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"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society. It is a necessary, but not sufficient, condition of efficiency.

"Pareto efficiency" is considered as a minimal notion of efficiency that does not necessarily result in a socially desirable distribution of resources: it makes no statement about equality, or the overall well-being of a society. It is a necessary, but not sufficient, condition of efficiency.

“帕累托最优”被认为是一种狭义的效率，它不一定会产生社会所期望的资源分配: 它没有为<font color="#ff8000">平等</font>或一个社会的总体福祉发声。<ref>{{cite journal |authorlink=Amartya Sen |first=A. |last=Sen |title=Markets and freedom: Achievements and limitations of the market mechanism in promoting individual freedoms |journal=Oxford Economic Papers |volume=45 |issue=4 |pages=519–541 |date=October 1993 |jstor=2663703 |url=http://www.cs.princeton.edu/courses/archive/spr06/cos444/papers/sen.pdf |doi=10.1093/oxfordjournals.oep.a042106 }}</ref><ref>{{cite book |first=N. |last=Barr |author-link=Nicholas Barr|chapter=3.2.2 The relevance of efficiency to different theories of society |title=Economics of the Welfare State |year=2012 |publisher=[[Oxford University Press]] |isbn=978-0-19-929781-8 |pages=[https://books.google.com/books?id=DOg0BM1XiqQC&pg=PA46 46–49] |edition=5th}}</ref>{{rp|46–49}}它是效率的必要不充分条件。

“帕累托最优”被认为是一种狭义的效率，它不一定会产生社会所期望的资源分配: 它没有为<font color="#ff8000">平等</font>或一个社会的总体福祉发声。<ref>{{cite journal |authorlink=Amartya Sen |first=A. |last=Sen |title=Markets and freedom: Achievements and limitations of the market mechanism in promoting individual freedoms |journal=Oxford Economic Papers |volume=45 |issue=4 |pages=519–541 |date=October 1993 |jstor=2663703 |url=http://www.cs.princeton.edu/courses/archive/spr06/cos444/papers/sen.pdf |doi=10.1093/oxfordjournals.oep.a042106 }}</ref><ref>{{cite book |first=N. |last=Barr |author-link=Nicholas Barr|chapter=3.2.2 The relevance of efficiency to different theories of society |title=Economics of the Welfare State |year=2012 |publisher=[[Oxford University Press]] |isbn=978-0-19-929781-8 |pages=[https://books.google.com/books?id=DOg0BM1XiqQC&pg=PA46 46–49] |edition=5th}}</ref>它是效率的必要不充分条件。

In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.

In addition to the context of efficiency in allocation, the concept of Pareto efficiency also arises in the context of efficiency in production vs. x-inefficiency: a set of outputs of goods is Pareto efficient if there is no feasible re-allocation of productive inputs such that output of one product increases while the outputs of all other goods either increase or remain the same.

除了分配效率的背景之外，帕累托最优的概念也出现在'''<font color="#ff8000">生产效率(efficiency in production)</font>'''对比于'''<font color="#ff8000">x-低效率(x-inefficiency)</font>'''的背景之下，即如果生产投入没有可行的再分配，使得一种产品的产出增加，而所有其他产品的产出增加或保持不变，那么这一组产品的产出就是帕累托最优的。<ref>[[John D. Black|Black, J. D.]], Hashimzade, N., & [[Gareth Myles|Myles, G.]], eds., ''A Dictionary of Economics'', 5th ed. (Oxford: Oxford University Press, 2017), [https://books.google.com/books?id=WyvYDQAAQBAJ&pg=PT459 p. 459].</ref>{{rp|459}}

除了分配效率的背景之外，帕累托最优的概念也出现在'''<font color="#ff8000">生产效率(efficiency in production)</font>'''对比于'''<font color="#ff8000">x-低效率(x-inefficiency)</font>'''的背景之下，即如果生产投入没有可行的再分配，使得一种产品的产出增加，而所有其他产品的产出增加或保持不变，那么这一组产品的产出就是帕累托最优的。<ref>[[John D. Black|Black, J. D.]], Hashimzade, N., & [[Gareth Myles|Myles, G.]], eds., ''A Dictionary of Economics'', 5th ed. (Oxford: Oxford University Press, 2017), [https://books.google.com/books?id=WyvYDQAAQBAJ&pg=PT459 p. 459].</ref>

Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.

Constrained Pareto optimality is a weakening of Pareto-optimality, accounting for the fact that a potential planner (e.g., the government) may not be able to improve upon a decentralized market outcome, even if that outcome is inefficient. This will occur if it is limited by the same informational or institutional constraints as are individual agents.

'''受约束的帕累托最优'''是帕累托最优的弱化，因为一个潜在的规划者(比如政府)可能无法改进分散市场的结果，即使这个结果是低效的。如果它受到与独立主体相同的信息或机构约束的限制，就会发生这种情况。<ref>Magill, M., & [[Martine Quinzii|Quinzii, M.]], ''Theory of Incomplete Markets'', MIT Press, 2002, [https://books.google.com/books?id=d66GXq2F2M0C&pg=PA104#v=onepage&q&f=false p. 104].</ref>{{rp|104}}

'''受约束的帕累托最优'''是帕累托最优的弱化，因为一个潜在的规划者(比如政府)可能无法改进分散市场的结果，即使这个结果是低效的。如果它受到与独立主体相同的信息或机构约束的限制，就会发生这种情况。<ref>Magill, M., & [[Martine Quinzii|Quinzii, M.]], ''Theory of Incomplete Markets'', MIT Press, 2002, [https://books.google.com/books?id=d66GXq2F2M0C&pg=PA104#v=onepage&q&f=false p. 104].</ref>

The notion of Pareto efficiency has been used in engineering. Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.

The notion of Pareto efficiency has been used in engineering. Given a set of choices and a way of valuing them, the Pareto frontier or Pareto set or Pareto front is the set of choices that are Pareto efficient. By restricting attention to the set of choices that are Pareto-efficient, a designer can make tradeoffs within this set, rather than considering the full range of every parameter.

帕累托最优的概念已经在工程中得到了应用。<ref>Goodarzi, E., Ziaei, M., & Hosseinipour, E. Z., ''Introduction to Optimization Analysis in Hydrosystem Engineering'' ([[Berlin]]/[[Heidelberg]]: [[Springer Science+Business Media|Springer]], 2014), [https://books.google.com/books?id=WjS8BAAAQBAJ&pg=PT111 pp. 111–148].</ref>{{rp|111–148}}给定一组选择和一种评估它们的方法，'''帕累托边界'''、'''帕累托解集'''或'''帕累托前沿'''就是帕累托有效的选择集。通过将注意力限制在帕累托有效的选择集上，设计者可以在这个集合中进行权衡，而不是考虑每个参数的全部范围。<ref>Jahan, A., Edwards, K. L., & Bahraminasab, M., ''Multi-criteria Decision Analysis'', 2nd ed. ([[Amsterdam]]: [[Elsevier]], 2013), [https://books.google.com/books?id=3mreBgAAQBAJ&pg=PA63 pp. 63–65].</ref>{{rp|63–65}}

帕累托最优的概念已经在工程中得到了应用。<ref>Goodarzi, E., Ziaei, M., & Hosseinipour, E. Z., ''Introduction to Optimization Analysis in Hydrosystem Engineering'' ([[Berlin]]/[[Heidelberg]]: [[Springer Science+Business Media|Springer]], 2014), [https://books.google.com/books?id=WjS8BAAAQBAJ&pg=PT111 pp. 111–148].</ref>给定一组选择和一种评估它们的方法，'''帕累托边界'''、'''帕累托解集'''或'''帕累托前沿'''就是帕累托有效的选择集。通过将注意力限制在帕累托有效的选择集上，设计者可以在这个集合中进行权衡，而不是考虑每个参数的全部范围。<ref>Jahan, A., Edwards, K. L., & Bahraminasab, M., ''Multi-criteria Decision Analysis'', 2nd ed. ([[Amsterdam]]: [[Elsevier]], 2013), [https://books.google.com/books?id=3mreBgAAQBAJ&pg=PA63 pp. 63–65].</ref>

 

For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.

For a given system, the Pareto frontier or Pareto set is the set of parameterizations (allocations) that are all Pareto efficient. Finding Pareto frontiers is particularly useful in engineering. By yielding all of the potentially optimal solutions, a designer can make focused tradeoffs within this constrained set of parameters, rather than needing to consider the full ranges of parameters.

对于一个给定的系统，'''<font color="#ff8000">帕累托边界(the Pareto frontier)</font>'''或'''<font color="#ff8000">帕累托集(the Pareto set)</font>'''是所有帕累托有效的参数化(分配)的集合。找到帕累托前沿在工程学中特别有用。通过产生所有潜在的最优解决方案，设计师可以在这个受限的参数集中进行集中的[[权衡]]，而不需要考虑所有的参数。<ref>Costa, N. R., & Lourenço, J. A., "Exploring Pareto Frontiers in the Response Surface Methodology", in G.-C. Yang, S.-I. Ao, & L. Gelman, eds., ''Transactions on Engineering Technologies: World Congress on Engineering 2014'' (Berlin/Heidelberg: Springer, 2015), [https://books.google.com/books?id=eMElCQAAQBAJ&pg=PA398 pp. 399–412].</ref>{{rp|399–412}}

对于一个给定的系统，'''<font color="#ff8000">帕累托边界(the Pareto frontier)</font>'''或'''<font color="#ff8000">帕累托集(the Pareto set)</font>'''是所有帕累托有效的参数化(分配)的集合。找到帕累托前沿在工程学中特别有用。通过产生所有潜在的最优解决方案，设计师可以在这个受限的参数集中进行集中的[[权衡]]，而不需要考虑所有的参数。<ref>Costa, N. R., & Lourenço, J. A., "Exploring Pareto Frontiers in the Response Surface Methodology", in G.-C. Yang, S.-I. Ao, & L. Gelman, eds., ''Transactions on Engineering Technologies: World Congress on Engineering 2014'' (Berlin/Heidelberg: Springer, 2015), [https://books.google.com/books?id=eMElCQAAQBAJ&pg=PA398 pp. 399–412].</ref>

Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.

Thus, in a Pareto-optimal allocation, the marginal rate of substitution must be the same for all consumers.

因此，在帕累托最优分配中，所有消费者的边际替代率必须相同。<ref>Wilkerson, T., ''Advanced Economic Theory'' ([[Waltham Abbey]]: Edtech Press, 2018), [https://books.google.com/books?id=UtW_DwAAQBAJ&pg=PA114 p. 114].</ref>{{rp|114}}

因此，在帕累托最优分配中，所有消费者的边际替代率必须相同。<ref>Wilkerson, T., ''Advanced Economic Theory'' ([[Waltham Abbey]]: Edtech Press, 2018), [https://books.google.com/books?id=UtW_DwAAQBAJ&pg=PA114 p. 114].</ref>

Pareto optimisation has also been studied in biological processes. In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).

Pareto optimisation has also been studied in biological processes. In bacteria, genes were shown to be either inexpensive to make (resource efficient) or easier to read (translation efficient). Natural selection acts to push highly expressed genes towards the Pareto frontier for resource use and translational efficiency. Genes near the Pareto frontier were also shown to evolve more slowly (indicating that they are providing a selective advantage).

帕累托最优化在生物过程中也有研究。<ref>Moore, J. H., Hill, D. P., Sulovari, A., & Kidd, L. C., "Genetic Analysis of Prostate Cancer Using Computational Evolution, Pareto-Optimization and Post-processing", in R. Riolo, E. Vladislavleva, M. D. Ritchie, & J. H. Moore, eds., ''Genetic Programming Theory and Practice X'' (Berlin/Heidelberg: Springer, 2013), [https://books.google.co.il/books?id=YZZAAAAAQBAJ&pg=PA86 pp. 87–102].</ref>{{rp|87–102}}在细菌中，基因要么生成成本低廉(资源节约型) ，要么更容易被读取(翻译效率型)。自然选择将高表达的基因推向资源利用和翻译效率的帕累托边界。帕累托边界附近基因的进化速度也较慢(这表明它们提供了一种选择优势)。<ref>{{Cite journal|doi=10.1186/s13059-018-1480-7|pmid=30064467|last1=Seward|first1=Emily A. |last2=Kelly|first2=Steven|title=Selection-driven cost-efficiency optimization of transcripts modulates gene evolutionary rate in bacteria.|journal=Genome Biology|volume=19|issue=1|pages=102|year=2018|pmc=6066932}}</ref>

帕累托最优化在生物过程中也有研究。<ref>Moore, J. H., Hill, D. P., Sulovari, A., & Kidd, L. C., "Genetic Analysis of Prostate Cancer Using Computational Evolution, Pareto-Optimization and Post-processing", in R. Riolo, E. Vladislavleva, M. D. Ritchie, & J. H. Moore, eds., ''Genetic Programming Theory and Practice X'' (Berlin/Heidelberg: Springer, 2013), [https://books.google.co.il/books?id=YZZAAAAAQBAJ&pg=PA86 pp. 87–102].</ref>在细菌中，基因要么生成成本低廉(资源节约型) ，要么更容易被读取(翻译效率型)。自然选择将高表达的基因推向资源利用和翻译效率的帕累托边界。帕累托边界附近基因的进化速度也较慢(这表明它们提供了一种选择优势)。<ref>{{Cite journal|doi=10.1186/s13059-018-1480-7|pmid=30064467|last1=Seward|first1=Emily A. |last2=Kelly|first2=Steven|title=Selection-driven cost-efficiency optimization of transcripts modulates gene evolutionary rate in bacteria.|journal=Genome Biology|volume=19|issue=1|pages=102|year=2018|pmc=6066932}}</ref>

It would be incorrect to treat Pareto efficiency as equivalent to societal optimization, as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution. An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.

It would be incorrect to treat Pareto efficiency as equivalent to societal optimization, as the latter is a normative concept that is a matter of interpretation that typically would account for the consequence of degrees of inequality of distribution. An example would be the interpretation of one school district with low property tax revenue versus another with much higher revenue as a sign that more equal distribution occurs with the help of government redistribution.

把帕累托最优等同于社会优化是不正确的，<ref>[[Jacques Drèze|Drèze, J.]], ''Essays on Economic Decisions Under Uncertainty'' ([[Cambridge]]: [[Cambridge University Press]], 1987), [https://books.google.com/books?id=LWE4AAAAIAAJ&pg=PA358 pp. 358–364]</ref>{{rp|358–364}}因为后者是一个规范性概念，是一个典型的解释性问题，可以解释分配不平等程度的后果。<ref>Backhaus, J. G., ''The Elgar Companion to Law and Economics'' ([[Cheltenham|Cheltenham, UK]] / [[Northampton, MA]]: [[Edward Elgar Publishing|Edward Elgar]], 2005), [https://books.google.com/books?id=EtguKoWHUHYC&lpg=PP1&hl=de&pg=PA10 pp. 10–15].</ref>{{rp|10–15}}一个例子就是对一个财产税收入较低的学区和另一个财政收入高很多的学区的解释，这表明在政府再分配的帮助下实现了更加平等的分配。<ref>Paulsen, M. B., "The Economics of the Public Sector: The Nature and Role of Public Policy in the Finance of Higher Education", in M. B. Paulsen, J. C. Smart, eds. ''The Finance of Higher Education: Theory, Research, Policy, and Practice'' (New York: Agathon Press, 2001), [https://books.google.com/books?id=BlkPAy-gb8sC&pg=PA95 pp. 95–132].</ref>{{rp|95–132}}

把帕累托最优等同于社会优化是不正确的，<ref>[[Jacques Drèze|Drèze, J.]], ''Essays on Economic Decisions Under Uncertainty'' ([[Cambridge]]: [[Cambridge University Press]], 1987), [https://books.google.com/books?id=LWE4AAAAIAAJ&pg=PA358 pp. 358–364]</ref>因为后者是一个规范性概念，是一个典型的解释性问题，可以解释分配不平等程度的后果。<ref>Backhaus, J. G., ''The Elgar Companion to Law and Economics'' ([[Cheltenham|Cheltenham, UK]] / [[Northampton, MA]]: [[Edward Elgar Publishing|Edward Elgar]], 2005), [https://books.google.com/books?id=EtguKoWHUHYC&lpg=PP1&hl=de&pg=PA10 pp. 10–15].</ref>一个例子就是对一个财产税收入较低的学区和另一个财政收入高很多的学区的解释，这表明在政府再分配的帮助下实现了更加平等的分配。<ref>Paulsen, M. B., "The Economics of the Public Sector: The Nature and Role of Public Policy in the Finance of Higher Education", in M. B. Paulsen, J. C. Smart, eds. ''The Finance of Higher Education: Theory, Research, Policy, and Practice'' (New York: Agathon Press, 2001), [https://books.google.com/books?id=BlkPAy-gb8sC&pg=PA95 pp. 95–132].</ref>

Pareto efficiency does not require a totally equitable distribution of wealth. An economy in which a wealthy few hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the status quo is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded. The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.

Pareto efficiency does not require a totally equitable distribution of wealth. An economy in which a wealthy few hold the vast majority of resources can be Pareto efficient. This possibility is inherent in the definition of Pareto efficiency; often the status quo is Pareto efficient regardless of the degree to which wealth is equitably distributed. A simple example is the distribution of a pie among three people. The most equitable distribution would assign one third to each person. However the assignment of, say, a half section to each of two individuals and none to the third is also Pareto optimal despite not being equitable, because none of the recipients could be made better off without decreasing someone else's share; and there are many other such distribution examples. An example of a Pareto inefficient distribution of the pie would be allocation of a quarter of the pie to each of the three, with the remainder discarded. The origin (and utility value) of the pie is conceived as immaterial in these examples. In such cases, whereby a "windfall" is gained that none of the potential distributees actually produced (e.g., land, inherited wealth, a portion of the broadcast spectrum, or some other resource), the criterion of Pareto efficiency does not determine a unique optimal allocation. Wealth consolidation may exclude others from wealth accumulation because of bars to market entry, etc.

帕累托效率并不需要完全公平的财富分配。<ref>Bhushi, K., ed., ''Farm to Fingers: The Culture and Politics of Food in Contemporary India'' (Cambridge: Cambridge University Press, 2018), [https://books.google.com/books?id=NYJIDwAAQBAJ&pg=PA222 p. 222].</ref>{{rp|222}}一个少数富人拥有绝大多数资源的经济体系可以是帕累托有效的。这种可能性是帕累托效率的固有定义; 通常情况下，无论财富的公平分配程度如何，现状都是帕累托有效的。一个简单的例子是在三个人之间分配馅饼。最公平的分配将分配给每个人三分之一。

帕累托效率并不需要完全公平的财富分配。<ref>Bhushi, K., ed., ''Farm to Fingers: The Culture and Politics of Food in Contemporary India'' (Cambridge: Cambridge University Press, 2018), [https://books.google.com/books?id=NYJIDwAAQBAJ&pg=PA222 p. 222].</ref>一个少数富人拥有绝大多数资源的经济体系可以是帕累托有效的。这种可能性是帕累托效率的固有定义; 通常情况下，无论财富的公平分配程度如何，现状都是帕累托有效的。一个简单的例子是在三个人之间分配馅饼。最公平的分配将分配给每个人三分之一。

   --[[用户:粲兰|袁一博]]（[[用户讨论:粲兰|讨论]]）   

   --[[用户:粲兰|袁一博]]（[[用户讨论:粲兰|讨论]]）   

另一种分配是两个人各占半部分，第三个人不占分毫。然而，尽管这种分配并不公平，它也是帕累托最优的，因为没有一个接受者能够在不减少其他人的份额的情况下得到更优的收益; 还有其他许多这样的分配例子。帕累托无效率的馅饼分配的一个例子是三者中的每一个分得馅饼的四分之一，剩下的部分丢弃。<ref>Wittman, D., ''Economic Foundations of Law and Organization'' (Cambridge: Cambridge University Press, 2006), [https://books.google.com/books?id=fOolQOtKM7QC&pg=PA18 p. 18].</ref>{{rp|18}}在这些示例中，馅饼的缘由(和实用价值)被认为是无关紧要的。在这种情况下，由于潜在的分配者都没有实际生产，却获得了“意外之财”(例如，土地、继承的财产、广播频谱的一部分或其他资源) ，帕累托最优的标准并不能决定唯一的最优分配。由于市场准入门槛等原因，财产整合可能会将他者排除在财产积累之外。

另一种分配是两个人各占半部分，第三个人不占分毫。然而，尽管这种分配并不公平，它也是帕累托最优的，因为没有一个接受者能够在不减少其他人的份额的情况下得到更优的收益; 还有其他许多这样的分配例子。帕累托无效率的馅饼分配的一个例子是三者中的每一个分得馅饼的四分之一，剩下的部分丢弃。<ref>Wittman, D., ''Economic Foundations of Law and Organization'' (Cambridge: Cambridge University Press, 2006), [https://books.google.com/books?id=fOolQOtKM7QC&pg=PA18 p. 18].</ref>在这些示例中，馅饼的缘由(和实用价值)被认为是无关紧要的。在这种情况下，由于潜在的分配者都没有实际生产，却获得了“意外之财”(例如，土地、继承的财产、广播频谱的一部分或其他资源) ，帕累托最优的标准并不能决定唯一的最优分配。由于市场准入门槛等原因，财产整合可能会将他者排除在财产积累之外。

The liberal paradox elaborated by Amartya Sen shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.

The liberal paradox elaborated by Amartya Sen shows that when people have preferences about what other people do, the goal of Pareto efficiency can come into conflict with the goal of individual liberty.

阿马蒂亚·森(Amartya Sen)阐述的'''<font color="#ff8000">自由主义悖论(The liberal paradox)'''表明，当人们对他人的行为有偏好时，帕累托有效的目标可能与个人自由的目标发生冲突。<ref>Sen, A., ''Rationality and Freedom'' ([[Cambridge, Massachusetts|Cambridge, MA]] / London: [[Harvard University Press|Belknep Press]], 2004), [https://books.google.cz/books?id=DaOY4DQ-MKAC&pg=PA92 pp. 92–94].</ref>{{rp|92–94}}

阿马蒂亚·森(Amartya Sen)阐述的'''<font color="#ff8000">自由主义悖论(The liberal paradox)'''表明，当人们对他人的行为有偏好时，帕累托有效的目标可能与个人自由的目标发生冲突。<ref>Sen, A., ''Rationality and Freedom'' ([[Cambridge, Massachusetts|Cambridge, MA]] / London: [[Harvard University Press|Belknep Press]], 2004), [https://books.google.cz/books?id=DaOY4DQ-MKAC&pg=PA92 pp. 92–94].</ref>