On the Characterization of Balancing Processes of Social Systems and the Derivation of the Minimal Balancing Processes

The psychological notion of cognitive balance by Cartwright and Harary offers a well-organized mode for consideration of systems theoretic approaches to social problems. The balancing processes of a social system, which transform an unbalanced system to a balanced one by changing the cognitive relations, are characterized in terms of signed graphs. First, the characterization of the balancing processes of the whole system is reduced to the characterization of each subsystem, which is obtained by block decomposition of the whole system. Second, the characterization is made in two different ways according to the planarity of the graph structure of the systems. For systems with planar graph structure, the characterization is effectively made by introducing the notion of dual graph. For systems with general graph structure, the balancing processes are characterized in terms of adjacency matrices. In each case, an efficient algorithm which derives the minimal balancing processes is presented. Finally, a quantitative approach incorporating the relative importance of each relation is examined.