Balance theory

Heider's P-O-X model

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

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

• ${\displaystyle P(+)>X}$
• ${\displaystyle P(-)>O}$
• ${\displaystyle O(+)>X}$

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.

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:

• Decide that ${\displaystyle O}$ isn't so bad after all,
• Decide that ${\displaystyle X}$ isn't as great as originally thought, or
• Conclude that ${\displaystyle O}$ couldn't really have made ${\displaystyle X}$.

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

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.

Determining if the triad is balanced is simple math:

${\displaystyle +++=+}$; Balanced.

${\displaystyle -+-=+}$; Balanced.

${\displaystyle -++=-}$; Unbalanced.

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.

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.

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.

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.

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

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

No cycle has exactly one negative edge.

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

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

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

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]

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.

• Information integration theory
• Social balance theory