Analysis of mean-field approximation for Deffuant opinion dynamics on networks

TL;DR

This paper analyzes mean-field equations for Deffuant opinion dynamics on networks, focusing on how the confidence bound influences opinion clustering and stability, with insights supported by mathematical analysis and simulations.

Contribution

It provides a mathematical analysis of mean-field equations for Deffuant models, revealing how confidence bounds affect opinion clustering and stability predictions.

Findings

Linear stability analysis predicts the number and location of opinion clusters.

Early-time dynamics and final cluster locations are accurately approximated.

The analysis applies to networks with two degree classes and fully-mixed populations.

Abstract

Mean-field equations have been developed recently to approximate the dynamics of the Deffuant model of opinion formation. These equations can describe both fully-mixed populations and the case where individuals interact only along edges of a network. In each case, interactions only occur between individuals whose opinions differ by less than a given parameter, called the confidence bound. The size of the confidence bound parameter is known to strongly affect both the dynamics and the number and location of opinion clusters. In this work we carry out a mathematical analysis of the mean-field equations to investigate the role of the confidence bound and boundaries on these important observables of the model. We consider the limit in which the confidence bound interval is small, and identify the key mechanisms driving opinion evolution. We show that linear stability analysis can predict the number and location of opinion clusters. Comparison with numerical simulations of the model illustrates that the early-time dynamics and the final cluster locations can be accurately approximated for networks composed of two degree classes, as well as for the case of a fully-mixed population.