The Coevolution of Appraisal and Influence Networks Leads to Structural Balance

Abstract

In sociology, an appraisal structure, represented by a signed matrix or a signed network, describes an evaluative cognitive configuration among individuals. In this article we argue that interpersonal influences originate from positive interpersonal appraisals and, in turn, adjust individuals’ appraisals of others. This mechanism amounts to a coevolution process of interpersonal appraisals and influences. We provide a mathematical formulation of the coevolutionary dynamics, characterize the invariant appraisal structures, and establish the convergence properties for all possible initial appraisals. Moreover, we characterize the implications of our model to the study of signed social networks. Specifically, our model predicts the convergence of the interpersonal appraisal network to a structure composed of multiple factions with multiple followers. A faction is a group of individuals with positive-complete interpersonal appraisals among them. We discuss how this factions-with-followers is a balanced structure with respect to an appropriate generalized model of balance theory.