Structural Balance, Mechanical Solidarity, and Interpersonal Relations

James A. Davis
1963 American Journal of Sociology  
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more » ... T Balance theory, a theoretical system developed by Cartwright and Harary to formalize concepts set forth by Heider, is used with slight modifications to restate fifty-six sociological and social-psychological propositions from the writings of Berelson, Lazarsfeld, and McPhee; Coleman; Davis; Durkheim; Festinger; Fiedler; Homans; Katz and Lazarsfeld; Lazarsfeld and Merton; Lipset, Trow, and Coleman; Merton and Kitt; and Stouffer et al. The propositions are grouped under (a) Person, Other, and X, (b) group structure, (c) changes in attitudes and opinions, and (d) values. 444 BALANCE, SOLIDARITY, AND INTERPERSONAL RELATIONS 445 (10, 13), self-selected and involuntary social relations (15), mechanical solidarity (5), "homophily" and "heterophily" (13). The remainder of this paper is an exposition of the theory organized as follows: (a) discussion of the formal language and concepts, (b) major postulates, (c) derived propositions about interpersonal relations, (d) derived propositions about group structure, (e) derived propositions about attitudes and values. This essay should be considered as an attempt at deductive theoretical analysis, not as a review of the literature. THE THEORY The theory submitted here consists of three parts: (a) a formal apparatus combining graph theory and elementary algebra, (b) an interpretation of the formal concepts in terms of social psychological concepts, and (c) a set of postulates that provide the basic propositions. With some slight modifications, the theory is that developed by Cartwright and Harary (2). THE P-O-X EQUATION The formal apparatus of the theory can be expressed in eight definitions: Def. 1. A linear graph, or briefly, a graph, consists of a finite collection of points, A, B, C . . . , together with all unordered pairs of distinct points. Each of these pairs (e.g., AB) is called a line. Def. 2. Lines may vary in type (or "kind" of relationship) and sign (plus or minus) or numerical value. Def. 3. The net value of a line of two or more types is the sum of the values for each type. Def. 4. A path is a collection of lines of the form AB, BC, ... DE, where the points A, B, C, D, and E are distinct. Def. 5. A cycle consists of the above path together with the line EA. Def. 6. The value of a cycle is the product of the net values of its lines. Def. 7. A cycle with a positive value is balanced, a cycle with a negative value is unbalanced. Def. 8. The net value of a graph at point P is the sum of the values of the cycles in which P is a point. Definitions 1, 2, 4, 5, 6, and 7 are taken almost literally from Cartwright and Harary.1
doi:10.1086/223401 fatcat:nkyump6vfnhnlczyguigylbb34