Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions

TL;DR

This paper introduces a hypergraph-based opinion model incorporating group opinions, revealing how group interactions can induce oscillatory and excitable opinion dynamics, with implications for understanding social phenomena like fads.

Contribution

It presents a novel hypergraph model of opinion dynamics that includes group opinions and analyzes how these influence collective behavior, including oscillations and excitability.

Findings

Group opinions can cause self-sustained oscillations in mean opinion.

Finite-size effects lead to large, short-lived opinion swings.

Oscillatory dynamics depend on the correlation between dyadic and polyadic interactions.

Abstract

In traditional models of opinion dynamics, each agent in a network has an opinion and changes in opinions arise from pairwise (i.e., dyadic) interactions between agents. However, in many situations, groups of individuals possess a collective opinion that can differ from the opinions of its constituent individuals. In this paper, we study the effects of group opinions on opinion dynamics. We formulate a hypergraph model in which both individual agents and groups of 3 agents have opinions, and we examine how opinions evolve through both dyadic interactions and group memberships. In some parameter regimes, we find that the presence of group opinions can lead to oscillatory and excitable opinion dynamics. In the oscillatory regime, the mean opinion of the agents in a network has self-sustained oscillations. In the excitable regime, finite-size effects create large but short-lived opinion swings (as in social fads). We develop a mean-field approximation of our model and obtain good agreement with direct numerical simulations. We also show -- both numerically and via our mean-field description -- that oscillatory dynamics occur only when the number of dyadic and polyadic interactions per agent are not completely correlated. Our results illustrate how polyadic structures, such as groups of agents, can have important effects on collective opinion dynamics.