Analyses of Subgroups and Clusterings within Groups: Attaining Knowledge of the Social Interaction Potential

Abstract

The evocative portrayal of small groups given by the group diagramming method naturally invites the further study of subgroups, behavioral clusters, and coalitions. Previous attempts at such study have depended on the mathematical formalism of Cluster Analysis. This is a natural choice, since much of the structure of a group is sure to be defined by the pairwise interactions which form the basis of Cluster Analytic techniques. However, several shortcomings of this method are apparent: While there is a straightforward measure of distance (the fundamental input to the Cluster Analysis) in the diagram plane, the dominance dimension appears to be qualitatively different; furthermore, it is most desirable that the analysis procedure consider all interactions simultaneously. We therefore turn to the Potential Theory of physical science which has long been used to describe assemblages of pairwise interacting “particles.” A method of characterizing probable clusters within a group is then possible based on the statistical moment description of a group —analogous to the multipole expansion of physical Potential Theory. It is hypothesized that there is an an underlying Social Interaction Potential which is clarified by the contours of the coalitions which thus emerge. Speculation on this Potential leads to other fruitful areas of inquiry.