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Structural Balance: a Generalization of Heider's Theory' VOL. 63, No. 5 SEPTEMBER, 1956 THE PSYCHOLOGICAL REVIEW STRUCTURAL BALANCE: A GENERALIZATION OF HEIDER'S THEORY' DORWIN CARTWRIGHT AND FRANK HARARY Research Center for Group Dynamics, University of Michigan A persistent problem of psychology will arise to change it toward a state has been how to deal conceptually of balance. These pressures may with patterns of interdependent prop- work to change the relation of affec- erties. This problem has been cen- tion between P and 0, the relation of tral, of course, in the theoretical responsibility between 0 and X, or the treatment by Gestalt psychologists of relation of evaluation between P phenomenal or neural configurations andX. or fields (12, 13, 15). It has also The purpose of this paper is to been of concern to social psychologists present and develop the consequences and sociologists who attempt to em- of a formal definition of balance which ploy concepts referring to social sys- is consistent with Heider's conception tems (18). and which may be employed in a more Heider (19), reflecting the general general treatment of empirical con- field-theoretical approach, has con- figurations. The definition is stated sidered certain aspects of cognitive in terms of the mathematical theory fields which contain perceived people of linear graphs (8, 14) and makes use and impersonal objects or events. of a distinction between a given rela- His analysis focuses upon what he calls tion and its opposite relation. Some the P-O-X unit of a cognitive field, of the ramifications of this definition consisting of P (one person), 0 (an- are then examined by means of other person), and X (an impersonal theorems derivable from the definition entity). Each relation among the and from graph theory. parts of the unit is conceived as inter- dependent with each other relation. HEIDER'S CONCEPTION OF Thus, for example, if P has a relation BALANCE of affection for 0 and if 0 is seen as responsible for X, then there will be In developing his analysis of bal- a tendency for P to like or approve anced cognitive units, Heider dis- of X. If the nature of X is such that tinguishes between two major types of it would "normally" be evaluated as relations. The first concerns atti- bad, the whole P-O-X unit is placed tudes, or the relation of liking or in a state of imbalance, and pressures evaluating. It is represented sym- 1 bolically as L when positive and as ~L This paper was prepared as part of a when negative. Thus, PLO means P project sponsored in the Research Center for Group Dynamics by the Rockefeller likes, loves, values, or approves 0, and Foundation. JP~LO means P dislikes, negatively 277 278 DORWIN CARTWRIGHT AND FRANK HARARY values, or disapproves 0. The second others as a point of departure for type of relation refers to cognitive further theoretical and empirical work. unit formation, that is, to such specific We shall summarize briefly some of relations as similarity, possession, the major results of this work. causality, proximity, or belonging. Horowitz, Lyons, and Perlmutter It is written as U or ~U. Thus, (10) attempted to demonstrate ten- according to Heider, PUX means that dencies toward balance in an experi- P owns, made, is close to, or is associ- ment employing members of a discus- ated with X, and P~ILY means that sion group as subjects. At the end of P does not own, did not make, or is a discussion period each subject was not associated with X. asked to indicate his evaluation of an A balanced state is then defined in event (PLX or P~LX) which had terms of certain combinations of these occurred during the course of the dis- relations. The definition is stated cussion. The event selected for evalu- separately for two and for three ation was one which would be clearly entities. seen as having been produced by a In the case of two entities, a balanced state single person (OUX). The liking re- exists if the relation between them is positive lation between each P and 0 (PLO (or negative) in all respects, i.e., in regard to or P~LO) had been determined by all meanings of L and U . In the case a sociometric questionnaire admin- of three entities, a balanced state exists if all three relations are positive in all respects, or istered before the meeting. Would if two are negative and one positive (9, p. 110). P's evaluation of the event be such as to produce a balanced P-O-X unit? These are examples of balanced If so, P's evaluation of 0 and X should states: P likes something he made be of the same sign. The experi- (PUX, FIX); P likes what his friend mental data tend to support the likes (PLO, OLX, PLX); P dislikes hypothesis that a P-O-X unit tends what his friend dislikes (PLO, 0~LX, toward a balanced state.2 P~LX"); P likes what his enemy dis- The social situation of a discussion likes (P~LO, 0~LX, PLX); and P's group can be better analyzed, accord- son likes what P likes (PU0, PLX, ing to Horowitz, Lyons, and Perl- OLX). mutter, by considering a somewhat Heider's basic hypothesis asserts more complex cognitive unit. The that there is a tendency for cognitive evaluation of X made by P, they units to achieve a balanced state. argue, will be determined not only by Pressures toward balance may pro- P's evaluation of 0 but also by his duce various effects. perception of the evaluation of X If no balanced state exists, then forces given by others (Qs) in the group. towards this state will arise. Either the dy- The basic unit of such a social situa- namic characters will change, or the unit tion, then, consists of the subject, a relations will be changed through action or through cognitive reorganization. If a change 2 One of the attractive features of this study is not possible, the state of imbalance will is that it was conducted in a natural "field" produce tension (9, pp. 107-109). setting, thus avoiding the dangers of artifici- ality. At the same time the setting placed The theory, stated here in sketchy certain restrictions on the possibility of outline, has been elaborated by Heider manipulation and control of the variables. so as to treat a fuller richness of cog- The data show a clear tendency for P to place nitive experience than would be sug- a higher evaluation on Xs produced by more attractive Os. It is not clearly demonstrated gested by our brief description. It that P likes Xs produced by liked Os and has been used, too, by a number of dislikes Xs produced by disliked Os. STRUCTURAL BALANCE 279 person who is responsible for the Jordan (11) presented subjects with event, and another person who will be 64 different hypothetical situations in seen by the subject as supporting or which the L and U relations between rejecting the event. This is called each pair of elements was systemati- a P-O-Q-X unit. The additional data cally varied. The subject was asked needed to describe these relations were to place himself in each situation by obtained from the sociometric ques- taking the part of P, and to indicate tionnaire which indicated P's evalua- on a scale the degree of pleasantness tion of Q (PLQ or P~L@), and from or unpleasantness he experienced. a question designed to reveal P's per- Unpleasantness was assumed to reflect ception of Q's support or rejection of the postulated tension produced by X, treated by the authors as a unit imbalanced units. Jordan's data tend relation (QUX or Q~UZ).3 to support Heider's hypothesis that Although these authors indicate the imbalanced units produce a state of possibility of treating the P-O-Q-X tension, but he too found that addi- unit in terms of balance, they do not tional factors need to be considered. develop a formal definition of a bal- He discovered, for example, that nega- anced configuration consisting of four tive relations were experienced as un- elements. They seem to imply that pleasant even when contained in the P-O-Q-X unit will be balanced if balanced units. This unpleasantness the P-O-X and the P-Q-X units are was particularly acute when P was a both balanced. They do not consider part of the negative relation. Jordan's the relation between Q and 0, nor the study permits a detailed analysis of logically possible components of which these additional influences, which we it could be a part. Their analysis is shall not consider here. concerned primarily with the two Newcomb (17), in his recent theory triangles (P-O-X and P-Q-X), which of interpersonal communication, has are interdependent, since both contain employed concepts rather similar to the relation of P's liking of X. We those of Heider. He conceives of the noted above that the data tend to simplest communicative act as one in support the hypothesis that the P- which one person A gives information 0-X unit will tend toward balance. to another person B about something The data even more strongly support the hypothesis when applied to the X. The similarity of this A-B-X P-Q-X unit; P's evaluation of X and model to Heider's P-O-X unit, to- his perception of Q's attitude toward gether with its applicability to objec- X tend to agree when P likes Q, and tive interpersonal relations (rather to disagree when P dislikes Q.
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