STUDY of the triad is one of the most interesting and satisfactory areas of current research activity in sociology. The relevant theory is unusually simple and straightforward. It lends itself to empirical verification more readily than most other models of interaction. The theory of the triad promises to be applicable to situations of different scale, although this advantage has not yet been fully exploited. It seems likely that generalizations developed in the three-person group will be applicable to situations where the interacting units are organized groups, even such very large groups as political parties and states. In his original discussion, Simmel deliberately compared intimate human situations such as the contention of two men for one woman with large scale situations like the European balance of power. For many years Simmel's powerful but unsystematic analysis was admired and neglected. The development of research evidence on the triad has come about very recently. The last two years have seen the publication of a series of brilliant experiments by Mills, Strodtbeck, Torrance, Bales and Borgatta. These experiments have demonstrated the reality of the phenomenon which Simmel stressed-the tendency of the triad to become a coalition of two against one. They have also demonstrated that small differences in power, activity, and other characteristics of the members of the triad have considerable influence upon the formation and persistence of coalitions. The purpose of this paper is to examine the model of the triad whose members are not identical in power and to call attention to a neglected feature of this model, namely, that the formation of given coalitions depends upon the initial distribution of power in the triad and, other things being equal, may be predicted to some extent when the initial distribution of power is known. In their discussion of the zero-sum threeperson game, von Neumann and Morgenstern consider at some length the case of unsymmetric distribution, i.e., those in which different coalitions receive different results. They remark, it seems that what a player can get in a definite coalition depends not only on what the rules of the game provide for that eventuality, but also on the other (competing) possibility of coalition for himself and for his partner. Since the rules of the game are absolute and inviolable, this means that under certain conditions comnpensations must be paid among coalition partners; i.e., that a player must have to pay a well defined price to a prospective coalition partner. The amount of the compensations will depend on what other alternatives are open to each of the players. 1 Concealed in this and subsequent discussions is the assumption of equality of power among the three players, even when they have different possibilities of gain or loss. (See especially their figure 51). This assumption does not fit many triads of sociological interest in which the typical gain consists of domination over other triad members, and not in an external reward to be obtained by a given coalition. This is the case in three-sibling rivalries, in three-cornered political contests, and in many other concrete situations. We shall consider six types. The following asumptions will apply:
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