A density description of a bounded-confidence model of opinion dynamics on hypergraphs

TL;DR

This paper develops a mean-field density model for a bounded-confidence opinion dynamics process on hypergraphs, capturing polyadic interactions, and demonstrates convergence to opinion clusters through analysis and simulations.

Contribution

It introduces a density-based mean-field equation for the bounded-confidence model on hypergraphs and proves its convergence to opinion clusters as the number of agents grows.

Findings

The density equation converges to noninteracting opinion clusters.

Numerical simulations show bifurcations in steady-state opinion clusters.

Agent-based model converges to the density description with many agents.

Abstract

Social interactions often occur between three or more agents simultaneously. Examining opinion dynamics on hypergraphs allows one to study the effect of such polyadic interactions on the opinions of agents. In this paper, we consider a bounded-confidence model (BCM), in which opinions take continuous values and interacting agents comprise their opinions if they are close enough to each other. We study a density description of a Deffuant--Weisbuch BCM on hypergraphs. We derive a rate equation for the mean-field opinion density as the number of agents becomes infinite, and we prove that this rate equation yields a probability density that converges to noninteracting opinion clusters. Using numerical simulations, we examine bifurcations of the density-based BCM's steady-state opinion clusters and demonstrate that the agent-based BCM converges to the density description of the BCM as the number of agents becomes infinite.