Interplay Between Homophily-Based Appraisal Dynamics and Influence-Based Opinion Dynamics: Modeling and Analysis

TL;DR

This paper introduces a novel model that captures the mutual influence between interpersonal appraisals and opinions, revealing how social balance and opinion consensus emerge through their interplay.

Contribution

It combines appraisal and opinion dynamics into a unified framework, providing new insights and theoretical analysis of their joint evolution and equilibrium states.

Findings

Equilibrium set characterized with social balance and opinion consensus.

Convergence of appraisals to social balance is equivalent to opinion modulus consensus.

Monte Carlo simulations confirm the non-vanishing appraisals condition for typical initial states.

Abstract

In social systems, the evolution of interpersonal appraisals and individual opinions are not independent processes but intertwine with each other. Despite extensive studies on both opinion dynamics and appraisal dynamics separately, no previous work has ever combined these two processes together. In this paper, we propose a novel and intuitive model on the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics. We assume that individuals' opinions are updated via the influence network constructed from their interpersonal appraisals, which are in turn updated based on the individual opinions via the homophily mechanism. By theoretical analysis, we characterize the set of equilibria and some transient behavior of our model. Moreover, we establish the equivalence among the convergence of the appraisal network to social balance, the modulus consensus of individual opinions, and the non-vanishing appraisals. Monte Carlo validations further show that the non-vanishing appraisals condition holds for generic initial conditions. Compared with previous works that explain the emergence of social balance via person-to-person homophily mechanism, our model provides an alternative explanation in terms of the person-to-entity homophily mechanism. In addition, our model also describes how individuals' opinions on multiple irrelevant issues become correlated and converge to modulus consensus over time-varying influence networks.