Studies in Mathematical Theory of Human Relations

Abstract

In continuation of previous studies, an abstract mathematical theory is developed for the interaction of several social classes, of which one influences and controls the behavior of the others. In some cases such interaction results in the existence of two configurations of equilibrium for the social structure, characterized by different types of behavior. Each configuration corresponds to one definite type of behavior. The transition from one configuration to the other, in other words, the transition from one behavior to another, occurs rather rapidly. Equations governing these transitions are given. In other cases, namely when the efforts of the individuals to influence others into a given behavior lessen as the success of this influence increases, there is only one stable configuration characterized by a mixed behavior. Due to the dissimilarity of parents and progeny, the composition of each social class changes with time, as generations change. This results in the appearance of instabilities of the social structure and in relatively sudden social changes. Possibilities of quasi-periodic alterations of different social structures are discussed. Finally, the developed equations are applied to the case of physical conflicts between groups of individuals, such as riots, wars, etc. Possible factors in addition to mere physical force which may determine the outcome of such conflicts are investigated.