Evolution of Social Power for Opinion Dynamics Networks

TL;DR

This paper introduces a comprehensive model for the evolution of opinions and influence structures in social networks, unifying existing models and proving the existence of equilibrium in opinion dynamics over multiple issues.

Contribution

It proposes a new opinion dynamics model based on cost minimization, unifies DeGroot and Friedkin-Johnsen models as special cases, and establishes the existence of equilibrium.

Findings

DeGroot and Friedkin-Johnsen models are special cases of the proposed model.

The model demonstrates the evolution of influence structures as a best response to neighbors.

An equilibrium in opinion and influence evolution is proven to exist.

Abstract

This article studies the evolution of opinions and interpersonal influence structures in a group of agents as they discuss a sequence of issues, each of which follows an opinion dynamics model. In this work, we propose a general opinion dynamics model and an evolution of interpersonal influence structures based on the model of reflected appraisals proposed by Friedkin. Our contributions can be summarized as follows: (i) we introduce a model of opinion dynamics and evolution of interpersonal influence structures between issues viewed as a best response cost minimization to the neighbor's actions, (ii) we show that DeGroot's and Friedkin-Johnsen's models of opinion dynamics and their evolution of interpersonal influence structures are particular cases of our proposed model, and (iii) we prove the existence of an equilibrium. This work is a step towards providing a solid formulation of the evolution of opinions and interpersonal influence structures over a sequence of issues.