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2020年9月23日 (三) 21:18的版本

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In the psychology of motivation, balance theory is a theory of attitude change, proposed by Fritz Heider.^[1] It conceptualizes the cognitive consistency motive as a drive toward psychological balance. The consistency motive is the urge to maintain one's values and beliefs over time. Heider proposed that "sentiment" or liking relationships are balanced if the affect valence in a system multiplies out to a positive result.

In the psychology of motivation, balance theory is a theory of attitude change, proposed by Fritz Heider. It conceptualizes the cognitive consistency motive as a drive toward psychological balance. The consistency motive is the urge to maintain one's values and beliefs over time. Heider proposed that "sentiment" or liking relationships are balanced if the affect valence in a system multiplies out to a positive result.

在动机心理学中，平衡理论是弗里茨·海德提出的一种态度变化理论。它将认知一致性动机概念化为一种促使心理平衡的驱动力。一致性动机是长期维持一个人的价值观和信仰的强烈愿望。海德提出，如果一个系统中的情感效价翻倍后得到积极的结果，那么“情感”或喜爱关系就是平衡的。

In social network analysis, balance theory is the extension proposed by Frank Harary and Dorwin Cartwright. It was the framework for the discussion at a Dartmouth College symposium in September 1975.^[2]

In social network analysis, balance theory is the extension proposed by Frank Harary and Dorwin Cartwright. It was the framework for the discussion at a Dartmouth College symposium in September 1975.

在社会网络分析中，平衡理论是由弗兰克·哈拉里和多尔文·卡特赖特提出的。这是1975年9月达特茅斯学院研讨会讨论的框架。

P-O-X model

Heider's P-O-X model

海德的 P-O-X 模型

For example: a Person ([math]\displaystyle{ P }[/math]) who likes ([math]\displaystyle{ + }[/math]) an Other ([math]\displaystyle{ O }[/math]) person will be balanced by the same valence attitude on behalf of the other. Symbolically, [math]\displaystyle{ P (+) \gt O }[/math] and [math]\displaystyle{ P \lt (+) O }[/math] results in psychological balance.

例如: 一个喜欢另一个人(O)的人(P)，会被代表他人的相同价态平衡。从符号上看， P(+)>O和P<(+)O导致了心理平衡。

This can be extended to things or objects ([math]\displaystyle{ X }[/math]) as well, thus introducing triadic relationships. If a person [math]\displaystyle{ P }[/math] likes object [math]\displaystyle{ X }[/math] but dislikes other person [math]\displaystyle{ O }[/math], what does [math]\displaystyle{ P }[/math] feel upon learning that person [math]\displaystyle{ O }[/math] created the object [math]\displaystyle{ X }[/math]? This is symbolized as such:

这也可以扩展到事物或对象(X)，从而引入三元关系。如果一个人P喜欢物体X但不喜欢另一个人O，那么当P得知这个人O创造了物体O会有什么感受？这用符号表示如下:

P (+) > X P (-) > O O (+) > X

Cognitive balance is achieved when there are three positive links or two negatives with one positive. Two positive links and one negative like the example above creates imbalance or cognitive dissonance.

当有三个正面关联或两个负面关联与一个正面关联时，就会实现认知平衡。当有两个正面关联和一个负面关联时，像上面的例子一样，就会产生不平衡或认知失调。

Multiplying the signs shows that the person will perceive imbalance (a negative multiplicative product) in this relationship, and will be motivated to correct the imbalance somehow. The Person can either:

不断增加的迹象表明，这个人会察觉到这种关系中的不平衡(一种负乘积效应) ，并且会主动以某种方式纠正这种不平衡。这个人可以:

认为O并不是那么差；认为X并不像原来想的那么好；得出O不可能真的创造了X的结论。

Decide that [math]\displaystyle{ X }[/math] isn't as great as originally thought, or

Conclude that [math]\displaystyle{ O }[/math] couldn't really have made [math]\displaystyle{ X }[/math].

Any of these will result in psychological balance, thus resolving the dilemma and satisfying the drive. (Person [math]\displaystyle{ P }[/math] could also avoid object [math]\displaystyle{ X }[/math] and other person [math]\displaystyle{ O }[/math] entirely, lessening the stress created by psychological imbalance.)

其中任何一种都会导致心理平衡，从而解决困境、满足需求。(人P也可以完全避开对象X和另一个人O，减轻心理不平衡造成的压力。)

To predict the outcome of a situation using Heider's balance theory, one must weigh the effects of all the potential results, and the one requiring the least amount of effort will be the likely outcome.

要使用海德的平衡理论来预测一种情况的结果，必须权衡所有潜在结果的影响，而最不费力的将是最可能的结果。

Determining if the triad is balanced is simple math:

判断三元组是否是平衡是简单的数学问题:

[math]\displaystyle{ + + + = + }[/math]; Balanced.

< math > + + + = + </math > ; Balanced.

[math]\displaystyle{ - + - = + }[/math]; Balanced.

< math >-+-= + </math > ; Balanced.

- + + = - ：平衡，

- + + = - ：不平衡。

Examples

Balance theory is useful in examining how celebrity endorsement affects consumers' attitudes toward products.^[3] If a person likes a celebrity and perceives (due to the endorsement) that said celebrity likes a product, said person will tend to like the product more, in order to achieve psychological balance.

Balance theory is useful in examining how celebrity endorsement affects consumers' attitudes toward products. If a person likes a celebrity and perceives (due to the endorsement) that said celebrity likes a product, said person will tend to like the product more, in order to achieve psychological balance.

平衡理论有助于研究名人代言如何影响消费者对产品的态度。如果一个人喜欢一个名人，并且认为（由于代言)该名人喜欢一个产品，那么这个人就会倾向于更喜欢该产品，以达到心理平衡。

However, if the person already had a dislike for the product being endorsed by the celebrity, they may begin disliking the celebrity, again to achieve psychological balance.

然而，如果这个人之前就不喜欢该名人代言的产品，他可能会开始讨厌这个名人，再次达到心理平衡。

Heider's balance theory can explain why holding the same negative attitudes of others promotes closeness.^[4]^:171 See The enemy of my enemy is my friend.

Heider's balance theory can explain why holding the same negative attitudes of others promotes closeness. See The enemy of my enemy is my friend.

海德的平衡理论可以解释为什么持有和他人相同的负面态度会促进亲近感。比如“敌人的敌人就是我的朋友”。

Signed graphs and social networks

Frank Harary and Dorwin Cartwright looked at Heider's triads as 3-cycles in a signed graph. The sign of a path in a graph is the product of the signs of its edges. They considered cycles in a signed graph representing a social network.

弗兰克·哈拉里和多尔温·卡特赖特在将海德的三角形看作一个符号图中的三个循环。图中路径的符号是其边缘符号的乘积。他们考虑了代表社会网络的符号图中的循环。

A balanced signed graph has only cycles of positive signs.

A balanced signed graph has only cycles of positive signs.

平衡的符号图中只有正符号的循环。

Harary proved that a balanced graph is polarized, that is, it decomposes into two positive subgraphs that are joined by negative edges.^[5]

Harary proved that a balanced graph is polarized, that is, it decomposes into two positive subgraphs that are joined by negative edges.

哈拉里证明了一个平衡图是两极化的，即它分解成两个由负边连接的正子图。

In the interest of realism, a weaker property was suggested by Davis:^[6]

In the interest of realism, a weaker property was suggested by Davis:

戴维斯代表现实主义提出了一个较弱的属性:

No cycle has exactly one negative edge.

没有一个循环恰好有一个负边。

Graphs with this property may decompose into more than two positive subgraphs called clusters.^[4]^:179 The property has been called the clusterability axiom.^[7] Then balanced graphs are recovered by assuming the

Graphs with this property may decompose into more than two positive subgraphs called clusters. Then balanced graphs are recovered by assuming the

具有这种属性的图可以分解为两个以上称为集群的正子图。然后通过假定简约公理来复原平衡图表。

Parsimony axiom: The subgraph of positive edges has at most two components.

Parsimony axiom: The subgraph of positive edges has at most two components.

简约公理: 正边子图最多有两个分支。

The significance of balance theory for social dynamics was expressed by Anatol Rapoport:

平衡理论对社会动力学的意义由阿纳托尔·拉波波特提出:

The hypothesis implies roughly that attitudes of the group members will tend to change in such a way that one's friends' friends will tend to become one's friends and one's enemies' enemies also one's friends, and one's enemies' friends and one's friends' enemies will tend to become one's enemies, and moreover, that these changes tend to operate even across several removes (one's friends' friends' enemies' enemies tend to become friends by an iterative process).^[8]

The hypothesis implies roughly that attitudes of the group members will tend to change in such a way that one's friends' friends will tend to become one's friends and one's enemies' enemies also one's friends, and one's enemies' friends and one's friends' enemies will tend to become one's enemies, and moreover, that these changes tend to operate even across several removes (one's friends' friends' enemies' enemies tend to become friends by an iterative process).

这个假设大致意味着群体成员的态度将倾向于这样的改变: 一个人的朋友的朋友倾向于变成这个人的朋友，一个人的敌人的敌人也倾向于变成这个人的朋友，一个人的敌人的朋友和一个人的朋友的敌人也倾向于变成一这个人的敌人，而且，这些改变甚至会跨越几个间距发生(一个人的朋友的朋友的敌人的敌人也会通过一个迭代过程变成朋友)。

Note that a triangle of three mutual enemies makes a clusterable graph but not a balanced one. Therefore, in a clusterable network one cannot conclude that the enemy of my enemy is my friend, although this aphorism is a fact in a balanced network.

Note that a triangle of three mutual enemies makes a clusterable graph but not a balanced one. Therefore, in a clusterable network one cannot conclude that the enemy of my enemy is my friend, although this aphorism is a fact in a balanced network.

请注意，由三个共同的敌人组成的三角形形成的是一个可集群的图，而不是一个平衡图。因此，在一个可集群的网络中，我们不能得出“敌人的敌人就是我的朋友”的结论，尽管这句格言在平衡的网络中是事实。

Criticism

Claude Flament^[9] expressed a limit to balance theory imposed by reconciling weak ties with relationships of stronger force such as family bonds:

Claude Flament expressed a limit to balance theory imposed by reconciling weak ties with relationships of stronger force such as family bonds:

克劳德·弗兰特通过调和弱关系与强关系(如家庭纽带)之间的关系，表达了平衡理论的一种限制:

One might think that a valued algebraic graph is necessary to represent psycho-social reality, if it is to take into account the degree of intensity of interpersonal relationships. But in fact it then seems hardly possible to define the balance of a graph, not for mathematical but for psychological reasons. If the relationship AB is +3, the relationship BC is –4, what should the AC relationship be in order that the triangle be balanced? The psychological hypotheses are wanting, or rather they are numerous and little justified.

如果要考虑人际关系的紧张程度，人们可能会认为有必要用一个有价值的代数图来表示心理社会现实。但事实上，定义一个图表的平衡似乎几近不可能，不是出于数学上的原因，而是出于心理学上的原因。如果 AB 的关系是 + 3，BC 的关系是-4，那么 AC 的关系应该是什么才能使三角形平衡？心理学上的假设是匮乏的，或者更确切地说，这些假设数量众多缺乏合理性。

At the 1975 Dartmouth College colloquium on balance theory, Bo Anderson struck at the heart of the notion:^[10]

At the 1975 Dartmouth College colloquium on balance theory, Bo Anderson struck at the heart of the notion:

在1975年达特茅斯学院关于平衡理论的座谈会上，波·安德森一针见血地指出了这个概念的核心：

In graph theory there exists a formal balance theory that contains theorems that are analytically true. The statement that Heider's psychological balance can be represented, in its essential aspects, by a suitable interpretation of that formal balance theory should, however, be regarded as problematical. We cannot routinely identify the positive and negative lines in the formal theory with the positive and negative "sentiment relations", and identify the formal balance notion with the psychological idea of balance or structural tension. .. It is puzzling that the fine structure of the relationships between formal and psychological balance has been given scant attention by balance theorists.

In graph theory there exists a formal balance theory that contains theorems that are analytically true. The statement that Heider's psychological balance can be represented, in its essential aspects, by a suitable interpretation of that formal balance theory should, however, be regarded as problematical. We cannot routinely identify the positive and negative lines in the formal theory with the positive and negative "sentiment relations", and identify the formal balance notion with the psychological idea of balance or structural tension. .. It is puzzling that the fine structure of the relationships between formal and psychological balance has been given scant attention by balance theorists.

在图表理论中，有一种形式的平衡理论，存在着一种形式上的平衡理论。然而，关于海德尔的心理平衡可以通过对该形式平衡理论的适当解释来体现其本质方面的说法，应该被视为是有问题的。我们不能常规地将形式理论中的正负线与正负的 "情感关系 "相区分，也不能将形式平衡概念与平衡或结构张力的心理学思想相区分。......令人费解的是，形式平衡与心理平衡关系的细微结构却很少受到平衡理论家的关注。

Notes

↑ Heider, Fritz (1958). The Psychology of Interpersonal Relations. John Wiley & Sons.

↑ Paul W. Holland & Samuel Leinhardt (editors) (1979) Perspectives on Social Network Research, Academic Press

↑ John C. Mowen and Stephen W. Brown (1981) ,"On Explaining and Predicting the Effectiveness of Celebrity Endorsers", in Advances in Consumer Research Volume 08, eds. Kent B. Monroe, Advances in Consumer Research Volume 08 : Association for Consumer Research, Pages: 437-441.

↑ ^4.0 ^4.1 Gary Chartrand (1977) Graphs as Mathematical Models, chapter 8: Graphs and Social Psychology, Prindle, Webber & Schmidt,

↑ Frank Harary (1953) On the Notion of Balance of a Signed Graph, Michigan Mathematical Journal 2(2): 153–6 via Project Euclid 模板:Mr
↑ James A. Davis (May 1967) "Clustering and structural balance in graphs", Human Relations 20:181–7
↑ Claude Flament (1979) "Independent generalizations of balance", in Perspectives on Social Network Research
↑ Anatol Rapoport (1963) "Mathematical models of social interaction", in Handbook of Mathematical Psychology, v. 2, pp 493 to 580, especially 541, editors: R.A. Galanter, R.R. Lace, E. Bush, John Wiley & Sons
↑ Claude Flament (1963) Application of Graph Theory to Group Structure, translators Maurice Pinard, Raymond Breton, Fernand Fontaine, chapter 3: Balancing Processes, page 92, Prentice-Hall
↑ Bo Anderson (1979) "Cognitive Balance Theory and Social Network Analysis: Remarks on some fundamental theoretical matters", pages 453 to 69 in Perspectives on Social Network Research, see page 462.

References

Heider, Fritz (1946). "Attitudes and Cognitive Organization". The Journal of Psychology. 21. doi:10.1080/00223980.1946.9917275. PMID 21010780. {{cite journal}}: Missing pipe in: |1946年

  pages= (help); Text "21" ignored (help); Text "弗里茨 · 海德" ignored (help); Text "心理学杂志" ignored (help); Text "态度和认知组织" ignored (help); Unknown parameter |2012年10月12日

  first= ignored (help); line feed character in |1946年

  pages= at position 8 (help)

|pmid=21010780}}

21010780}

Cartwright, D. and Frank Harary (1956)Structural balance: a generalization of Heider's theory, Psychological Review 63: 277–293 link from Stanford University

Category:Attitude change

类别: 态度转变

Category:Psychological theories

范畴: 心理学理论

Category:Social networks

分类: 社交网络

Category:Methods in sociology

范畴: 社会学方法

This page was moved from wikipedia:en:Balance theory. Its edit history can be viewed at 平衡理论/edithistory

[1] Heider, Fritz (1958). The Psychology of Interpersonal Relations. John Wiley & Sons.

[2] Paul W. Holland & Samuel Leinhardt (editors) (1979) Perspectives on Social Network Research, Academic Press
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[3] John C. Mowen and Stephen W. Brown (1981) ,"On Explaining and Predicting the Effectiveness of Celebrity Endorsers", in Advances in Consumer Research Volume 08, eds. Kent B. Monroe, Advances in Consumer Research Volume 08 : Association for Consumer Research, Pages: 437-441.

[GC-4] 4.0 ^4.1 Gary Chartrand (1977) Graphs as Mathematical Models, chapter 8: Graphs and Social Psychology, Prindle, Webber & Schmidt,
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[5] Frank Harary (1953) On the Notion of Balance of a Signed Graph, Michigan Mathematical Journal 2(2): 153–6 via Project Euclid 模板:Mr

[6] James A. Davis (May 1967) "Clustering and structural balance in graphs", Human Relations 20:181–7

[7] Claude Flament (1979) "Independent generalizations of balance", in Perspectives on Social Network Research

[8] Anatol Rapoport (1963) "Mathematical models of social interaction", in Handbook of Mathematical Psychology, v. 2, pp 493 to 580, especially 541, editors: R.A. Galanter, R.R. Lace, E. Bush, John Wiley & Sons

[9] Claude Flament (1963) Application of Graph Theory to Group Structure, translators Maurice Pinard, Raymond Breton, Fernand Fontaine, chapter 3: Balancing Processes, page 92, Prentice-Hall

[10] Bo Anderson (1979) "Cognitive Balance Theory and Social Network Analysis: Remarks on some fundamental theoretical matters", pages 453 to 69 in Perspectives on Social Network Research, see page 462.

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@@ 第5行： / 第5行： @@
 In the psychology of motivation, balance theory is a theory of attitude change, proposed by Fritz Heider. It conceptualizes the cognitive consistency motive as a drive toward psychological balance. The consistency motive is the urge to maintain one's values and beliefs over time.  Heider proposed that "sentiment" or liking relationships are balanced if the affect valence in a system multiplies out to a positive result.
-在动机心理学中，平衡理论是弗里茨 · 海德提出的态度变化理论。它将认知一致性动机概念化为一种心理平衡的驱动力。一致性的动机是随着时间的推移保持一个人的价值观和信仰的强烈愿望。海德提出，如果一个系统中的情感效价翻倍成一个积极的结果，那么“情感”或喜欢关系就是平衡的。
+在动机心理学中，平衡理论是弗里茨·海德提出的一种态度变化理论。它将认知一致性动机概念化为一种促使心理平衡的驱动力。一致性动机是长期维持一个人的价值观和信仰的强烈愿望。海德提出，如果一个系统中的情感效价翻倍后得到积极的结果，那么“情感”或喜爱关系就是平衡的。
@@ 第13行： / 第13行： @@
 In social network analysis, balance theory is the extension proposed by Frank Harary and Dorwin Cartwright.  It was the framework for the discussion at a Dartmouth College symposium in September 1975.
-在社会网络分析中，平衡理论是由弗兰克 · 哈拉里和多尔文 · 卡特赖特提出的。这是1975年9月达特茅斯学院研讨会讨论的框架。
+在社会网络分析中，平衡理论是由弗兰克·哈拉里和多尔文·卡特赖特提出的。这是1975年9月达特茅斯学院研讨会讨论的框架。
@@ 第29行： / 第29行： @@
 For example: a Person (<math>P</math>) who likes (<math>+</math>) an Other (<math>O</math>) person will be balanced by the same valence attitude on behalf of the other.  Symbolically, <math>P (+) > O</math> and <math>P < (+) O</math> results in psychological balance.
-例如: 一个人(数学)喜欢(数学)另一个人(数学)代表另一个人的态度是相同的。从象征意义上来说，《数学》和《数学》导致了心理平衡。
+例如: 一个喜欢另一个人(O)的人(P)，会被代表他人的相同价态平衡。从符号上看， P(+)>O和P<(+)O导致了心理平衡。
@@ 第37行： / 第37行： @@
 This can be extended to things or objects (<math>X</math>) as well, thus introducing triadic relationships.  If a person <math>P</math> likes object <math>X</math> but dislikes other person <math>O</math>, what does <math>P</math> feel upon learning that person <math>O</math> created the object <math>X</math>?  This is symbolized as such:
-这也可以扩展到事物或对象(< math > x </math >) ，从而引入三元关系。如果一个人喜欢数学物体但不喜欢别人数学物体，那么学习数学物体时的感觉是什么？这是如此象征的:
+这也可以扩展到事物或对象(X)，从而引入三元关系。如果一个人P喜欢物体X但不喜欢另一个人O，那么当P得知这个人O创造了物体O会有什么感受？这用符号表示如下:
-*<math> P (+) > X </math>
+P (+) > X
+P (-) > O
-*<math> P (-) > O </math>
+O (+) > X
-*<math> O (+) > X </math>
@@ 第51行： / 第49行： @@
 Cognitive balance is achieved when there are three positive links or two negatives with one positive. Two positive links and one negative like the example above creates imbalance or cognitive dissonance.
-当有三个正面联系或两个负面与一个正面联系时，认知平衡就会实现。两个正面的链接和一个负面的链接，就像上面的例子一样，会产生不平衡或认知失调。
+当有三个正面关联或两个负面关联与一个正面关联时，就会实现认知平衡。当有两个正面关联和一个负面关联时，像上面的例子一样，就会产生不平衡或认知失调。
@@ 第59行： / 第57行： @@
 Multiplying the signs shows that the person will perceive imbalance (a negative multiplicative product) in this relationship, and will be motivated to correct the imbalance somehow.  The Person can either:
-不断增加的迹象表明，这个人会察觉到这种关系中的不平衡(负乘法产品) ，并且会有动力以某种方式纠正这种不平衡。这个人可以:
+不断增加的迹象表明，这个人会察觉到这种关系中的不平衡(一种负乘积效应) ，并且会主动以某种方式纠正这种不平衡。这个人可以:
+认为O并不是那么差；
+认为X并不像原来想的那么好；
+得出O不可能真的创造了X的结论。
-* Decide that <math>O</math> isn't so bad after all,
 * Decide that <math>X</math> isn't as great as originally thought, or
@@ 第73行： / 第74行： @@
 Any of these will result in psychological balance, thus resolving the dilemma and satisfying the drive.  (Person <math>P</math> could also avoid object <math>X</math> and other person <math>O</math> entirely, lessening the stress created by psychological imbalance.)
-其中任何一个都会导致心理平衡，从而解决困境和满足驱动力。(人也可以完全避开数学和其他人，减轻心理不平衡带来的压力)
+其中任何一种都会导致心理平衡，从而解决困境、满足需求。(人P也可以完全避开对象X和另一个人O，减轻心理不平衡造成的压力。)
@@ 第81行： / 第82行： @@
 To predict the outcome of a situation using Heider's balance theory, one must weigh the effects of all the potential results, and the one requiring the least amount of effort will be the likely outcome.
-为了使用海德的平衡理论来预测一个情况的结果，我们必须权衡所有可能结果的影响，而最不需要付出努力的结果就是可能的结果。
+要使用海德的平衡理论来预测一种情况的结果，必须权衡所有潜在结果的影响，而最不费力的将是最可能的结果。
@@ 第89行： / 第90行： @@
 Determining if the triad is balanced is simple math:
-判断三元组是否是平衡的简单数学:
+判断三元组是否是平衡是简单的数学问题:
@@ 第109行： / 第110行： @@
-<math> - + + = - </math>; Unbalanced.
+- + + = - ：平衡，
-<math> - + + = - </math>; Unbalanced.
-《数学》-+ + = -。
+- + + = - ：平衡，
+- + + = - ：不平衡。
@@ 第123行： / 第123行： @@
 Balance theory is useful in examining how celebrity endorsement affects consumers' attitudes toward products. If a person likes a celebrity and perceives (due to the endorsement) that said celebrity likes a product, said person will tend to like the product more, in order to achieve psychological balance.
-平衡理论有助于研究名人代言如何影响消费者对产品的态度。如果一个人喜欢一个名人，并且察觉到(由于代言)这个名人喜欢一个产品，那么这个人就会倾向于更喜欢这个产品，以达到心理平衡。
+平衡理论有助于研究名人代言如何影响消费者对产品的态度。如果一个人喜欢一个名人，并且认为（由于代言)该名人喜欢一个产品，那么这个人就会倾向于更喜欢该产品，以达到心理平衡。
@@ 第131行： / 第131行： @@
 However, if the person already had a dislike for the product being endorsed by the celebrity, they may begin disliking the celebrity, again to achieve psychological balance.
-然而，如果这个人已经不喜欢名人代言的产品，他们可能会开始不喜欢名人，再次达到心理平衡。
+然而，如果这个人之前就不喜欢该名人代言的产品，他可能会开始讨厌这个名人，再次达到心理平衡。
@@ 第139行： / 第139行： @@
 Heider's balance theory can explain why holding the same negative attitudes of others promotes closeness. See The enemy of my enemy is my friend.
-海德的平衡理论可以解释为什么持有他人同样的消极态度会促进亲密。敌人的敌人就是我的朋友。
+海德的平衡理论可以解释为什么持有和他人相同的负面态度会促进亲近感。比如“敌人的敌人就是我的朋友”。
@@ 第149行： / 第149行： @@
 Frank Harary and Dorwin Cartwright looked at Heider's triads as 3-cycles in a signed graph. The sign of a path in a graph is the product of the signs of its edges. They considered cycles in a signed graph representing a social network.
-弗兰克 · 哈拉里和多尔温 · 卡特赖特在一个有符号图中将海德的三角形看作三个圈。图中路径的符号是其边的符号的乘积。他们考虑了代表社会网络的有符号图中的圈。
+弗兰克·哈拉里和多尔温·卡特赖特在将海德的三角形看作一个符号图中的三个循环。图中路径的符号是其边缘符号的乘积。他们考虑了代表社会网络的符号图中的循环。
 : A balanced signed graph has only cycles of positive signs.
@@ 第155行： / 第155行： @@
   A balanced signed graph has only cycles of positive signs.
-平衡有符号图只有正符号圈。
+平衡的符号图中只有正符号的循环。
 Harary proved that a balanced graph is polarized, that is, it decomposes into two positive subgraphs that are joined by negative edges.<ref>[[Frank Harary]] (1953) [https://projecteuclid.org/euclid.mmj/1028989917 On the Notion of Balance of a Signed Graph], [[Michigan Mathematical Journal]] 2(2): 153–6 via [[Project Euclid]] {{mr|id=0067468}}</ref>
@@ 第161行： / 第161行： @@
 Harary proved that a balanced graph is polarized, that is, it decomposes into two positive subgraphs that are joined by negative edges.
-Harary 证明了一个平衡图是极化的，即它分解成两个由负边连接的正子图。
+哈拉里证明了一个平衡图是两极化的，即它分解成两个由负边连接的正子图。
@@ 第169行： / 第169行： @@
 In the interest of realism, a weaker property was suggested by Davis:
-出于现实主义的考虑，戴维斯提出了一个较弱的属性:
+戴维斯代表现实主义提出了一个较弱的属性:
 :No cycle has exactly one negative edge.
@@ 第181行： / 第181行： @@
 Graphs with this property may decompose into more than two positive subgraphs called clusters. Then balanced graphs are recovered by assuming the
-具有此属性的图可以分解为两个以上称为集群的正子图。然后通过假设
+具有这种属性的图可以分解为两个以上称为集群的正子图。然后通过假定简约公理来复原平衡图表。
 : Parsimony axiom: The subgraph of positive edges has at most two [[component (graph theory)|component]]s.
@@ 第195行： / 第194行： @@
 The significance of balance theory for social dynamics was expressed by Anatol Rapoport:
-平衡理论对社会动力学的意义由 Anatol Rapoport 表达:
+平衡理论对社会动力学的意义由阿纳托尔·拉波波特提出:
 :The hypothesis implies roughly that attitudes of the group members will tend to change in such a way that one's [[friend of a friend|friends' friends]] will tend to become one's friends and one's enemies' enemies also one's friends, and one's enemies' friends and one's friends' enemies will tend to become one's enemies, and moreover, that these changes tend to operate even across several removes (one's friends' friends' enemies' enemies tend to become friends by an iterative process).<ref>[[Anatol Rapoport]] (1963) "Mathematical models of social interaction", in [https://archive.org/details/handbookofmathem017893mbp ''Handbook of Mathematical Psychology'', v. 2], pp 493 to 580, especially 541, editors: R.A. Galanter, R.R. Lace, E. Bush, [[John Wiley & Sons]]</ref>
 The hypothesis implies roughly that attitudes of the group members will tend to change in such a way that one's friends' friends will tend to become one's friends and one's enemies' enemies also one's friends, and one's enemies' friends and one's friends' enemies will tend to become one's enemies, and moreover, that these changes tend to operate even across several removes (one's friends' friends' enemies' enemies tend to become friends by an iterative process).
-这个假设大致意味着群体成员的态度会倾向于这样的改变: 一个人的朋友的朋友会变成一个人的朋友，一个人的敌人的敌人也会变成一个人的朋友，一个人的敌人的朋友和一个人的朋友的敌人也会变成一个人的敌人，而且，这些改变甚至会在几次移除中发生(一个人的朋友的朋友的敌人的敌人也会通过一个迭代过程变成朋友)。
+这个假设大致意味着群体成员的态度将倾向于这样的改变: 一个人的朋友的朋友倾向于变成这个人的朋友，一个人的敌人的敌人也倾向于变成这个人的朋友，一个人的敌人的朋友和一个人的朋友的敌人也倾向于变成一这个人的敌人，而且，这些改变甚至会跨越几个间距发生(一个人的朋友的朋友的敌人的敌人也会通过一个迭代过程变成朋友)。
 Note that a triangle of three mutual enemies makes a clusterable graph but ''not'' a balanced one. Therefore, in a clusterable network one ''cannot'' conclude that [[the enemy of my enemy is my friend]], although this aphorism is a fact in a balanced network.
@@ 第207行： / 第205行： @@
 Note that a triangle of three mutual enemies makes a clusterable graph but not a balanced one. Therefore, in a clusterable network one cannot conclude that the enemy of my enemy is my friend, although this aphorism is a fact in a balanced network.
-请注意，由三个共同的敌人组成的三角形形成的是一个可聚集的图，而不是一个平衡的图。因此，在一个可聚集的网络中，不能断定敌人的敌人就是我的朋友，尽管这句格言在一个平衡的网络中是一个事实。
+请注意，由三个共同的敌人组成的三角形形成的是一个可集群的图，而不是一个平衡图。因此，在一个可集群的网络中，我们不能得出“敌人的敌人就是我的朋友”的结论，尽管这句格言在平衡的网络中是事实。
@@ 第217行： / 第215行： @@
 Claude Flament expressed a limit to balance theory imposed by reconciling weak ties with relationships of stronger force such as family bonds:
-克劳德 · 弗兰特通过调和弱关系与强关系(如家庭纽带)之间的关系，表达了对平衡理论的限制:
+克劳德·弗兰特通过调和弱关系与强关系(如家庭纽带)之间的关系，表达了平衡理论的一种限制:
 :One might think that a [[graph (abstract data type)|valued algebraic graph]] is necessary to represent psycho-social reality, if it is to take into account the degree of intensity of interpersonal relationships. But in fact it then seems hardly possible to define the balance of a graph, not for mathematical but for psychological reasons. If the relationship ''AB'' is +3, the relationship ''BC'' is –4, what should the ''AC'' relationship be in order that the triangle be balanced? The psychological hypotheses are wanting, or rather they are numerous and little justified.
@@ 第223行： / 第221行： @@
 One might think that a valued algebraic graph is necessary to represent psycho-social reality, if it is to take into account the degree of intensity of interpersonal relationships. But in fact it then seems hardly possible to define the balance of a graph, not for mathematical but for psychological reasons. If the relationship AB is +3, the relationship BC is –4, what should the AC relationship be in order that the triangle be balanced? The psychological hypotheses are wanting, or rather they are numerous and little justified.
-如果要考虑人际关系的紧张程度，人们可能会认为有必要用一个有价值的代数图来表示心理社会现实。但事实上，定义一个图表的平衡似乎几乎是不可能的，不是出于数学上的原因，而是出于心理学上的原因。如果 AB 的关系是 + 3，BC 的关系是-4，那么 AC 的关系应该是什么，才能使三角形平衡？心理学上的假设是缺乏的，或者更确切地说，这些假设数量众多，而且没有多少合理性。
+如果要考虑人际关系的紧张程度，人们可能会认为有必要用一个有价值的代数图来表示心理社会现实。但事实上，定义一个图表的平衡似乎几近不可能，不是出于数学上的原因，而是出于心理学上的原因。如果 AB 的关系是 + 3，BC 的关系是-4，那么 AC 的关系应该是什么才能使三角形平衡？心理学上的假设是匮乏的，或者更确切地说，这些假设数量众多缺乏合理性。
@@ 第231行： / 第229行： @@
 At the 1975 Dartmouth College colloquium on balance theory, Bo Anderson struck at the heart of the notion:
-在1975年达特茅斯学院关于平衡理论的座谈会上，Bo Anderson 触及了这个概念的核心:
+在1975年达特茅斯学院关于平衡理论的座谈会上，波·安德森一针见血地指出了这个概念的核心：
 :In graph theory there exists a ''formal'' balance theory that contains theorems that are ''analytically'' true. The statement that Heider's ''psychological'' balance can be represented, in its essential aspects, by a suitable interpretation of that ''formal balance theory'' should, however, be regarded as problematical. We cannot routinely identify the positive and negative lines in the formal theory with the positive and negative "sentiment relations", and identify the formal balance notion with the ''psychological'' idea of balance or structural tension. .. It is puzzling that the fine structure of the relationships between formal and psychological balance has been given scant attention by balance theorists.
@@ 第237行： / 第235行： @@
 In graph theory there exists a formal balance theory that contains theorems that are analytically true. The statement that Heider's psychological balance can be represented, in its essential aspects, by a suitable interpretation of that formal balance theory should, however, be regarded as problematical. We cannot routinely identify the positive and negative lines in the formal theory with the positive and negative "sentiment relations", and identify the formal balance notion with the psychological idea of balance or structural tension. .. It is puzzling that the fine structure of the relationships between formal and psychological balance has been given scant attention by balance theorists.
-在图论中，有一种形式的平衡理论，其中包含的定理在分析上是正确的。然而，关于海德尔的心理平衡可以通过对形式平衡理论的适当解释来体现其本质方面的说法，应该被视为是有问题的。我们不能将形式理论中的积极与消极的“情感关系”常规性地区分为积极与消极的“情感关系” ，也不能将形式平衡概念与心理学中的平衡或结构张力概念相区分。..形式平衡与心理平衡之间关系的精细结构一直没有得到平衡理论家的重视，这一点令人费解。
+在图表理论中，有一种形式的平衡理论，存在着一种形式上的平衡理论。然而，关于海德尔的心理平衡可以通过对该形式平衡理论的适当解释来体现其本质方面的说法，应该被视为是有问题的。我们不能常规地将形式理论中的正负线与正负的 "情感关系 "相区分，也不能将形式平衡概念与平衡或结构张力的心理学思想相区分。......令人费解的是，形式平衡与心理平衡关系的细微结构却很少受到平衡理论家的关注。