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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.

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，'''<font color="#ff8000"> 平衡理论 Balance Theory</font>'''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。

在动机心理学中，'''<font color="#ff8000"> 平衡理论 Balance Theory</font>'''是弗里茨·海德提出的一种态度变化理论。它将认知一致性的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推动力。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，那么这种“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.

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.

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.

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。

例如: 如果一个人（P）喜欢另一个人(O)，则这个人会被代表另一方的相同价态所平衡。从符号上看， P(+)>O和P<(+)O导致这种心理平衡。

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:

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(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:

这也可以扩展到事物或对象(X)，从而引入了三元关系。如果一个人P喜欢对象X但不喜欢另一个人O，那么当P得知这个人O创造了对象X会有什么感受？这用符号表示如下:

P (+) > X  

P (+) > 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.

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.

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:

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:

倍增的迹象表明，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:

* Decide that <math>O</math> isn't bad,

* Decide that <math>O</math> isn't bad,

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.)

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。)

其中任何一种都会导致心理平衡，从而解决困境、满足需求。(这个人P也可以完全地避开对象X和另一个人O，以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.

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.

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

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

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

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

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

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

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

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

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

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

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

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

- + + = - ：平衡，

+ + + = + ：平衡，

- + + = - ：平衡，

- + - = + ：平衡，

- + + = - ：不平衡。

- + + = - ：不平衡。

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.

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.

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.

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.

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.

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.

: A balanced signed graph has only cycles of positive signs.

: A balanced signed graph has only cycles of positive signs.

没有一个循环恰好有一个负边。

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'''.<ref name=GC/>{{rp|179}} The property has been called the ''clusterability axiom''.<ref>Claude Flament (1979) "Independent generalizations of balance", in ''Perspectives on Social Network Research''</ref> Then balanced graphs are recovered by assuming the  

Graphs with this property may decompose into more than two positive subgraphs called '''clusters'''.<ref name=GC/>{{rp|179}} The property has been called the ''clusterability axiom''.<ref>Claude Flament (1979) "Independent generalizations of balance", in ''Perspectives on Social Network Research''</ref> Then balanced graphs are recovered by assuming the Parsimony axiom.

Graphs with this property may decompose into more than two positive subgraphs called clusters. 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 Parsimony axiom.

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。

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。

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).

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).

社会动力学中平衡理论的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)。

社会动力学中平衡理论的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.

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.

Claude Flament 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，阐述了平衡理论的一种限制:

克劳德·弗兰特通过调和弱联系与强联系(如家庭纽带)之间的关系，阐述了平衡理论的一种局限:

: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.

: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.

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.

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几乎不可能，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。

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，定义一个图的平衡几乎不可能，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，这些假设数量众多却缺乏合理性。

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，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。

在图论中，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。

==See also==

==See also==