Dynamic sociometry*

I am indebted to Ralph Levine and Stanley Cohen for comments on drafts of this paper but especially to Stuart Thomas. I am also thankful for assistance by Kay Hamming and Ronda Hunter. Part of this work resulted from two Mathematical Social Science Board conferences; one in Cambridge, Massachusetts, 1973, and one in Morgantown, West Virginia, 1974.

This paper presents a model of change in sociometric structure in an idealized “small” group where everyone is in constant, uniform interaction. After the model is discussed dynamically, the set of invariant sociograms for this model is defined and compared to those defined for other theories. The model is shown to include the strong forms of balance theory, clustering, transitivity, and positive balance. The model predicts that the weak forms become strong forms under constant contact. Equilibrium conditions are discussed in some detail, and specific examples are displayed, including examples which are not predicted by balance theory, clustering, or other theories.

Notes

I am indebted to Ralph Levine and Stanley Cohen for comments on drafts of this paper but especially to Stuart Thomas. I am also thankful for assistance by Kay Hamming and Ronda Hunter. Part of this work resulted from two Mathematical Social Science Board conferences; one in Cambridge, Massachusetts, 1973, and one in Morgantown, West Virginia, 1974.