Opinion Dynamics and the Evolution of Social Power in Influence Networks

This paper studies the evolution of self appraisal, social power and interpersonal influencesfor a group of individuals who discuss and form opinions about a sequence of issues. Our empirical modelcombines the averaging rule by DeGroot to describe opinion formation processes and the reflected appraisalmechanism by Friedkin to describe the dynamics of individuals’ self appraisal and social power. Given aset of relative interpersonal weights, the DeGroot-Friedkin model predicts the evolution of the influencenetwork governing the opinion formation process. We provide a rigorous mathematical formulation of theinfluence network dynamics, characterize its equilibria and establish its convergence properties for all possiblestructures of the relative interpersonal weights and corresponding eigenvector centrality scores. The modelpredicts that the social power ranking among individuals is asymptotically equal to their centrality ranking,that social power tends to accumulate at the top of the hierarchy, and that an autocratic (resp. democratic)power structure arises when the centrality scores are maximally non-uniform (resp. uniform).