A model of human group dynamics

A mathematical model is presented which describes the changes in affective and effective interaction in theoretically closed human groups. Its assumptions lie mainly in the field of cognitive dissonance. The temporal behavior and steady-state structure of many examples of closed groups are given, and it is shown that a basic unit for their description is the "snowball," which is a maximal, strongly connected set (on effective communication). If the maximum eigenvalue of a certain matrix is less than or equal to unity, the steady snowball is completely connected on effect and mutually positive affect. The relation of the model's predictions with the concepts of balance, clustering, transitivity, and positive balance is given, together with a comparison with Hunter's (1974) model. The stability of the solutions is discussed, together with a brief section on the comparison of models with reality. The main results of the model are: (1) All communication to a person may cease without his feelings toward others becoming neutral. (2) As time tends to infinity, the model achieves a steady state for all groups. (3) The steady state is quantitatively unstable but (mainly) qualitatively stable. (4) The final state of many groups, especially those with much disagreement, is no communication. (5) A new basic unit, called the snowball, emerges; it resembles a clique, or subgroup. (6) There are three types of snowball: subcritical, critical, and supercritical, the first two of which are connected by all-positive, mutual feelings; supercritical snowballs contain negative feelings and agree about no member of the group. (7) A balanced group stays balanced. (8) In a critical snowball, of all the suggested modes of group structure, only positive balance holds for relations involving people outside the snowball.