be fragile anomalies. [[Stephen Smale]] was able to show that his [[horseshoe map]] was [[structural stability|robust]] and that its attractor had the structure of a [[Cantor set]].<br />
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Attractors are portions or subsets of the phase space of a dynamical system. Until the 1960s, attractors were thought of as being simple geometric subsets of the phase space, like points, lines, surfaces, and simple regions of three-dimensional space. More complex attractors that cannot be categorized as simple geometric subsets, such as topologically wild sets, were known of at the time but were thought to be fragile anomalies. Stephen Smale was able to show that his horseshoe map was robust and that its attractor had the structure of a Cantor set.<br />
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<font color="#ff8000"> 吸引子</font>是动力系统的<font color="#ff8000"> 相空间</font>的一部分或<font color="#ff8000"> 子集</font>。直到20世纪60年代,吸引子被认为是相空间的简单几何子集,像点、线、面和简单的三维空间。更复杂的吸引子,不能被归类为简单的几何子集,如<font color="#ff8000"> 拓扑野生集Topologically wild sets,</font>,在当时是已知的,但被认为是脆弱的异常。斯蒂芬 · 斯梅尔Stephen Smale能够证明他的马蹄地图是健壮的,它的吸引子具有<font color="#ff8000"> 康托集Cantor set</font>的结构。<br />
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Two simple attractors are a [[Fixed point (mathematics)|fixed point]] and the [[limit cycle]]. Attractors can take on many other geometric shapes (phase space subsets). But when these sets (or the motions within them) cannot be easily described as simple combinations (e.g. [[intersection (set theory)|intersection]] and [[union (set theory)|union]]) of [[Geometric primitive|fundamental geometric objects]] (e.g. [[Line (mathematics)|lines]], [[Surface (topology)|surface]]s, [[sphere]]s, [[toroid]]s, [[manifold]]s), then the attractor is called a ''[[attractor#Strange attractor|strange attractor]]''.<br />
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Two simple attractors are a fixed point and the limit cycle. Attractors can take on many other geometric shapes (phase space subsets). But when these sets (or the motions within them) cannot be easily described as simple combinations (e.g. intersection and union) of fundamental geometric objects (e.g. lines, surfaces, spheres, toroids, manifolds), then the attractor is called a strange attractor.<br />
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两个简单的<font color="#ff8000"> 吸引子</font>是一个<font color="#ff8000"> 不动点</font>和一个<font color="#ff8000"> 极限环</font>。<font color="#ff8000"> 吸引子</font>可以呈现许多其他几何形状(相空间子集)。但当这些集合(或其中的运动)不能简单地描述为[[几何本原|基本几何对象]](例如,[直线(数学)|直线]],[[曲面(拓扑)|曲面]]s,[[球体]]s,[[环面]]s,[[环面]]s,[[流形]]s的简单组合(例如,[交集(集合论)|交集]]和[[并集理论)|并集]],则这个吸引子被称为“[[奇怪吸引子]]”。<br />
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=== Fixed point驻点 ===<br />
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[[File:Critical orbit 3d.png|right|thumb|Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial]]. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.]]<br />
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[[文件:临界轨道3d.png |右|拇指|根据[[复二次多项式]]演化的复数的弱吸引不动点。相空间是水平复平面;纵轴测量访问复平面中的点的频率。复平面中峰值频率正下方的点是不动点吸引子。]]<br />
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Weakly attracting fixed point for a complex number evolving according to a [[complex quadratic polynomial. The phase space is the horizontal complex plane; the vertical axis measures the frequency with which points in the complex plane are visited. The point in the complex plane directly below the peak frequency is the fixed point attractor.]]<br />
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根据[[复二次多项式演化的复数的弱吸引不动点。相空间是水平复平面;纵轴测量访问复平面中的点的频率。复平面中峰值频率正下方的点是不动点吸引子。]]<br />
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A [[Fixed point (mathematics)|fixed point]] of a function or transformation is a point that is mapped to itself by the function or transformation. If we regard the evolution of a dynamical system as a series of transformations, then there may or may not be a point which remains fixed under each transformation. The final state that a dynamical system evolves towards corresponds to an attracting fixed point of the evolution function for that system, such as the center bottom position of a [[damping ratio|damped]] [[pendulum]], the level and flat water line of sloshing water in a glass, or the bottom center of a bowl contain a rolling marble. But the fixed point(s) of a dynamic system is not necessarily an attractor of the system. For example, if the bowl containing a rolling marble was inverted and the marble was balanced on top of the bowl, the center bottom (now top) of the bowl is a fixed state, but not an attractor. This is equivalent to the difference between [[Stability theory#Stability of fixed points|stable and unstable equilibria]]. In the case of a marble on top of an inverted bowl (a hill), that point at the top of the bowl (hill) is a fixed point (equilibrium), but not an attractor (stable equilibrium).<br />
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A fixed point of a function or transformation is a point that is mapped to itself by the function or transformation. If we regard the evolution of a dynamical system as a series of transformations, then there may or may not be a point which remains fixed under each transformation. The final state that a dynamical system evolves towards corresponds to an attracting fixed point of the evolution function for that system, such as the center bottom position of a damped pendulum, the level and flat water line of sloshing water in a glass, or the bottom center of a bowl contain a rolling marble. But the fixed point(s) of a dynamic system is not necessarily an attractor of the system. For example, if the bowl containing a rolling marble was inverted and the marble was balanced on top of the bowl, the center bottom (now top) of the bowl is a fixed state, but not an attractor. This is equivalent to the difference between stable and unstable equilibria. In the case of a marble on top of an inverted bowl (a hill), that point at the top of the bowl (hill) is a fixed point (equilibrium), but not an attractor (stable equilibrium).<br />
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函数或变换的不动点是通过函数或变换映射到自身的点。如果我们把动力系统的演化看作是一系列的转变,那么在每一个转变下,可能会有一个点是固定的,也可能没有。动力系统的最终状态对应于该系统演化函数的吸引固定点,例如阻尼摆的中心底部位置,玻璃杯中晃动水的水平线和平坦线,或碗的底部中心含有滚动的大理石。但是动态系统的不动点不一定是系统的吸引子。例如,如果装有滚动大理石的碗被倒置,大理石平衡在碗的顶部,碗的中心底部(现在是顶部)是一个固定的状态,但不是一个吸引子。这等价于稳定平衡点和不稳定平衡点之差。如果一个大理石在一个倒碗(山)的顶部,这个点在碗(山)的顶部是一个固定点(平衡) ,但不是一个吸引子(稳定的平衡)。<br />
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In addition, physical dynamic systems with at least one fixed point invariably have multiple fixed points and attractors due to the reality of dynamics in the physical world, including the [[nonlinear dynamics]] of [[stiction]], [[friction]], [[surface roughness]], [[Deformation (engineering)|deformation]] (both [[Elastic deformation|elastic]] and [[plastic]]ity), and even [[quantum mechanics]].<ref name="Contact of Nominally Flat Surfaces">{{cite journal|last=Greenwood|first=J. A.|author2=J. B. P. Williamson|title=Contact of Nominally Flat Surfaces|journal=Proceedings of the Royal Society|date=6 December 1966|volume=295|issue=1442|pages=300–319|doi=10.1098/rspa.1966.0242}}</ref> In the case of a marble on top of an inverted bowl, even if the bowl seems perfectly [[Sphere#Hemisphere|hemispherical]], and the marble's [[sphere|spherical]] shape, are both much more complex surfaces when examined under a microscope, and their [[Contact mechanics#History|shapes change]] or [[deformation (mechanics)|deform]] during contact. Any physical surface can be seen to have a rough terrain of multiple peaks, valleys, saddle points, ridges, ravines, and plains.<ref name="NISTIR 89-4088">{{cite book|last=Vorberger|first=T. V.|title=Surface Finish Metrology Tutorial|year=1990|publisher=U.S. Department of Commerce, National Institute of Standards (NIST)|page=5|url=https://www.nist.gov/calibrations/upload/89-4088.pdf}}</ref> There are many points in this surface terrain (and the dynamic system of a similarly rough marble rolling around on this microscopic terrain) that are considered [[Critical point (mathematics)|stationary]] or fixed points, some of which are categorized as attractors.<br />
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In addition, physical dynamic systems with at least one fixed point invariably have multiple fixed points and attractors due to the reality of dynamics in the physical world, including the nonlinear dynamics of stiction, friction, surface roughness, deformation (both elastic and plasticity), and even quantum mechanics. In the case of a marble on top of an inverted bowl, even if the bowl seems perfectly hemispherical, and the marble's spherical shape, are both much more complex surfaces when examined under a microscope, and their shapes change or deform during contact. Any physical surface can be seen to have a rough terrain of multiple peaks, valleys, saddle points, ridges, ravines, and plains. There are many points in this surface terrain (and the dynamic system of a similarly rough marble rolling around on this microscopic terrain) that are considered stationary or fixed points, some of which are categorized as attractors.<br />
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此外,至少有一个固定点的物理动力系统,由于物理世界动力学的现实性,包括非线性动力学的粘滞,摩擦,表面粗糙度,变形(弹性和塑性) ,甚至量子力学,总是有多个固定点和吸引子。在倒置碗顶的大理石上,即使碗看起来完美的半球形,和大理石的球形,在显微镜下观察时都是更复杂的表面,它们的形状在接触过程中改变或变形。任何物理表面都可以看到一个由多个山峰、山谷、鞍点、山脊、峡谷和平原组成的崎岖地形。在这个表面地形中有许多点(以及在这个微观地形上滚动的同样粗糙的大理石的动力系统)被认为是静止的或不动的点,其中一些被归类为吸引子。<br />
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===Finite number of points有限点数===<br />
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In a [[Discrete time and continuous time|discrete-time]] system, an attractor can take the form of a finite number of points that are visited in sequence. Each of these points is called a [[periodic point]]. This is illustrated by the [[logistic map]], which depending on its specific parameter value can have an attractor consisting of 2<sup>''n''</sup> points, 3×2<sup>''n''</sup> points, etc., for any value of ''n''.<br />
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In a discrete-time system, an attractor can take the form of a finite number of points that are visited in sequence. Each of these points is called a periodic point. This is illustrated by the logistic map, which depending on its specific parameter value can have an attractor consisting of 2<sup>n</sup> points, 3×2<sup>n</sup> points, etc., for any value of n.<br />
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在一个[[离散和连续时间|离散时间]]系统中,<font color="#ff8000"> 吸引子</font>可以以有限数量的点的形式依次访问。每个点都称为[[周期点]]。[[逻辑图]]说明了这一点,根据其特定参数值,对于任何“n”值,可以有由2<sup>''n''</sup>点、3×2<sup>''n''</sup>点等组成的<font color="#ff8000"> 吸引子</font>。<br />
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=== Limit cycle 极限环===<br />
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{{main|Limit cycle}}<br />
{{main |极限环}}<br />
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A [[limit cycle]] is a periodic orbit of a continuous dynamical system that is [[isolated point|isolated]]. Examples include the swings of a [[pendulum clock]], and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).<br />
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A limit cycle is a periodic orbit of a continuous dynamical system that is isolated. Examples include the swings of a pendulum clock, and the heartbeat while resting. (The limit cycle of an ideal pendulum is not an example of a limit cycle attractor because its orbits are not isolated: in the phase space of the ideal pendulum, near any point of a periodic orbit there is another point that belongs to a different periodic orbit, so the former orbit is not attracting).<br />
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[[极限环]]是连续动力系统的周期轨道,它是[[孤立点|孤立]]。例如[[钟摆时钟]]的摆动,以及休息时的心跳。(理想摆的极限环不是极限环吸引子的一个例子,因为它的轨道不是孤立的:在理想摆的相空间中,在一个周期轨道的任何一个点附近都有另一个点属于不同周期轨道,因此前一个轨道不具有吸引力)。<br />
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[[File:VanDerPolPhaseSpace.png|center|250px|thumb|<center>[[Van der Pol oscillator|Van der Pol]] [[phase portrait]]: an attracting limit cycle</center>]]<br />
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[[文件:VanDerPolPhaseSpace.png|center| 250px |拇指|<center>[[Van der Pol振荡器| Van der Pol]][[相位肖像]]:吸引极限环</center>]]<br />
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Van der Pol phase portrait: an attracting limit cycle</center>]]<br />
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范德波尔相图: 一个吸引极限环 </center>]]<br />
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=== Limit torus 极限环===<br />
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There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an [[irrational number|irrational fraction]] (i.e. they are [[commensurability (mathematics)|incommensurate]]), the trajectory is no longer closed, and the limit cycle becomes a limit [[torus]]. This kind of attractor is called an {{math|''N''<sub>''t''</sub>}} -torus if there are {{math|N<sub>t</sub>}} incommensurate frequencies. For example, here is a 2-torus:<br />
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There may be more than one frequency in the periodic trajectory of the system through the state of a limit cycle. For example, in physics, one frequency may dictate the rate at which a planet orbits a star while a second frequency describes the oscillations in the distance between the two bodies. If two of these frequencies form an irrational fraction (i.e. they are incommensurate), the trajectory is no longer closed, and the limit cycle becomes a limit torus. This kind of attractor is called an -torus if there are incommensurate frequencies. For example, here is a 2-torus:<br />
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在系统通过极限循环状态的周期轨迹中,可能存在多个频率。例如,在物理学中,一个频率可以决定一颗行星围绕恒星运行的速率,而第二个频率则描述了两个天体之间距离的振荡。如果其中两个频率形成[[无理数|无理分数]](即它们是[[可公度(数学)|不公度]]),则轨迹不再闭合,极限循环变成<font color="#ff8000"> 极限[[环]]</font>。如果存在 {{math|N<sub>t</sub>}}非公度频率,这种吸引子被称为{{math|''N''<sub>''t''</sub>}} 环面。例如,这个2环面体:<br />
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[[File:torus.png|300px]]<br />
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A time series corresponding to this attractor is a [[quasiperiodic]] series: A discretely sampled sum of {{math|N<sub>t</sub>}} periodic functions (not necessarily [[sine]] waves) with incommensurate frequencies. Such a time series does not have a strict periodicity, but its [[power spectrum]] still consists only of sharp lines.<br />
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A time series corresponding to this attractor is a quasiperiodic series: A discretely sampled sum of periodic functions (not necessarily sine waves) with incommensurate frequencies. Such a time series does not have a strict periodicity, but its power spectrum still consists only of sharp lines.<br />
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与这个吸引子对应的时间序列是一个准周期序列: 具有非公度频率的周期函数(不一定是正弦波)的离散采样和。这样的时间序列不具有严格的周期性,但其功率谱仍然只包含锐线。<br />
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=== Strange attractor 奇异吸引子===<!-- This section is linked from [[Lorenz attractor]] 本节链接自[[洛伦兹吸引子]]--><br />
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[[File:Lorenz attractor yb.svg|thumb|200px|right|A plot of Lorenz's strange attractor for values&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3]]<br />
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[[文件:洛伦兹吸引子yb.svg公司|thumb | 200px | right | 洛伦兹奇异吸引子的图,&nbsp;''ρ''&nbsp;=&nbsp;28,&nbsp;''σ''&nbsp;=&nbsp;10,&nbsp;''β''&nbsp;=&nbsp;8/3]]<br />
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A plot of Lorenz's strange attractor for values&nbsp;ρ&nbsp;=&nbsp;28,&nbsp;σ&nbsp;=&nbsp;10,&nbsp;β&nbsp;=&nbsp;8/3<br />
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关于洛伦兹奇怪吸引子 ρ = 28,σ = 10,β = 8/3的图<br />
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An attractor is called '''strange''' if it has a [[fractal]] structure. This is often the case when the dynamics on it are [[chaos theory|chaotic]], but [[strange nonchaotic attractor]]s also exist. If a strange attractor is chaotic, exhibiting [[sensitive dependence on initial conditions]], then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.<ref>{{cite journal | author = Grebogi Celso, Ott Edward, Yorke James A | year = 1987 | title = Chaos, Strange Attractors, and Fractal Basin Boundaries in Nonlinear Dynamics | url = | journal = Science | volume = 238 | issue = 4827| pages = 632–638 | doi = 10.1126/science.238.4827.632 | pmid = 17816542 | bibcode = 1987Sci...238..632G }}</ref><br />
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An attractor is called strange if it has a fractal structure. This is often the case when the dynamics on it are chaotic, but strange nonchaotic attractors also exist. If a strange attractor is chaotic, exhibiting sensitive dependence on initial conditions, then any two arbitrarily close alternative initial points on the attractor, after any of various numbers of iterations, will lead to points that are arbitrarily far apart (subject to the confines of the attractor), and after any of various other numbers of iterations will lead to points that are arbitrarily close together. Thus a dynamic system with a chaotic attractor is locally unstable yet globally stable: once some sequences have entered the attractor, nearby points diverge from one another but never depart from the attractor.<br />
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如果吸引子具有[[分形]]结构,则称为“奇异”。当它的动力学是[[混沌理论|混沌]]时,通常会出现这种情况,但是[[奇异的非混沌吸引子]]也存在。如果一个<font color="#ff8000"> 奇异吸引子</font>是混沌的,表现出[[对初始条件的敏感依赖性]],那么在吸引子上两个任意接近的备选初始点,经过任意多次迭代后,都会导致任意相距很远的点(受吸引子的限制),而在其他次数的迭代之后,都会导致任意接近的点。因此,具有混沌吸引子的动态系统是局部不稳定的但全局稳定的:一旦一些序列进入<font color="#ff8000"> 吸引子</font>,附近的点就会彼此发散,但不会离开<font color="#ff8000"> 吸引子</font>。<br />
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The term '''strange attractor''' was coined by [[David Ruelle]] and [[Floris Takens]] to describe the attractor resulting from a series of [[bifurcation theory|bifurcations]] of a system describing fluid flow.<ref>{{cite journal |last=Ruelle |first=David |last2=Takens |first2=Floris |date=1971 |title=On the nature of turbulence |url=http://projecteuclid.org/euclid.cmp/1103857186 |journal=Communications in Mathematical Physics |volume=20 |issue=3 |pages=167–192 |doi=10.1007/bf01646553}}</ref> Strange attractors are often [[Differentiable function|differentiable]] in a few directions, but some are [[homeomorphic|like]] a [[Cantor dust]], and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.<ref name="Stochastic climate dynamics: Random attractors and time-dependent invariant measures">{{cite journal|author1=Chekroun M. D. |author2=Simonnet E. |author3=Ghil M. |author-link3=Michael Ghil |name-list-style=amp|<br />
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The term strange attractor was coined by David Ruelle and Floris Takens to describe the attractor resulting from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable. Strange attractors may also be found in the presence of noise, where they may be shown to support invariant random probability measures of Sinai–Ruelle–Bowen type.<br />
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术语“奇异吸引子”是由[[David Ruelle]]和[[Floris Takens]]提出,用来描述一个描述流体流动的系统的一系列[[分岔理论|分叉]]所产生的吸引子。<ref>{{cite journal |last=Ruelle |first=David |last2=Takens |first2=Floris |date=1971 |title=On the nature of turbulence |url=http://projecteuclid.org/euclid.cmp/1103857186 |journal=Communications in Mathematical Physics |volume=20 |issue=3 |pages=167–192 |doi=10.1007/bf01646553}}</ref> 奇异吸引子通常在几个方向上[[可微函数|可微]],但有些吸引子是[[同胚|类似]]的一个[[康托尘埃]],因此不可微。在存在噪声的情况下,也可以发现奇异的吸引子,它们可以证明支持Sinai-Ruelle-Bowen型的不变随机概率测度。<ref name="Stochastic climate dynamics: Random attractors and time-dependent invariant measures">{{cite journal|author1=Chekroun M. D. |author2=Simonnet E. |author3=Ghil M. |author-link3=Michael Ghil |name-list-style=amp|<br />
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year = 2011 |<br />
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title = Stochastic climate dynamics: Random attractors and time-dependent invariant measures |<br />
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Examples of strange attractors include the double-scroll attractor, Hénon attractor, Rössler attractor, and Lorenz attractor.<br />
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<font color="#ff8000"> 奇异吸引子</font>的例子包括<font color="#ff8000"> 双涡卷吸引子double-scroll attractor、埃农吸引子Hénon attractor、Rössler吸引子Rössler attractor和洛伦兹吸引子Lorenz attractor</font>。<br />
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journal = Physica D |<br />
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volume = 240 |<br />
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issue = 21 |<br />
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pages = 1685–1700 |<br />
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Bifurcation diagram of the [[logistic map. The attractor(s) for any value of the parameter r are shown on the ordinate in the domain <math>0<x<1</math>. The colour of a point indicates how often the point <math>(r, x)</math> is visited over the course of 10<sup>6</sup> iterations: frequently encountered values are coloured in blue, less frequently encountered values are yellow. A bifurcation appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).]]<br />
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[[逻辑映射的分岔图。参数r的任何值的吸引子显示在区间<math>0<x<1</math>的纵坐标上。点的颜色表示在10<sup>6</sup>次迭代过程中访问点<math>(r, x)</math>的频率:经常遇到的值用蓝色表示,不太常见的值用黄色表示。在<math>r\approx3.0</math>附近出现分叉,在<math>r\approx3.5</math>附近出现第二个分叉(导致四个吸引子值)。当<math>r>3.6</math>时,行为变得越来越复杂,中间穿插着行为更简单的区域(白色条纹)。]]<br />
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doi = 10.1016/j.physd.2011.06.005|citeseerx=10.1.1.156.5891 }}</ref><br />
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The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied logistic map, <math>x_{n+1}=rx_n(1-x_n)</math>, whose basins of attraction for various values of the parameter r are shown in the figure. If <math>r=2.6</math>, all starting x values of <math>x<0</math> will rapidly lead to function values that go to negative infinity; starting x values of <math>x>0</math> will go to infinity. But for <math>0<x<1</math> the x values rapidly converge to <math>x\approx0.615</math>, i.e. at this value of r, a single value of x is an attractor for the function's behaviour. For other values of r, more than one value of x may be visited: if r is 3.2, starting values of <math>0<x<1</math> will lead to function values that alternate between <math>x\approx0.513</math> and <math>x\approx0.799</math>. At some values of r, the attractor is a single point (a "fixed point"), at other values of r two values of x are visited in turn (a period-doubling bifurcation); at yet other values of r, any given number of values of x are visited in turn; finally, for some values of r, an infinitude of points are visited. Thus one and the same dynamic equation can have various types of attractors, depending on its starting parameters.<br />
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动力学方程的参数随着方程的迭代而变化,具体值可能取决于初始参数。一个例子是研究得很好的logistic地图,<math>x{n+1}=rx}n(1-xun)</math>,图中显示了参数r的各种值的吸引域。如果<math>r=2.6</math>,则<math>x<0</math>的所有起始x值将迅速导致函数值变为负无穷大;<math>x>0</math>的起始x值将变为无穷大。但是对于<math>0<x<1</math>,x值迅速收敛到<math>x\approx0.615</math>,也就是说,在这个r值下,x的单个值是函数行为的吸引子。对于r的其他值,可以访问x的多个值:如果r为3.2,<math>0<x<1</math>的起始值将导致函数值在<math>x\approx0.513</math>和<math>x\approx0.799</math>之间交替。在r的某些值处,吸引子是一个单点(“不动点”),在r的其他值处,依次访问x的两个值(倍周期分岔);在r的其他值处,依次访问任意数量的x值;最后,对于r的某些值,访问无穷多个点。因此,同一个动力学方程可以有不同类型的吸引子,这取决于它的起始参数。<br />
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Examples of strange attractors include the [[Double scroll attractor|double-scroll attractor]], [[Hénon map|Hénon attractor]], [[Rössler attractor]], and [[Lorenz attractor]].<br />
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奇异吸引子的例子包括[[双涡旋吸引子|双涡旋吸引子]]、[[Hénon-map | Hénon吸引子]]、[[Rössler吸引子]]和[[Lorenz吸引子]]。<br />
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==Attractors characterize the evolution of a system吸引子表征系统的演化==<br />
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An attractor's basin of attraction is the region of the phase space, over which iterations are defined, such that any point (any initial condition) in that region will asymptotically be iterated into the attractor. For a stable linear system, every point in the phase space is in the basin of attraction. However, in nonlinear systems, some points may map directly or asymptotically to infinity, while other points may lie in a different basin of attraction and map asymptotically into a different attractor; other initial conditions may be in or map directly into a non-attracting point or cycle.<br />
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吸引子的吸引域是相空间的区域,在这个区域上定义了迭代,使得该区域中的任何点(任何初始条件)都将渐近地迭代到吸引子中。对于一个稳定的线性系统,相空间中的每一点都在吸引域中。然而,在非线性系统中,有些点可能直接或渐近地映射到无穷大,而另一些点可能位于不同的吸引域中并渐近映射到不同的吸引子;其他初始条件可能位于或直接映射到非吸引点或循环中。<br />
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[[File:Logistic Map Bifurcation Diagram, Matplotlib.svg|350px|thumb|right|Bifurcation diagram of the [[logistic map]]. The attractor(s) for any value of the parameter ''r'' are shown on the ordinate in the domain <math>0<x<1</math>. The colour of a point indicates how often the point <math>(r, x)</math> is visited over the course of 10<sup>6</sup> iterations: frequently encountered values are coloured in blue, less frequently encountered values are yellow. A [[period-doubling bifurcation|bifurcation]] appears around <math>r\approx3.0</math>, a second bifurcation (leading to four attractor values) around <math>r\approx3.5</math>. The behaviour is increasingly complicated for <math>r>3.6</math>, interspersed with regions of simpler behaviour (white stripes).]]<br />
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[[文件:逻辑图分岔图,Matplotlib.svg|350px |拇指|右|分岔图[[逻辑图]]。参数“r”的任何值的吸引子显示在域<math>0<x<1</math>的纵坐标上。点的颜色表示在10次<sup>6次迭代过程中访问点<math>(r,x)</math>的频率:经常遇到的值用蓝色表示,不太常见的值用黄色表示。在<math>r\approx3.0</math>附近出现[[倍周期分岔|分岔]],在<math>r\approx3.5</math>附近出现第二个分岔(导致四个吸引子值)。当<math>r>3.6<math>时,行为变得越来越复杂,中间穿插着行为更简单的区域(白色条纹)。]]<br />
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The parameters of a dynamic equation evolve as the equation is iterated, and the specific values may depend on the starting parameters. An example is the well-studied [[logistic map]], <math>x_{n+1}=rx_n(1-x_n)</math>, whose basins of attraction for various values of the parameter ''r'' are shown in the figure. If <math>r=2.6</math>, all starting ''x'' values of <math>x<0</math> will rapidly lead to function values that go to negative infinity; starting ''x'' values of <math>x>0</math> will go to infinity. But for <math>0<x<1</math> the ''x'' values rapidly converge to <math>x\approx0.615</math>, i.e. at this value of ''r'', a single value of ''x'' is an attractor for the function's behaviour. For other values of ''r'', more than one value of x may be visited: if ''r'' is 3.2, starting values of <math>0<x<1</math> will lead to function values that alternate between <math>x\approx0.513</math> and <math>x\approx0.799</math>. At some values of ''r'', the attractor is a single point (a [[#Fixed_point|"fixed point"]]), at other values of ''r'' two values of ''x'' are visited in turn (a [[period-doubling bifurcation]]); at yet other values of r, any given number of values of ''x'' are visited in turn; finally, for some values of ''r'', an infinitude of points are visited. Thus one and the same dynamic equation can have various types of attractors, depending on its starting parameters.<br />
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动力学方程的参数随着方程的迭代而变化,具体值可能取决于初始参数。一个例子是经过充分研究的[[logistic map]],<math>x{n+1}=rx\u n(1-xün)</math>,其对参数“r”的各种值的吸引范围如图所示。如果<math>r=2.6</math>,所有开始的<math>x<0</math>的“x”值将迅速导致函数值变为负无穷大;<math>x>0开始的“x”值将变为无穷大。但对于<math>0<x<1</math>“x”值迅速收敛到<math>x\approx0.615</math>,即在“r”值处,单个值“x”是函数行为的吸引子。对于“r”的其他值,可以访问x的多个值:如果“r”为3.2,<math>0<x<1</math>的起始值将导致函数值在<math>x\approx0.513</math>和<math>x\approx0.799</math>之间交替。在“r”的某些值处,吸引子是一个单点(a[[#不动点|“不动点”]]),在“r”的其他值处,依次访问“x”的两个值(a[[倍周期分岔]]);在r的其他值处,依次访问任意给定数量的“x”值;最后,对于“r”的某些值,访问无穷多个点。因此,同一个动力学方程可以有不同类型的吸引子,这取决于它的起始参数。<br />
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A single-variable (univariate) linear difference equation of the homogeneous form <math>x_t=ax_{t-1}</math> diverges to infinity if |a| > 1 from all initial points except 0; there is no attractor and therefore no basin of attraction. But if |a| < 1 all points on the number line map asymptotically (or directly in the case of 0) to 0; 0 is the attractor, and the entire number line is the basin of attraction.<br />
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齐次形式的单变量(单变量)线性差分方程<math>x_t=ax{t-1}</math>从除0以外的所有初始点| A>1发散到无穷大;没有吸引子,因此没有吸引池。但是如果| a |<1,则数线图上的所有点渐进地(或在0的情况下直接)到0;0是吸引子,整个数线是吸引域。<br />
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==Basins of attraction吸引池==<br />
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Likewise, a linear matrix difference equation in a dynamic vector X, of the homogeneous form <math>X_t=AX_{t-1}</math> in terms of square matrix A will have all elements of the dynamic vector diverge to infinity if the largest eigenvalue of A is greater than 1 in absolute value; there is no attractor and no basin of attraction. But if the largest eigenvalue is less than 1 in magnitude, all initial vectors will asymptotically converge to the zero vector, which is the attractor; the entire n-dimensional space of potential initial vectors is the basin of attraction.<br />
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同样地,动态向量X中的线性矩阵差分方程,如果a的最大特征值绝对值大于1,则动态向量X中的所有元素<math>X_t=AX_{t-1}</math> 都将发散到无穷大;不存在<font color="#ff8000"> 吸引子</font>和吸引池。但如果最大特征值小于1,则所有初始向量将渐近收敛于零向量,即零为吸引子;潜在初始向量的整个n维空间就是<font color="#ff8000"> 吸引池</font>。<br />
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An attractor's '''basin of attraction''' is the region of the [[phase space]], over which iterations are defined, such that any point (any [[initial condition]]) in that region will [[asymptotic behavior|asymptotically]] be iterated into the attractor. For a [[stability (mathematics)|stable]] [[linear system]], every point in the phase space is in the basin of attraction. However, in [[nonlinear system]]s, some points may map directly or asymptotically to infinity, while other points may lie in a different basin of attraction and map asymptotically into a different attractor; other initial conditions may be in or map directly into a non-attracting point or cycle.<ref>{{cite journal|last1=Strelioff|first1=C.|last2=Hübler|first2=A.|title=Medium-Term Prediction of Chaos|journal=Phys. Rev. Lett.|date=2006|volume=96|issue=4|doi=10.1103/PhysRevLett.96.044101|pmid=16486826|page=044101}}</ref><br />
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吸引子的“吸引池”是[[相空间]]的区域,在该区域上定义迭代,因此该区域中的任何点(任何[[初始条件]])将[[渐近行为|渐进]]迭代到<font color="#ff8000"> 吸引子</font>中。对于一个[[稳定性(数学)|稳定]][[线性系统]],相空间中的每一点都在吸引池中。然而,在[[非线性系统]]s中,有些点可能直接或渐近地映射到无穷大,而另一些点可能位于不同的吸引池中并渐进地映射到不同的吸引子;其他初始条件可能位于或直接映射到一个非吸引点或循环中。<ref>{{cite journal|last1=Strelioff|first1=C.|last2=Hübler|first2=A.|title=Medium-Term Prediction of Chaos|journal=Phys. Rev. Lett.|date=2006|volume=96|issue=4|doi=10.1103/PhysRevLett.96.044101|pmid=16486826|page=044101}}</ref><br />
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Similar features apply to linear differential equations. The scalar equation <math> dx/dt =ax</math> causes all initial values of x except zero to diverge to infinity if a > 0 but to converge to an attractor at the value 0 if a < 0, making the entire number line the basin of attraction for 0. And the matrix system <math>dX/dt=AX</math> gives divergence from all initial points except the vector of zeroes if any eigenvalue of the matrix A is positive; but if all the eigenvalues are negative the vector of zeroes is an attractor whose basin of attraction is the entire phase space.<br />
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类似的特征也适用于线性微分方程。标量方程<math> dx/dt =ax</math> 导致除0以外的所有 x 的初始值在 a > 0时发散到无穷大,但在 a < 0时收敛到<font color="#ff8000"> 吸引子</font>,使整条数线成为0的吸引池。矩阵系统 <math>dX/dt=AX</math>如果矩阵 A 的任何特征值是正的,则该矩阵系统从除零向量以外的所有初始点发散; 但如果所有特征值都是负的,则零向量是吸引池为整个相空间的<font color="#ff8000"> 吸引子</font>。<br />
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===Linear equation or system线性方程或系统===<br />
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A single-variable (univariate) linear [[difference equation]] of the [[homogeneous equation|homogeneous form]] <math>x_t=ax_{t-1}</math> diverges to infinity if |''a''| > 1 from all initial points except 0; there is no attractor and therefore no basin of attraction. But if |''a''| < 1 all points on the number line map asymptotically (or directly in the case of 0) to 0; 0 is the attractor, and the entire number line is the basin of attraction.<br />
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[[齐次方程|齐次形式]]<math>x|t=ax{t-1}</math>的单变量(单变量)线性[[差分方程]]发散到无穷大,如果除了0以外的所有初始点|“A”>>1;没有<font color="#ff8000"> 吸引子</font>,因此没有吸引池。但如果 |''a''| < 1,则数线图上的所有点渐进地(或在0的情况下直接映射)到0;0是吸引子,整个数线是吸引池。<br />
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Equations or systems that are nonlinear can give rise to a richer variety of behavior than can linear systems. One example is Newton's method of iterating to a root of a nonlinear expression. If the expression has more than one real root, some starting points for the iterative algorithm will lead to one of the roots asymptotically, and other starting points will lead to another. The basins of attraction for the expression's roots are generally not simple&mdash;it is not simply that the points nearest one root all map there, giving a basin of attraction consisting of nearby points. The basins of attraction can be infinite in number and arbitrarily small. For example, for the function <math>f(x)=x^3-2x^2-11x+12</math>, the following initial conditions are in successive basins of attraction:<br />
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与线性系统相比,非线性方程或系统可以产生更多种类的行为。一个例子是非线性表达式根的牛顿迭代法。如果表达式有多个实根,则迭代算法的某些起始点会渐近地得出其中一个根,而其他起始点会得出另一个根。表达式根的吸引池通常并不简单,最接近一个根的点都映射到那里,从而形成由附近点组成的吸引区。吸引的区域在数值上可以是无限的,可以任意小。例如,对于函数<math>f(x)=x^3-2x^2-11x+12</math>,以下初始条件在连续的吸引池中:<br />
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Likewise, a linear [[matrix difference equation]] in a dynamic [[coordinate vector|vector]] ''X'', of the homogeneous form <math>X_t=AX_{t-1}</math> in terms of [[square matrix]] ''A'' will have all elements of the dynamic vector diverge to infinity if the largest [[eigenvalue]] of ''A'' is greater than 1 in absolute value; there is no attractor and no basin of attraction. But if the largest eigenvalue is less than 1 in magnitude, all initial vectors will asymptotically converge to the zero vector, which is the attractor; the entire ''n''-dimensional space of potential initial vectors is the basin of attraction.<br />
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同样地,在动态[[坐标向量|向量]''X''中的线性[[矩阵差分方程]]在[[平方矩阵]]''a'中的齐次形式<math>X|t=AX{t-1}</math>中,如果“a”的最大[[特征值]]在绝对值上大于1,则动态向量的所有元素将发散到无穷大;没有吸引子,也没有吸引池。但如果最大特征值小于1,则所有初始向量将渐近收敛于零向量,即零为吸引子;潜在初始向量的整个n维空间就是吸引池。<br />
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Basins of attraction in the complex plane for using Newton's method to solve x<sup>5</sup>&nbsp;−&nbsp;1&nbsp;=&nbsp;0. Points in like-colored regions map to the same root; darker means more iterations are needed to converge.<br />
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用牛顿法求解 x<sup>5</sup>&nbsp;−&nbsp;1&nbsp;=&nbsp;0。相似颜色区域中的点映射到同一个根; 颜色较深意味着需要更多的迭代来收敛。<br />
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Similar features apply to linear [[differential equation]]s. The scalar equation <math> dx/dt =ax</math> causes all initial values of ''x'' except zero to diverge to infinity if ''a'' > 0 but to converge to an attractor at the value 0 if ''a'' < 0, making the entire number line the basin of attraction for 0. And the matrix system <math>dX/dt=AX</math> gives divergence from all initial points except the vector of zeroes if any eigenvalue of the matrix ''A'' is positive; but if all the eigenvalues are negative the vector of zeroes is an attractor whose basin of attraction is the entire phase space.<br />
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类似的特征也适用于线性[[微分方程]]s。标量方程<math>dx/dt=ax</math>会导致“x”的所有初始值(除了0)发散到无穷大,如果“a”<0,则收敛到值为0的吸引子,使整条数线成为0的吸引域。如果矩阵“A”的任何特征值为正,则矩阵系统的dX/dt=AX除了零向量外,会从所有初始点发散;但如果所有特征值都为负,则零点向量是一个吸引子,其吸引域是整个相空间。<br />
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2.35287527 converges to 4;<br />
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2.35287527汇聚到4;<br />
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===Nonlinear equation or system非线性方程或系统===<br />
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2.35284172 converges to −3;<br />
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2.35284172 收敛到 −3;<br />
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2.35283735 converges to 4;<br />
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2.35283735收敛到4;<br />
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Equations or systems that are [[nonlinear system|nonlinear]] can give rise to a richer variety of behavior than can linear systems. One example is [[Newton's method]] of iterating to a root of a nonlinear expression. If the expression has more than one [[real number|real]] root, some starting points for the iterative algorithm will lead to one of the roots asymptotically, and other starting points will lead to another. The basins of attraction for the expression's roots are generally not simple&mdash;it is not simply that the points nearest one root all map there, giving a basin of attraction consisting of nearby points. The basins of attraction can be infinite in number and arbitrarily small. For example,<ref>Dence, Thomas, "Cubics, chaos and Newton's method", ''[[Mathematical Gazette]]'' 81, November 1997, 403–408.</ref> for the function <math>f(x)=x^3-2x^2-11x+12</math>, the following initial conditions are in successive basins of attraction:<br />
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与线性系统相比,[[非线性系统|非线性]]的方程或系统可以产生更丰富的行为。一个例子是迭代到非线性表达式根的[[牛顿方法]]。如果表达式有多个[[实数|实]]根,则迭代算法的某些起始点将渐近地导致其中一个根,而其他起点将导致另一个根。表达式根的吸引域通常并不简单,最接近一个根的点都映射到那里,从而形成由附近点组成的吸引区。吸引的盆地可以是无限的,可以任意小。例如,<ref>dance,Thomas,“Cubics,chaos and Newton's method”,“[[mathematic Gazette]]”811997年11月,403–408。</ref>对于函数<math>f(x)=x^3-2x^2-11x+12</math>,以下初始条件在连续的吸引域中:<br />
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2.352836327 converges to −3;<br />
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2.352836327 converges to −3;<br />
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2.352836323 converges to 1.<br />
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2.352836323汇聚为1。<br />
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[[File:newtroot 1 0 0 0 0 m1.png|thumb|Basins of attraction in the complex plane for using Newton's method to solve ''x''<sup>5</sup>&nbsp;−&nbsp;1&nbsp;=&nbsp;0. Points in like-colored regions map to the same root; darker means more iterations are needed to converge.]]<br />
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[[文件:newtroot 10 0 0 0 m1.png |拇指|复杂平面中的吸引盆地,用于使用牛顿法求解“x”<sup>5</sup>—1&nbsp;=0。相同颜色区域中的点映射到同一根;较暗表示需要更多迭代才能收敛。]]<br />
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Newton's method can also be applied to complex functions to find their roots. Each root has a basin of attraction in the complex plane; these basins can be mapped as in the image shown. As can be seen, the combined basin of attraction for a particular root can have many disconnected regions. For many complex functions, the boundaries of the basins of attraction are fractals.<br />
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牛顿法也可以应用于求复变函数的根。在复杂的平面上,每个根部都有一个吸引池; 这些区域可以如图所示绘制出来。可以看出,组合区域的吸引力为一个特定的根可以有许多不相连的地区。对于许多复杂的函数,吸引池的边界是分形。<br />
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:2.35287527 converges to 4;<br />
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:2.35284172 converges to −3;<br />
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:2.35283735 converges to 4;<br />
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Parabolic partial differential equations may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The Ginzburg–Landau, the Kuramoto–Sivashinsky, and the two-dimensional, forced Navier–Stokes equations are all known to have global attractors of finite dimension.<br />
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<font color="#ff8000"> 抛物型偏微分方程</font>可能具有有限维<font color="#ff8000"> 吸引子</font>。方程的扩散部分阻尼更高的频率,在某些情况下导致一个全局吸引子。<font color="#ff8000"> Ginzburg-Landau 方程、 Kuramoto-Sivashinsky 方程和二维强迫 Navier-Stokes 方程</font>都具有有限维的全局吸引子。<br />
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:2.352836327 converges to −3;<br />
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:2.352836323 converges to 1.<br />
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For the three-dimensional, incompressible Navier–Stokes equation with periodic boundary conditions, if it has a global attractor, then this attractor will be of finite dimensions.<br />
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对于具有周期边界条件的三维不可压 Navier-Stokes 方程,如果它有一个全局吸引子,那么这个吸引子将是有限维的。<br />
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Newton's method can also be applied to [[complex analysis|complex functions]] to find their roots. Each root has a basin of attraction in the [[complex plane]]; these basins can be mapped as in the image shown. As can be seen, the combined basin of attraction for a particular root can have many disconnected regions. For many complex functions, the boundaries of the basins of attraction are [[fractal]]s.<br />
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== Partial differential equations偏微分方程 ==<br />
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[[File:Chua-chaotic-hidden-attractor.jpg|thumb|<br />
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[文件: Chua-chaotic-hidden-attractor. jpg | thumb | <br />
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[[Parabolic partial differential equation]]s may have finite-dimensional attractors. The diffusive part of the equation damps higher frequencies and in some cases leads to a global attractor. The ''Ginzburg–Landau'', the ''Kuramoto–Sivashinsky'', and the two-dimensional, forced [[Navier–Stokes equation]]s are all known to have global attractors of finite dimension.<br />
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[[抛物型偏微分方程]]可能具有有限维吸引子。方程的扩散部分会阻尼更高的频率,在某些情况下会导致全局吸引子。<font color="#ff8000"> “金茨堡-兰道”、“库拉莫托-西瓦辛斯基”和二维受迫[[纳维-斯托克斯方程]]</font>都具有有限维的全局吸引子。<br />
<br />
Chaotic hidden attractor (green domain) in Chua's system.<br />
<br />
蔡氏系统中的混沌隐藏吸引子(绿域)。<br />
<br />
<br />
<br />
Trajectories with initial data in a neighborhood of two saddle points (blue) tend (red arrow) to infinity or tend (black arrow) to stable zero equilibrium point (orange).<br />
<br />
带有初始数据的一个邻近鞍点(蓝色)的轨迹趋向(红色箭头)至无穷大或趋向(黑色箭头)至稳定的零平衡点(橙色)。<br />
<br />
For the three-dimensional, incompressible Navier–Stokes equation with periodic [[boundary condition]]s, if it has a global attractor, then this attractor will be of finite dimensions.<ref>[[Geneviève Raugel]], Global Attractors in Partial Differential Equations, ''Handbook of Dynamical Systems'', Elsevier, 2002, pp. 885–982.</ref><br />
对于具有周期[[边界条件]]s的三维不可压缩Navier–Stokes方程,如果它有一个全局吸引子,那么这个吸引子将是有限维的。<ref>[[Geneviève Raugel]], Global Attractors in Partial Differential Equations, ''Handbook of Dynamical Systems'', Elsevier, 2002, pp. 885–982.</ref><br />
<br />
]]<br />
<br />
]]<br />
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<!-- This should be uncommented once the <nowiki>{{Notability}}</nowiki> in [[hidden attractor]] is solved. See the talk page for more information.<br />
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From a computational point of view, attractors can be naturally regarded as self-excited attractors or<br />
<br />
从计算的角度来看,吸引子可以自然地被看作自激吸引子或<br />
<br />
== Numerical localization (visualization) of attractors: self-excited and hidden attractors 吸引子的数值局部化(可视化):自激吸引子和隐吸引子==<br />
<br />
hidden attractors. Self-excited attractors can be localized numerically by standard computational procedures, in which after a transient sequence, a trajectory starting from a point on an unstable manifold in a small neighborhood of an unstable equilibrium reaches an attractor, such as the classical attractors in the Van der Pol, Belousov–Zhabotinsky, Lorenz, and many other dynamical systems. In contrast, the basin of attraction of a hidden attractor does not contain neighborhoods of equilibria, so the hidden attractor cannot be localized by standard computational procedures.<br />
<br />
隐藏吸引子。<font color="#ff8000"> 自激吸引子</font>可以用标准的计算程序进行数值局部化,在一个瞬态序列之后,从不稳定平衡点的小邻域的不稳定流形上的一个点出发的轨迹将到达一个吸引子,如 Van der Pol、 Belousov-Zhabotinsky、 Lorenz 等许多其他动力系统中的经典吸引子。相反,一个隐藏吸引子的吸引池不包含平衡邻域,因此隐藏吸引子不能被标准的计算程序局部化。<br />
<br />
[[File:Chua-chaotic-hidden-attractor.jpg|thumb|<br />
<br />
--><br />
<br />
--><br />
<br />
Chaotic [[hidden attractor]] (green domain) in [[Chua's circuit|Chua's system]].<br />
[[蔡氏电路|蔡氏系统]]中的混沌[[隐藏吸引子]](绿域)。<br />
<br />
Trajectories with initial data in a neighborhood of two saddle points (blue) tend (red arrow) to infinity or tend (black arrow) to stable zero equilibrium point (orange).<br />
<br />
初始数据位于两个鞍点附近(蓝色)的轨迹趋向于无穷大(红色箭头)或趋向于(黑色箭头)稳定的零平衡点(橙色)。<br />
<br />
]]<br />
<br />
<br />
<br />
From a computational point of view, attractors can be naturally regarded as ''self-excited attractors'' or<br />
<br />
''[[hidden attractor]]s''.<ref name="2011-PLA-Hidden-Chua-attractor">{{cite journal |author1=Leonov G.A. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |<br />
<br />
从计算的角度来看,吸引子可以自然地看作是“自激吸引子”或''[[隐藏吸引子]]s''<ref name="2011-PLA-Hidden-Chua-attractor">{{cite journal |author1=Leonov G.A. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |<br />
<br />
year = 2011 |<br />
<br />
title = Localization of hidden Chua's attractors |<br />
<br />
journal = Physics Letters A |<br />
<br />
volume = 375 |<br />
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issue = 23 |<br />
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pages = 2230–2233 |<br />
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url = http://www.math.spbu.ru/user/nk/PDF/2011-PhysLetA-Hidden-Attractor-Chua.pdf |<br />
<br />
doi = 10.1016/j.physleta.2011.04.037}}<br />
<br />
</ref><ref>{{cite journal<br />
<br />
|author1=Bragin V.O. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |author4=Leonov G.A. | year = 2011<br />
<br />
| title = Algorithms for Finding Hidden Oscillations in Nonlinear Systems. The Aizerman and Kalman Conjectures and Chua's Circuits<br />
<br />
| journal = Journal of Computer and Systems Sciences International<br />
<br />
| volume = 50<br />
<br />
| number = 5<br />
<br />
| pages = 511–543<br />
<br />
| last = Ruelle<br />
<br />
| last = Ruelle<br />
<br />
| url = http://www.math.spbu.ru/user/nk/PDF/2011-TiSU-Hidden-oscillations-attractors-Aizerman-Kalman-conjectures.pdf<br />
<br />
| first = David<br />
<br />
第一名: David<br />
<br />
| doi = 10.1134/S106423071104006X}}<br />
<br />
| authorlink = David Ruelle<br />
<br />
| authorlink = David Ruelle<br />
<br />
</ref><ref name="2012-Physica-D-Hidden-attractor-Chua-circuit-smooth">{{cite journal |author1=Leonov G.A. |author2=Vagaitsev V.I. |author3=Kuznetsov N.V. |<br />
<br />
| title = What is...a Strange Attractor?<br />
<br />
| title = 什么是... 奇异吸引子?<br />
<br />
year = 2012 |<br />
<br />
| journal = Notices of the American Mathematical Society<br />
<br />
| journal = 美国数学学会公告<br />
<br />
title = Hidden attractor in smooth Chua systems |<br />
<br />
|date=August 2006<br />
<br />
| date = August 2006<br />
<br />
journal = Physica D |<br />
<br />
| volume = 53<br />
<br />
53<br />
<br />
volume = 241 |<br />
<br />
| issue = 7<br />
<br />
第7期<br />
<br />
issue = 18 |<br />
<br />
| pages = 764–765<br />
<br />
| 页 = 764-765<br />
<br />
pages = 1482–1486 |<br />
<br />
| url = http://www.ams.org/notices/200607/what-is-ruelle.pdf<br />
<br />
Http://www.ams.org/notices/200607/what-is-ruelle.pdf<br />
<br />
url = http://www.math.spbu.ru/user/nk/PDF/2012-Physica-D-Hidden-attractor-Chua-circuit-smooth.pdf |<br />
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| accessdate = 16 January 2008 }}<br />
<br />
16 January 2008}}<br />
<br />
doi = 10.1016/j.physd.2012.05.016}}<br />
<br />
</ref><ref name="2013-IJBC-Hidden-attractors">{{cite journal |author1=Leonov G.A. |author2=Kuznetsov N.V. |<br />
<br />
year = 2013 |<br />
<br />
title = Hidden attractors in dynamical systems. From hidden oscillations in Hilbert–Kolmogorov, Aizerman, and Kalman problems to hidden chaotic attractor in Chua circuits |<br />
<br />
journal = International Journal of Bifurcation and Chaos |<br />
<br />
volume = 23 |<br />
<br />
issue = 1 |<br />
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pages = art. no. 1330002|<br />
<br />
doi = 10.1142/S0218127413300024|<br />
<br />
doi-access = free }}<br />
<br />
</ref> Self-excited attractors can be localized numerically by standard computational procedures, in which after a transient sequence, a trajectory starting from a point on an unstable manifold in a small neighborhood of an unstable equilibrium reaches an attractor, such as the classical attractors in the [[Van der Pol oscillator|Van der Pol]], [[Belousov–Zhabotinsky reaction|Belousov–Zhabotinsky]], [[Lorenz attractor|Lorenz]], and many other dynamical systems. In contrast, the basin of attraction of a [[hidden attractor]] does not contain neighborhoods of equilibria, so the [[hidden attractor]] cannot be localized by standard computational procedures.<br />
<br />
自激吸引子可以用标准的计算程序进行数值定域,在一个瞬态序列之后,从不稳定平衡小邻域中不稳定流形上的点开始的轨迹到达吸引子,例如[[Van der Pol振荡器| Van der Pol]]中的经典吸引子,[[Belousov–Zhabotinsky reaction | Belousov–Zhabotinsky]],[[Lorenz吸引子| Lorenz]],以及许多其他动力系统。相比之下,[[隐藏吸引子]]的吸引域不包含平衡邻域,因此[[隐藏吸引子]]不能用标准的计算程序进行局部化。<br />
--><br />
<br />
== See also 请参阅==<br />
<br />
{{commons|Attractor}}<br />
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* [[Cycle detection]]<br />
<br />
* [[Hyperbolic set]]<br />
<br />
* [[Stable manifold]]<br />
<br />
* [[Steady state]]<br />
<br />
{{常见 |吸引子}}<br />
<br />
*[[循环检测]]<br />
<br />
*[双曲线集][]<br />
<br />
*[[稳定流形]]<br />
<br />
*[[稳态]]<br />
<br />
Category:Limit sets<br />
<br />
类别: 极限集<br />
<br />
<noinclude><br />
<br />
<small>This page was moved from [[wikipedia:en:Attractor]]. Its edit history can be viewed at [[吸引子/edithistory]]</small></noinclude><br />
<br />
[[Category:待整理页面]]</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%B8%89%E4%BD%93%E9%97%AE%E9%A2%98&diff=20367三体问题2020-12-21T08:03:13Z<p>Vicky:</p>
<hr />
<div>已由Lincent审校。<br />
<br />
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.[1] The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists,[1] as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.<br />
<br />
在物理学和经典力学领域中,三体问题是根据牛顿运动定律和牛顿万有引力定律按照三点处质量体的初始位置和速度(或动量)求出它们随后的运动的问题。三体是n体问题中的一个特例。与双体问题不同的是,三体问题不存在一般的闭式解,因为产生的动力系统对于大多数初始条件来说是混沌的,所以一般需要数值方法求解。<br />
<br />
--[[用户:Vicky|Vicky]]([[用户讨论:Vicky|讨论]])n-body problem 翻译为 “多体问题”或“N体问题”会不会更好一些?<br />
<br />
Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, and the Sun.[2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles.<br />
<br />
历史上看,第一个被拓展研究的特定三体问题是月球、地球和太阳构成的“三体”问题。从现代意义上讲,拓展的三体问题可以是经典力学或量子力学中模拟三个粒子运动的任何问题。<br />
<br />
==数学描述==<br />
<br />
三体的数学表达式可以用三个质量为<math>m_i</math>的相互作用的物体的矢量位置<math>\mathbf{r_i} = (x_i, y_i, z_i)</math>的牛顿运动方程来表示:<br />
<br />
<math>\begin{align}<br />
\ddot\mathbf{r}_{\mathbf{1}} &= -G m_2 \frac{\mathbf{r_1} - \mathbf{r_2}}{|\mathbf{r_1} - \mathbf{r_2}|^3} - G m_3 \frac{\mathbf{r_1} - \mathbf{r_3}}{|\mathbf{r_1} - \mathbf{r_3}|^3}, \\<br />
\ddot\mathbf{r}_{\mathbf{2}} &= -G m_3 \frac{\mathbf{r_2} - \mathbf{r_3}}{|\mathbf{r_2} - \mathbf{r_3}|^3} - G m_1 \frac{\mathbf{r_2} - \mathbf{r_1}}{|\mathbf{r_2} - \mathbf{r_1}|^3}, \\<br />
\ddot\mathbf{r}_{\mathbf{3}} &= -G m_1 \frac{\mathbf{r_3} - \mathbf{r_1}}{|\mathbf{r_3} - \mathbf{r_1}|^3} - G m_2 \frac{\mathbf{r_3} - \mathbf{r_2}}{|\mathbf{r_3} - \mathbf{r_2}|^3}.<br />
\end{align}</math><br />
<br />
其中<math>G</math>为万有引力常数。这是一组9个二阶微分方程构成的方程组。这个问题也可以用哈密顿形式等价表示,此时可以用一组18个一阶微分方程来描述,这些方程分别对应于位置<math>\mathbf{r_i}</math>和动量<math>\mathbf{p_i}</math>的一个分量:<br />
<br />
:<math><br />
\frac{d \mathbf{r_i}}{dt} = \frac{\partial \mathcal{H}}{\partial \mathbf{p_i}}, \qquad \frac{d\mathbf{p_i}}{dt} = -\frac{\partial \mathcal{H}}{\partial \mathbf{r_i}},<br />
</math><br />
<br />
其中<math>\mathcal{H}</math>是哈密顿 Hamiltonian函数:<br />
<br />
:<math><br />
\mathcal{H} = -\frac{G m_1 m_2}{|\mathbf{r_1} - \mathbf{r_2}|}-\frac{G m_2 m_3}{|\mathbf{r_3} - \mathbf{r_2}|} -\frac{G m_3 m_1}{|\mathbf{r_3} - \mathbf{r_1}|} + \frac{\mathbf{p_1}^2}{2m_1} + \frac{\mathbf{p_2}^2}{2m_2} + \frac{\mathbf{p_3}^2}{2m_3}.<br />
</math><br />
<br />
这种情况下,<math>\mathcal{H}</math>仅仅是系统的总能量,重力加上动能。<br />
<br />
==受限制的三题问题==<br />
<br />
In the restricted three-body problem,[3] a body of negligible mass (the "planetoid") moves under the influence of two massive bodies. Having negligible mass, the force that the planetoid exerts on the two massive bodies may be neglected, and the system can be analysed and can therefore be described in terms of a two-body motion. Usually this two-body motion is taken to consist of circular orbits around the center of mass, and the planetoid is assumed to move in the plane defined by the circular orbits.<br />
<br />
在受限制的三体问题中,一个质量可忽略不计的天体(“小行星”)在两个质量巨大的天体的影响下运动。由于质量可忽略不计,小行星对这两个质量巨大的天体所施加的力可忽略不计,因此可以可以用两个物体的运动来描述,对该系统进行分析。通常这种两体运动被认为是由围绕质心的圆形轨道组成的,并且假定小行星在圆形轨道所定义的平面内运动。<br />
<br />
The restricted three-body problem is easier to analyze theoretically than the full problem. It is of practical interest as well since it accurately describes many real-world problems, the most important example being the Earth–Moon–Sun system. For these reasons, it has occupied an important role in the historical development of the three-body problem.<br />
<br />
受限制的三体问题比完全的三体问题更容易从理论上分析。它也具有实际意义,因为它准确地描述了许多现实世界的问题,其中最重要的例子是地球-月亮-太阳的系统,这也是在三体问题的历史发展中有重要地位的一个典型。<br />
<br />
Mathematically, the problem is stated as follows. Let {\displaystyle m_{1,2}} {\displaystyle m_{1,2}} be the masses of the two massive bodies, with (planar) coordinates {\displaystyle (x_{1},y_{1})} (x_{1},y_{1}) and {\displaystyle (x_{2},y_{2})} (x_{2},y_{2}), and let {\displaystyle (x,y)} (x,y) be the coordinates of the planetoid. For simplicity, choose units such that the distance between the two massive bodies, as well as the gravitational constant, are both equal to {\displaystyle 1} 1. Then, the motion of the planetoid is given by<br />
<br />
在数学的表述上,设<math>m_{1,2}</math>为两个大质量天体的质量,二维平面坐标<math>(x_1, y_1)</math>和<math>(x_2, y_2)</math>分别为小行星的坐标。简单起见,选择的单位应该要确保两大质量天体的距离和重力常数都等于1。则小行星的运动可以用公式描述为:<br />
<br />
:<math><br />
\begin{align}<br />
\frac{d^2 x}{dt^2} = -m_1 \frac{x - x_1}{r_1^3} - m_2 \frac{x - x_2}{r_2^3} \\<br />
\frac{d^2 y}{dt^2} = -m_1 \frac{y - y_1}{r_1^3} - m_2 \frac{y - y_2}{r_2^3},<br />
\end{align}<br />
</math><br />
<br />
其中<math>r_i = \sqrt{(x - x_i)^2 + (y - y_i)^2}</math>,在这种形式下,运动方程通过坐标具有明确的时间依赖性<math>x_i(t), y_i(t)</math>。但可以通过转换为旋转参考系来消除这种时间相关性,从而简化了后续的分析。<br />
<br />
==求解==<br />
<br />
There is no general analytical solution to the three-body problem given by simple algebraic expressions and integrals.[1] Moreover, the motion of three bodies is generally non-repeating, except in special cases.[5]<br />
<br />
由简单的代数表达式和积分给出的三体没有一般的解析解。此外,除特殊情况,三个物体的运动一般是不重复的。<br />
<br />
<br />
On the other hand, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists a series solution in powers of t1/3 for the 3-body problem.[6] This series converges for all real t, except for initial conditions corresponding to zero angular momentum. (In practice the latter restriction is insignificant since such initial conditions are rare, having Lebesgue measure zero.)<br />
<br />
另一方面,1912年芬兰数学家**Karl Fritiof Sundman**证明了三体问题存在一个 {{math|''t''<sup>1/3</sup>}}幂次方的级数解。除了对应于角动量为零的初始条件外,这个级数对所有实数t都收敛。<br />
<br />
An important issue in proving this result is the fact that the radius of convergence for this series is determined by the distance to the nearest singularity. Therefore, it is necessary to study the possible singularities of the 3-body problems. As it will be briefly discussed below, the only singularities in the 3-body problem are binary collisions (collisions between two particles at an instant) and triple collisions (collisions between three particles at an instant).<br />
<br />
证明这个结果的一个重要问题是,该序列的收敛半径是由到最近奇点的距离决定的。因此,有必要研究三体问题的可能奇点。三体问题中唯一的奇点是二元碰撞(两个粒子在瞬间的碰撞)和三元碰撞(三个粒子在瞬间的碰撞),下面会进行简单的讨论。<br />
<br />
Collisions, whether binary or triple (in fact, any number), are somewhat improbable, since it has been shown that they correspond to a set of initial conditions of measure zero. However, there is no criterion known to be put on the initial state in order to avoid collisions for the corresponding solution. So Sundman's strategy consisted of the following steps:<br />
<br />
无论是二元的还是三元的(事实上是任何数目) 碰撞都不太可能发生,因为已经证明它们对应于测度为零的一组初始条件。然而,没有已知的标准被放在初始状态,以对相应的解避免碰撞。因此,**Sundman**的求解方法包括以下步骤:<br />
<br />
<br />
1. Using an appropriate change of variables to continue analyzing the solution beyond the binary collision, in a process known as regularization.<br />
2. Proving that triple collisions only occur when the angular momentum L vanishes. By restricting the initial data to L ≠ 0, he removed all real singularities from the transformed equations for the 3-body problem.<br />
3. Showing that if L ≠ 0, then not only can there be no triple collision, but the system is strictly bounded away from a triple collision. This implies, by using Cauchy's existence theorem for differential equations, that there are no complex singularities in a strip (depending on the value of L) in the complex plane centered around the real axis (shades of Kovalevskaya).<br />
4. Find a conformal transformation that maps this strip into the unit disc. For example, if s = t1/3 (the new variable after the regularization) and if |ln s| ≤ β,[clarification needed] then this map is given by<br />
<br />
<br />
1. 使用适当的变量变化来继续分析二元碰撞之外的解,这个过程称为正则化。<br />
<br />
2. 证明只有在角动量L消失时才会发生三元碰撞。通过将初始数据限制为L ≠ 0,从三体问题的变换方程中删除了所有实数奇点。<br />
<br />
3. 证明了如果L≠0,则不仅不存在三元碰撞,而且系统严格有界远离三元碰撞。这意味着,通过对微分方程使用柯西存在性定理,在以实际轴为中心的复平面(Kovalevskaya的阴影)中,一个条带区域(取决于L的值)中不存在复奇点。<br />
<br />
4. 找到一个保角变换,把这个条带映射到单位圆盘。例如,如果s={{math|''t''<sup>1/3</sup>}}(正则化后的新变量),并且{{math|{{abs|ln ''s''}} ≤ ''β''}}(需要证明),则映射可由下式给出:<br />
<br />
:<math>\sigma = \frac{e^\frac{\pi s}{2\beta} - 1}{e^\frac{\pi s}{2\beta} + 1}.</math><br />
<br />
This finishes the proof of Sundman's theorem.<br />
上述即为完整的Sundman定律的证明。<br />
<br />
Unfortunately, the corresponding series converges very slowly. That is, obtaining a value of meaningful precision requires so many terms that this solution is of little practical use. Indeed, in 1930, David Beloriszky calculated that if Sundman's series were to be used for astronomical observations, then the computations would involve at least 108000000 terms.[7]<br />
<br />
但不幸运的是,对应的级数收敛得非常慢。也就是说,为了获得一定精度的值需要很多级数项,这样的解法并没有什么实际用途。的确,在1930年,David Beloriszky计算出,如果将Sundman级数用于天文观测,则计算将至少涉及10<sup>{{val|8000000}}</sup>项。<br />
<br />
==特殊的求解方法==<br />
<br />
In 1767, Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. See Euler's three-body problem.<br />
<br />
1767年,**Leonhard Euler**提出了三个周期解系列,其中三个质量在每个瞬间共线。<br />
<br />
1772年,拉格朗日(Lagrange)找到了一系列解,其中三个质量在每个瞬间形成一个等边三角形。这些解决方案与Euler的共线解一起构成了三体问题的中心配置。这些解决方案对于任何质量比均有效,并且质量沿开普勒椭圆形运动。这四个族是唯一有明确解析公式的已知解决方案。在圆形受限三体问题的特殊情况下,这些解决方案在与原边一起旋转的框架中观察时,变为称为L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>, L<sub>4</sub>和L<sub>5</sub>,并且叫做拉格朗日点,其中L<sub>3</sub>, L<sub>4</sub>是拉格朗日的对称解的实例。<br />
<br />
在1892年至1899年的工作中,**Henri Poincaré**建立了无穷有限三体问题的周期解,以及将这些解法继续推广到一般三体问题的技巧。<br />
<br />
1893年,迈塞尔提出了现在所说的毕达哥拉斯三体问题:将比例为3:4:5的三个质量置于3:4:5直角三角形的顶点处。Burrau在1913年进一步研究了这个问题。1967年,Victor Szebehely和C. Frederick Peters利用数值积分理论建立了这个问题的最终逃逸模型,同时找到了附近的周期解。<br />
<br />
20世纪70年代,**Michel Hénon**和 '''Roger A. Broucke'''各自找到了一套解决方案,这些解决方案构成了同一系列解决方案的一部分: Broucke–Henon–Hadjidemetriou族。在这个家族中,这三个物体都具有相同的质量,可以表现出逆行和直行两种形式。在、Broucke的一些解中,两个物体遵循同样的路径。<br />
<br />
<br />
1993年,[[圣塔菲研究所]]的物理学家'''Cris Moore'''提出了一种零角动量解,该解适用于三个相等质量围绕一个八字形运动。这种方法在2000年由数学家'''Alain Chenciner'''和'''Richard Montgomery'''证明。在数值上证明了该解对于质量和轨道参数的小扰动是稳定的,这增加了在物理宇宙中可以观察到这种轨道的可能性。但有人认为不太可能发生这种情况,因为稳定性的范围小。例如,1993年,圣达菲研究所的物理学家克里斯·摩尔(Cris Moore)在数字上发现了一个零角动量解,该解的三个相等质量围绕一个八字形运动。[12]它的正式存在后来在2000年由数学家Alain Chenciner和Richard Montgomery 证明。[13] [14]在数值上证明了该解对于质量和轨道参数的小扰动是稳定的,这增加了在物理宇宙中可以观察到这种轨道的可能性。但是,由于稳定性的范围小,因此不太可能发生这种情况。例如,二元-二元散射事件导标号-8轨道的概率估计为1%的一小部分。<br />
<br />
In 2013, physicists Milovan Šuvakov and Veljko Dmitrašinović at the Institute of Physics in Belgrade discovered 13 new families of solutions for the equal-mass zero-angular-momentum three-body problem.<br />
<br />
2013年,贝尔格莱德物理研究所的物理学家Milovan uvakov 和 Veljko dmitra inovi 发现了等质量零角动量三体问题的13种新的解族。<br />
<br />
In 2015, physicist Ana Hudomal discovered 14 new families of solutions for the equal-mass zero-angular-momentum three-body problem.<br />
<br />
2015年,物理学家 Ana Hudomal 发现了14种等质量零角动量三体问题的新解族。<br />
<br />
In 2017, researchers Xiaoming Li and Shijun Liao found 669 new periodic orbits of the equal-mass zero-angular-momentum three-body problem.[17] This was followed in 2018 by an additional 1223 new solutions for a zero-momentum system of unequal masses.[18]<br />
<br />
2017年,研究人员Xiaoming Li 和Shijun Liao发现了669个等质量零角动量三体问题的新周期轨道。2018年,不等质量的零动量系统又增加了1223个新解。<br />
<br />
In 2018, Li and Liao reported 234 solutions to the unequal-mass "free-fall" three body problem.[19] The free fall formulation of the three body problem starts with all three bodies at rest. Because of this, the masses in a free-fall configuration do not orbit in a closed "loop", but travel forwards and backwards along an open "track".<br />
<br />
<br />
2018年,Li和Liao提出了234个不等质量“自由落体”三体问题的解。三体问题的自由落体公式从所有三个静止的物体开始。正因为如此,质量在一个自由落体配置不在一个闭合的“循环”轨道上运行,而是沿着一个开放的“轨道”向前和向后运行。<br />
<br />
===数值方法===<br />
<br />
Using a computer, the problem may be solved to arbitrarily high precision using numerical integration although high precision requires a large amount of CPU time. In 2019, Breen et al. announced a fast neural network solver, trained using a numerical integrator.[20]<br />
<br />
尽管高精度需要大量的CPU时间,但是通过计算机可以使用数值积分可以得到问题的任意高精度解。在2019年,Breen等人。提出了一种快速的神经网络求解器,使用数字积分器对其进行训练。<br />
<br />
==历史==<br />
<br />
The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Principia (Philosophiæ Naturalis Principia Mathematica). In Proposition 66 of Book 1 of the Principia, and its 22 Corollaries, Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions. In Propositions 25 to 35 of Book 3, Newton also took the first steps in applying his results of Proposition 66 to the lunar theory, the motion of the Moon under the gravitational influence of the Earth and the Sun.<br />
<br />
传统意义上的三个物体的引力问题可以追溯到1687年,当时牛顿发表了他的《自然哲学的数学原理》。在《原理》第一卷的第66号提案及其22个推论中,牛顿首次定义和研究了三个受相互扰动的重力吸引影响的巨大物体的运动问题。在第三册的第25至35条命题中,牛顿也迈出了第一步,将他的66号提案的结果应用到月球理论中,即月球在地球和太阳的引力影响下的运动。<br />
<br />
The physical problem was addressed by Amerigo Vespucci and subsequently by Galileo Galilei; in 1499, Vespucci used knowledge of the position of the Moon to determine his position in Brazil. It became of technical importance in the 1720s, as an accurate solution would be applicable to navigation, specifically for the determination of longitude at sea, solved in practice by John Harrison's invention of the marine chronometer. However the accuracy of the lunar theory was low, due to the perturbing effect of the Sun and planets on the motion of the Moon around the Earth.<br />
<br />
Amerigo Vespucci和随后的Galileo Galilei提出了三体问题; 1499年,Vespucci利用对月球位置的了解来确定自己在巴西的位置。因为这种方法适用于导航,特别是在海上确定经度,1720年代该方法变得非常技术实用。事实上确定经度的问题被John Harrison发明的航海经线仪所解决。但是,由于太阳和行星对月球绕地球运动的干扰作用,月球理论的准确性很低。<br />
<br />
<br />
Jean le Rond d'Alembert and Alexis Clairaut, who developed a longstanding rivalry, both attempted to analyze the problem in some degree of generality; they submitted their competing first analyses to the Académie Royale des Sciences in 1747.[21] It was in connection with their research, in Paris during the 1740s, that the name "three-body problem" (French: Problème des trois Corps) began to be commonly used. An account published in 1761 by Jean le Rond d'Alembert indicates that the name was first used in 1747.<br />
<br />
建立了长期竞争关系的Jean le Rond d'Alembert和Alexis Clairaut都试图以某种普遍性来分析该问题。他们于1747年向皇家科学研究院提交了他们的第一批竞争分析。在1740年代的巴黎,“三体问题”(法语:Problèmedes trois Corps)这个名字开始被普遍使用,与他们的研究有关。Jean le Rond d'Alembert于1761年发布的文章表明该名称最早于1747年使用。<br />
<br />
<br />
==其他涉及三体的问题==<br />
<br />
The term 'three-body problem' is sometimes used in the more general sense to refer to any physical problem involving the interaction of three bodies.<br />
三体问题这个术语有时用在更一般的意义上来指涉及三个物体相互作用的任何物理问题。<br />
<br />
A quantum mechanical analogue of the gravitational three-body problem in classical mechanics is the helium atom, in which a helium nucleus and two electrons interact according to the inverse-square Coulomb interaction. Like the gravitational three-body problem, the helium atom cannot be solved exactly.[23]<br />
<br />
<br />
氦原子是经典力学中引力三体问题的量子力学模拟,其中一个氦原子核和两个电子会产生反平方库仑相互作用,这种相互作用称为经典力学中的三体问题。就像重力三体问题一样,氦原子的三体问题没有精确解。<br />
<br />
In both classical and quantum mechanics, however, there exist nontrivial interaction laws besides the inverse-square force which do lead to exact analytic three-body solutions. One such model consists of a combination of harmonic attraction and a repulsive inverse-cube force.[24] This model is considered nontrivial since it is associated with a set of nonlinear differential equations containing singularities (compared with, e.g., harmonic interactions alone, which lead to an easily solved system of linear differential equations). In these two respects it is analogous to (insoluble) models having Coulomb interactions, and as a result has been suggested as a tool for intuitively understanding physical systems like the helium atom.[24][25]<br />
<br />
<br />
然而,在经典力学和量子力学中,除了平方反力外,还存在着一些非平凡相互作用规律,这些规律可以得到精确的解析解。有一种模型是由谐波吸引和排斥反立方体力的组合而成的。该模型被认为是非平凡的,因为它与一组包含奇异性的非线性微分方程组相关联(例如,与单独的谐波相互作用相比,该关联能够得到易于求解的线性微分方程组)。在这两种情况下,三体问题类似于具有库仑相互作用的(无法解释的)模型,因此,有人提出将其作为直观理解诸如氦原子之类的物理系统的工具。<br />
<br />
The gravitational three-body problem has also been studied using general relativity. Physically, a relativistic treatment becomes necessary in systems with very strong gravitational fields, such as near the event horizon of a black hole. However, the relativistic problem is considerably more difficult than in Newtonian mechanics, and sophisticated numerical techniques are required. Even the full two-body problem (i.e. for arbitrary ratio of masses) does not have a rigorous analytic solution in general relativity.[26]<br />
<br />
引力三体问题也被通过广义相对论进行了研究。在物理上,相对论性的处理在引力场非常强的系统中变得非常必要,比如在黑洞的视界附近。然而,相对论性问题比牛顿力学困难得多,需要复杂的数值技术。即使是完整的两体问题(即任意质量比)在广义相对论中也没有严格的解析解。<br />
<br />
==n体问题==<br />
<br />
The three-body problem is a special case of the n-body problem, which describes how n objects will move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details). However, the Sundman and Wang series converge so slowly that they are useless for practical purposes;[27] therefore, it is currently necessary to approximate solutions by numerical analysis in the form of numerical integration or, for some cases, classical trigonometric series approximations (see n-body simulation). Atomic systems, e.g. atoms, ions, and molecules, can be treated in terms of the quantum n-body problem. Among classical physical systems, the n-body problem usually refers to a galaxy or to a cluster of galaxies; planetary systems, such as stars, planets, and their satellites, can also be treated as n-body systems. Some applications are conveniently treated by perturbation theory, in which the system is considered as a two-body problem plus additional forces causing deviations from a hypothetical unperturbed two-body trajectory.<br />
<br />
三体问题是n体问题的一个特例,它描述了n个物体在其中一种物理力(如重力)下如何运动。这些问题具有收敛幂级数形式的全局解析解,比如,Karl F.Sundman证明n=3的情况,qaudong Wang证明n>3的情况。然而,Sundman级数和Wang级数收敛速度太慢,无法用于实际目的;因此,目前有必要通过数值分析以数值积分的形式来近似解,或者在某些情况下,采用经典三角级数近似。原子系统,例如原子、离子和分子,可以用量子n体问题来处理。在经典物理系统中,n体问题通常是指一个星系或一个星系团;行星系统,如恒星、行星及其卫星,也可以被视为n体系统。一些应用可以方便地用扰动理论来处理,其中系统被认为是一个两体问题加上导致偏离假设的无扰动两体轨道的附加力。<br />
<br />
==三体小说==<br />
<br />
The problem is a plot device in the science fiction trilogy by Chinese author Cixin Liu, and its name has been used for both the first volume and the trilogy as a whole<br />
<br />
三体问题是中国作家刘慈欣的科幻三部曲中有所提及的模拟游戏,也被用于第一卷和整个三部曲的书名。<br />
<br />
--[[用户:Vicky|Vicky]]([[用户讨论:Vicky|讨论]])是否翻译为“三体问题被应用于中国作家刘慈欣科幻小说三部曲中的情节设计中,也被用于第一卷和整个三部曲的书名。”更好?</div>Vickyhttps://wiki.swarma.org/index.php?title=%E4%B8%89%E4%BD%93%E9%97%AE%E9%A2%98&diff=20366三体问题2020-12-21T07:55:04Z<p>Vicky:</p>
<hr />
<div>已由Lincent审校。<br />
<br />
In physics and classical mechanics, the three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.[1] The three-body problem is a special case of the n-body problem. Unlike two-body problems, no general closed-form solution exists,[1] as the resulting dynamical system is chaotic for most initial conditions, and numerical methods are generally required.<br />
<br />
在物理学和经典力学领域中,三体问题是根据牛顿运动定律和牛顿万有引力定律按照三点处质量体的初始位置和速度(或动量)求出它们随后的运动的问题。三体是n体问题中的一个特例。与双体问题不同的是,三体问题不存在一般的闭式解,因为产生的动力系统对于大多数初始条件来说是混沌的,所以一般需要数值方法求解。<br />
<br />
--[[用户:Vicky|Vicky]]([[用户讨论:Vicky|讨论]])n-body problem 翻译为 “多体问题”或“N体问题”会不会更好一些?<br />
<br />
Historically, the first specific three-body problem to receive extended study was the one involving the Moon, the Earth, and the Sun.[2] In an extended modern sense, a three-body problem is any problem in classical mechanics or quantum mechanics that models the motion of three particles.<br />
<br />
历史上看,第一个被拓展研究的特定三体问题是月球、地球和太阳构成的“三体”问题。从现代意义上讲,拓展的三体问题可以是经典力学或量子力学中模拟三个粒子运动的任何问题。<br />
<br />
==数学描述==<br />
<br />
三体的数学表达式可以用三个质量为<math>m_i</math>的相互作用的物体的矢量位置<math>\mathbf{r_i} = (x_i, y_i, z_i)</math>的牛顿运动方程来表示:<br />
<br />
<math>\begin{align}<br />
\ddot\mathbf{r}_{\mathbf{1}} &= -G m_2 \frac{\mathbf{r_1} - \mathbf{r_2}}{|\mathbf{r_1} - \mathbf{r_2}|^3} - G m_3 \frac{\mathbf{r_1} - \mathbf{r_3}}{|\mathbf{r_1} - \mathbf{r_3}|^3}, \\<br />
\ddot\mathbf{r}_{\mathbf{2}} &= -G m_3 \frac{\mathbf{r_2} - \mathbf{r_3}}{|\mathbf{r_2} - \mathbf{r_3}|^3} - G m_1 \frac{\mathbf{r_2} - \mathbf{r_1}}{|\mathbf{r_2} - \mathbf{r_1}|^3}, \\<br />
\ddot\mathbf{r}_{\mathbf{3}} &= -G m_1 \frac{\mathbf{r_3} - \mathbf{r_1}}{|\mathbf{r_3} - \mathbf{r_1}|^3} - G m_2 \frac{\mathbf{r_3} - \mathbf{r_2}}{|\mathbf{r_3} - \mathbf{r_2}|^3}.<br />
\end{align}</math><br />
<br />
其中<math>G</math>为万有引力常数。这是一组9个二阶微分方程构成的方程组。这个问题也可以用哈密顿形式等价表示,此时可以用一组18个一阶微分方程来描述,这些方程分别对应于位置<math>\mathbf{r_i}</math>和动量<math>\mathbf{p_i}</math>的一个分量:<br />
<br />
:<math><br />
\frac{d \mathbf{r_i}}{dt} = \frac{\partial \mathcal{H}}{\partial \mathbf{p_i}}, \qquad \frac{d\mathbf{p_i}}{dt} = -\frac{\partial \mathcal{H}}{\partial \mathbf{r_i}},<br />
</math><br />
<br />
其中<math>\mathcal{H}</math>是哈密顿 Hamiltonian函数:<br />
<br />
:<math><br />
\mathcal{H} = -\frac{G m_1 m_2}{|\mathbf{r_1} - \mathbf{r_2}|}-\frac{G m_2 m_3}{|\mathbf{r_3} - \mathbf{r_2}|} -\frac{G m_3 m_1}{|\mathbf{r_3} - \mathbf{r_1}|} + \frac{\mathbf{p_1}^2}{2m_1} + \frac{\mathbf{p_2}^2}{2m_2} + \frac{\mathbf{p_3}^2}{2m_3}.<br />
</math><br />
<br />
这种情况下,<math>\mathcal{H}</math>仅仅是系统的总能量,重力加上动能。<br />
<br />
==受限制的三题问题==<br />
<br />
In the restricted three-body problem,[3] a body of negligible mass (the "planetoid") moves under the influence of two massive bodies. Having negligible mass, the force that the planetoid exerts on the two massive bodies may be neglected, and the system can be analysed and can therefore be described in terms of a two-body motion. Usually this two-body motion is taken to consist of circular orbits around the center of mass, and the planetoid is assumed to move in the plane defined by the circular orbits.<br />
<br />
在受限制的三体问题中,一个质量可忽略不计的天体(“小行星”)在两个质量巨大的天体的影响下运动。由于质量可忽略不计,小行星对这两个质量巨大的天体所施加的力可忽略不计,因此可以可以用两个物体的运动来描述,对该系统进行分析。通常这种两体运动被认为是由围绕质心的圆形轨道组成的,并且假定小行星在圆形轨道所定义的平面内运动。<br />
<br />
The restricted three-body problem is easier to analyze theoretically than the full problem. It is of practical interest as well since it accurately describes many real-world problems, the most important example being the Earth–Moon–Sun system. For these reasons, it has occupied an important role in the historical development of the three-body problem.<br />
<br />
受限制的三体问题比完全的三体问题更容易从理论上分析。它也具有实际意义,因为它准确地描述了许多现实世界的问题,其中最重要的例子是地球-月亮-太阳的系统,这也是在三体问题的历史发展中有重要地位的一个典型。<br />
<br />
Mathematically, the problem is stated as follows. Let {\displaystyle m_{1,2}} {\displaystyle m_{1,2}} be the masses of the two massive bodies, with (planar) coordinates {\displaystyle (x_{1},y_{1})} (x_{1},y_{1}) and {\displaystyle (x_{2},y_{2})} (x_{2},y_{2}), and let {\displaystyle (x,y)} (x,y) be the coordinates of the planetoid. For simplicity, choose units such that the distance between the two massive bodies, as well as the gravitational constant, are both equal to {\displaystyle 1} 1. Then, the motion of the planetoid is given by<br />
<br />
在数学的表述上,设<math>m_{1,2}</math>为两个大质量天体的质量,二维平面坐标<math>(x_1, y_1)</math>和<math>(x_2, y_2)</math>分别为小行星的坐标。简单起见,选择的单位应该要确保两大质量天体的距离和重力常数都等于1。则小行星的运动可以用公式描述为:<br />
<br />
:<math><br />
\begin{align}<br />
\frac{d^2 x}{dt^2} = -m_1 \frac{x - x_1}{r_1^3} - m_2 \frac{x - x_2}{r_2^3} \\<br />
\frac{d^2 y}{dt^2} = -m_1 \frac{y - y_1}{r_1^3} - m_2 \frac{y - y_2}{r_2^3},<br />
\end{align}<br />
</math><br />
<br />
其中<math>r_i = \sqrt{(x - x_i)^2 + (y - y_i)^2}</math>,在这种形式下,运动方程通过坐标具有明确的时间依赖性<math>x_i(t), y_i(t)</math>。但可以通过转换为旋转参考系来消除这种时间相关性,从而简化了后续的分析。<br />
<br />
==求解==<br />
<br />
There is no general analytical solution to the three-body problem given by simple algebraic expressions and integrals.[1] Moreover, the motion of three bodies is generally non-repeating, except in special cases.[5]<br />
<br />
由简单的代数表达式和积分给出的三体没有一般的解析解。此外,除特殊情况,三个物体的运动一般是不重复的。<br />
<br />
<br />
On the other hand, in 1912 the Finnish mathematician Karl Fritiof Sundman proved that there exists a series solution in powers of t1/3 for the 3-body problem.[6] This series converges for all real t, except for initial conditions corresponding to zero angular momentum. (In practice the latter restriction is insignificant since such initial conditions are rare, having Lebesgue measure zero.)<br />
<br />
另一方面,1912年芬兰数学家**Karl Fritiof Sundman**证明了三体问题存在一个 {{math|''t''<sup>1/3</sup>}}幂次方的级数解。除了对应于角动量为零的初始条件外,这个级数对所有实数t都收敛。<br />
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An important issue in proving this result is the fact that the radius of convergence for this series is determined by the distance to the nearest singularity. Therefore, it is necessary to study the possible singularities of the 3-body problems. As it will be briefly discussed below, the only singularities in the 3-body problem are binary collisions (collisions between two particles at an instant) and triple collisions (collisions between three particles at an instant).<br />
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证明这个结果的一个重要问题是,该序列的收敛半径是由到最近奇点的距离决定的。因此,有必要研究三体问题的可能奇点。三体问题中唯一的奇点是二元碰撞(两个粒子在瞬间的碰撞)和三元碰撞(三个粒子在瞬间的碰撞),下面会进行简单的讨论。<br />
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Collisions, whether binary or triple (in fact, any number), are somewhat improbable, since it has been shown that they correspond to a set of initial conditions of measure zero. However, there is no criterion known to be put on the initial state in order to avoid collisions for the corresponding solution. So Sundman's strategy consisted of the following steps:<br />
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无论是二元的还是三元的(事实上是任何数目) 碰撞都不太可能发生,因为已经证明它们对应于测度为零的一组初始条件。然而,没有已知的标准被放在初始状态,以对相应的解避免碰撞。因此,**Sundman**的求解方法包括以下步骤:<br />
<br />
<br />
1. Using an appropriate change of variables to continue analyzing the solution beyond the binary collision, in a process known as regularization.<br />
2. Proving that triple collisions only occur when the angular momentum L vanishes. By restricting the initial data to L ≠ 0, he removed all real singularities from the transformed equations for the 3-body problem.<br />
3. Showing that if L ≠ 0, then not only can there be no triple collision, but the system is strictly bounded away from a triple collision. This implies, by using Cauchy's existence theorem for differential equations, that there are no complex singularities in a strip (depending on the value of L) in the complex plane centered around the real axis (shades of Kovalevskaya).<br />
4. Find a conformal transformation that maps this strip into the unit disc. For example, if s = t1/3 (the new variable after the regularization) and if |ln s| ≤ β,[clarification needed] then this map is given by<br />
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1. 使用适当的变量变化来继续分析二元碰撞之外的解,这个过程称为正则化。<br />
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2. 证明只有在角动量L消失时才会发生三元碰撞。通过将初始数据限制为L ≠ 0,从三体问题的变换方程中删除了所有实数奇点。<br />
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3. 证明了如果L≠0,则不仅不存在三元碰撞,而且系统严格有界远离三元碰撞。这意味着,通过对微分方程使用柯西存在性定理,在以实际轴为中心的复平面(Kovalevskaya的阴影)中,一个条带区域(取决于L的值)中不存在复奇点。<br />
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4. 找到一个保角变换,把这个条带映射到单位圆盘。例如,如果s={{math|''t''<sup>1/3</sup>}}(正则化后的新变量),并且{{math|{{abs|ln ''s''}} ≤ ''β''}}(需要证明),则映射可由下式给出:<br />
<br />
:<math>\sigma = \frac{e^\frac{\pi s}{2\beta} - 1}{e^\frac{\pi s}{2\beta} + 1}.</math><br />
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This finishes the proof of Sundman's theorem.<br />
上述即为完整的Sundman定律的证明。<br />
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Unfortunately, the corresponding series converges very slowly. That is, obtaining a value of meaningful precision requires so many terms that this solution is of little practical use. Indeed, in 1930, David Beloriszky calculated that if Sundman's series were to be used for astronomical observations, then the computations would involve at least 108000000 terms.[7]<br />
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但不幸运的是,对应的级数收敛得非常慢。也就是说,为了获得一定精度的值需要很多级数项,这样的解法并没有什么实际用途。的确,在1930年,David Beloriszky计算出,如果将Sundman级数用于天文观测,则计算将至少涉及10<sup>{{val|8000000}}</sup>项。<br />
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==特殊的求解方法==<br />
<br />
In 1767, Leonhard Euler found three families of periodic solutions in which the three masses are collinear at each instant. See Euler's three-body problem.<br />
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1767年,**Leonhard Euler**提出了三个周期解系列,其中三个质量在每个瞬间共线。<br />
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1772年,拉格朗日(Lagrange)找到了一系列解,其中三个质量在每个瞬间形成一个等边三角形。这些解决方案与Euler的共线解一起构成了三体问题的中心配置。这些解决方案对于任何质量比均有效,并且质量沿开普勒椭圆形运动。这四个族是唯一有明确解析公式的已知解决方案。在圆形受限三体问题的特殊情况下,这些解决方案在与原边一起旋转的框架中观察时,变为称为L<sub>1</sub>, L<sub>2</sub>, L<sub>3</sub>, L<sub>4</sub>和L<sub>5</sub>,并且叫做拉格朗日点,其中L<sub>3</sub>, L<sub>4</sub>是拉格朗日的对称解的实例。<br />
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在1892年至1899年的工作中,**Henri Poincaré**建立了无穷有限三体问题的周期解,以及将这些解法继续推广到一般三体问题的技巧。<br />
<br />
1893年,迈塞尔提出了现在所说的毕达哥拉斯三体问题:将比例为3:4:5的三个质量置于3:4:5直角三角形的顶点处。Burrau在1913年进一步研究了这个问题。1967年,Victor Szebehely和C. Frederick Peters利用数值积分理论建立了这个问题的最终逃逸模型,同时找到了附近的周期解。<br />
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20世纪70年代,**Michel Hénon**和 '''Roger A. Broucke'''各自找到了一套解决方案,这些解决方案构成了同一系列解决方案的一部分: Broucke–Henon–Hadjidemetriou族。在这个家族中,这三个物体都具有相同的质量,可以表现出逆行和直行两种形式。在、Broucke的一些解中,两个物体遵循同样的路径。<br />
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1993年,[[圣塔菲研究所]]的物理学家'''Cris Moore'''提出了一种零角动量解,该解适用于三个相等质量围绕一个八字形运动。这种方法在2000年由数学家'''Alain Chenciner'''和'''Richard Montgomery'''证明。在数值上证明了该解对于质量和轨道参数的小扰动是稳定的,这增加了在物理宇宙中可以观察到这种轨道的可能性。但有人认为不太可能发生这种情况,因为稳定性的范围小。例如,1993年,圣达菲研究所的物理学家克里斯·摩尔(Cris Moore)在数字上发现了一个零角动量解,该解的三个相等质量围绕一个八字形运动。[12]它的正式存在后来在2000年由数学家Alain Chenciner和Richard Montgomery 证明。[13] [14]在数值上证明了该解对于质量和轨道参数的小扰动是稳定的,这增加了在物理宇宙中可以观察到这种轨道的可能性。但是,由于稳定性的范围小,因此不太可能发生这种情况。例如,二元-二元散射事件导标号-8轨道的概率估计为1%的一小部分。<br />
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In 2013, physicists Milovan Šuvakov and Veljko Dmitrašinović at the Institute of Physics in Belgrade discovered 13 new families of solutions for the equal-mass zero-angular-momentum three-body problem.<br />
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2013年,贝尔格莱德物理研究所的物理学家Milovan uvakov 和 Veljko dmitra inovi 发现了等质量零角动量三体问题的13种新的解族。<br />
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In 2015, physicist Ana Hudomal discovered 14 new families of solutions for the equal-mass zero-angular-momentum three-body problem.<br />
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2015年,物理学家 Ana Hudomal 发现了14种等质量零角动量三体问题的新解族。<br />
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In 2017, researchers Xiaoming Li and Shijun Liao found 669 new periodic orbits of the equal-mass zero-angular-momentum three-body problem.[17] This was followed in 2018 by an additional 1223 new solutions for a zero-momentum system of unequal masses.[18]<br />
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2017年,研究人员Xiaoming Li 和Shijun Liao发现了669个等质量零角动量三体问题的新周期轨道。2018年,不等质量的零动量系统又增加了1223个新解。<br />
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In 2018, Li and Liao reported 234 solutions to the unequal-mass "free-fall" three body problem.[19] The free fall formulation of the three body problem starts with all three bodies at rest. Because of this, the masses in a free-fall configuration do not orbit in a closed "loop", but travel forwards and backwards along an open "track".<br />
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2018年,Li和Liao提出了234个不等质量“自由落体”三体问题的解。三体问题的自由落体公式从所有三个静止的物体开始。正因为如此,质量在一个自由落体配置不在一个闭合的“循环”轨道上运行,而是沿着一个开放的“轨道”向前和向后运行。<br />
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===数值方法===<br />
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Using a computer, the problem may be solved to arbitrarily high precision using numerical integration although high precision requires a large amount of CPU time. In 2019, Breen et al. announced a fast neural network solver, trained using a numerical integrator.[20]<br />
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尽管高精度需要大量的CPU时间,但是通过计算机可以使用数值积分可以得到问题的任意高精度解。在2019年,Breen等人。提出了一种快速的神经网络求解器,使用数字积分器对其进行训练。<br />
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==历史==<br />
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The gravitational problem of three bodies in its traditional sense dates in substance from 1687, when Isaac Newton published his Principia (Philosophiæ Naturalis Principia Mathematica). In Proposition 66 of Book 1 of the Principia, and its 22 Corollaries, Newton took the first steps in the definition and study of the problem of the movements of three massive bodies subject to their mutually perturbing gravitational attractions. In Propositions 25 to 35 of Book 3, Newton also took the first steps in applying his results of Proposition 66 to the lunar theory, the motion of the Moon under the gravitational influence of the Earth and the Sun.<br />
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传统意义上的三个物体的引力问题可以追溯到1687年,当时牛顿发表了他的《自然哲学的数学原理》。在《原理》第一卷的第66号提案及其22个推论中,牛顿首次定义和研究了三个受相互扰动的重力吸引影响的巨大物体的运动问题。在第三册的第25至35条命题中,牛顿也迈出了第一步,将他的66号提案的结果应用到月球理论中,即月球在地球和太阳的引力影响下的运动。<br />
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The physical problem was addressed by Amerigo Vespucci and subsequently by Galileo Galilei; in 1499, Vespucci used knowledge of the position of the Moon to determine his position in Brazil. It became of technical importance in the 1720s, as an accurate solution would be applicable to navigation, specifically for the determination of longitude at sea, solved in practice by John Harrison's invention of the marine chronometer. However the accuracy of the lunar theory was low, due to the perturbing effect of the Sun and planets on the motion of the Moon around the Earth.<br />
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Amerigo Vespucci和随后的Galileo Galilei提出了三体问题; 1499年,Vespucci利用对月球位置的了解来确定自己在巴西的位置。因为这种方法适用于导航,特别是在海上确定经度,1720年代该方法变得非常技术实用。事实上确定经度的问题被John Harrison发明的航海经线仪所解决。但是,由于太阳和行星对月球绕地球运动的干扰作用,月球理论的准确性很低。<br />
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Jean le Rond d'Alembert and Alexis Clairaut, who developed a longstanding rivalry, both attempted to analyze the problem in some degree of generality; they submitted their competing first analyses to the Académie Royale des Sciences in 1747.[21] It was in connection with their research, in Paris during the 1740s, that the name "three-body problem" (French: Problème des trois Corps) began to be commonly used. An account published in 1761 by Jean le Rond d'Alembert indicates that the name was first used in 1747.<br />
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建立了长期竞争关系的Jean le Rond d'Alembert和Alexis Clairaut都试图以某种普遍性来分析该问题。他们于1747年向皇家科学研究院提交了他们的第一批竞争分析。在1740年代的巴黎,“三体问题”(法语:Problèmedes trois Corps)这个名字开始被普遍使用,与他们的研究有关。Jean le Rond d'Alembert于1761年发布的文章表明该名称最早于1747年使用。<br />
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<br />
==其他涉及三体的问题==<br />
<br />
The term 'three-body problem' is sometimes used in the more general sense to refer to any physical problem involving the interaction of three bodies.<br />
三体问题这个术语有时用在更一般的意义上来指涉及三个物体相互作用的任何物理问题。<br />
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A quantum mechanical analogue of the gravitational three-body problem in classical mechanics is the helium atom, in which a helium nucleus and two electrons interact according to the inverse-square Coulomb interaction. Like the gravitational three-body problem, the helium atom cannot be solved exactly.[23]<br />
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氦原子是经典力学中引力三体问题的量子力学模拟,其中一个氦原子核和两个电子会产生反平方库仑相互作用,这种相互作用称为经典力学中的三体问题。就像重力三体问题一样,氦原子的三体问题没有精确解。<br />
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In both classical and quantum mechanics, however, there exist nontrivial interaction laws besides the inverse-square force which do lead to exact analytic three-body solutions. One such model consists of a combination of harmonic attraction and a repulsive inverse-cube force.[24] This model is considered nontrivial since it is associated with a set of nonlinear differential equations containing singularities (compared with, e.g., harmonic interactions alone, which lead to an easily solved system of linear differential equations). In these two respects it is analogous to (insoluble) models having Coulomb interactions, and as a result has been suggested as a tool for intuitively understanding physical systems like the helium atom.[24][25]<br />
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然而,在经典力学和量子力学中,除了平方反力外,还存在着一些非平凡相互作用规律,这些规律可以得到精确的解析解。有一种模型是由谐波吸引和排斥反立方体力的组合而成的。该模型被认为是非平凡的,因为它与一组包含奇异性的非线性微分方程组相关联(例如,与单独的谐波相互作用相比,该关联能够得到易于求解的线性微分方程组)。在这两种情况下,三体问题类似于具有库仑相互作用的(无法解释的)模型,因此,有人提出将其作为直观理解诸如氦原子之类的物理系统的工具。<br />
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The gravitational three-body problem has also been studied using general relativity. Physically, a relativistic treatment becomes necessary in systems with very strong gravitational fields, such as near the event horizon of a black hole. However, the relativistic problem is considerably more difficult than in Newtonian mechanics, and sophisticated numerical techniques are required. Even the full two-body problem (i.e. for arbitrary ratio of masses) does not have a rigorous analytic solution in general relativity.[26]<br />
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引力三体问题也被通过广义相对论进行了研究。在物理上,相对论性的处理在引力场非常强的系统中变得非常必要,比如在黑洞的视界附近。然而,相对论性问题比牛顿力学困难得多,需要复杂的数值技术。即使是完整的两体问题(即任意质量比)在广义相对论中也没有严格的解析解。<br />
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==n体问题==<br />
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The three-body problem is a special case of the n-body problem, which describes how n objects will move under one of the physical forces, such as gravity. These problems have a global analytical solution in the form of a convergent power series, as was proven by Karl F. Sundman for n = 3 and by Qiudong Wang for n > 3 (see n-body problem for details). However, the Sundman and Wang series converge so slowly that they are useless for practical purposes;[27] therefore, it is currently necessary to approximate solutions by numerical analysis in the form of numerical integration or, for some cases, classical trigonometric series approximations (see n-body simulation). Atomic systems, e.g. atoms, ions, and molecules, can be treated in terms of the quantum n-body problem. Among classical physical systems, the n-body problem usually refers to a galaxy or to a cluster of galaxies; planetary systems, such as stars, planets, and their satellites, can also be treated as n-body systems. Some applications are conveniently treated by perturbation theory, in which the system is considered as a two-body problem plus additional forces causing deviations from a hypothetical unperturbed two-body trajectory.<br />
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三体问题是n体问题的一个特例,它描述了n个物体在其中一种物理力(如重力)下如何运动。这些问题具有收敛幂级数形式的全局解析解,比如,Karl F.Sundman证明n=3的情况,qaudong Wang证明n>3的情况。然而,Sundman级数和Wang级数收敛速度太慢,无法用于实际目的;因此,目前有必要通过数值分析以数值积分的形式来近似解,或者在某些情况下,采用经典三角级数近似。原子系统,例如原子、离子和分子,可以用量子n体问题来处理。在经典物理系统中,n体问题通常是指一个星系或一个星系团;行星系统,如恒星、行星及其卫星,也可以被视为n体系统。一些应用可以方便地用扰动理论来处理,其中系统被认为是一个两体问题加上导致偏离假设的无扰动两体轨道的附加力。<br />
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==三体小说==<br />
<br />
The problem is a plot device in the science fiction trilogy by Chinese author Cixin Liu, and its name has been used for both the first volume and the trilogy as a whole<br />
<br />
三体问题是中国作家刘慈欣的科幻三部曲中有所提及的模拟游戏,也被用于第一卷和整个三部曲的书名。</div>Vicky