A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs

Abstract

People's opinions evolve over time as they interact with their friends, family, colleagues, and others. In the study of dynamics on networks, one often encodes interactions between people in the form of dyadic relationships, but many social interactions in real life are polyadic (i.e., they involve three or more people). In this paper, we extend an asynchronous bounded-confidence model (BCM) on graphs, in which nodes are connected pairwise by edges, to hypergraphs. We show that our hypergraph BCM converges to consensus under a wide range of initial conditions for the opinions of the nodes. We show that, under suitable conditions, echo chambers can form on hypergraphs with community structure. We also observe that the opinions of individuals can sometimes jump from one cluster to another in a single time step, a phenomenon (which we call opinion jumping) that is not possible in standard dyadic BCMs. We also show that there is a phase transition in the convergence time on the complete hypergraph when the variance $\sigma^2$ of the initial distribution equals the confidence bound $c$. Therefore, to determine the convergence properties of our hypergraph BCM when the variance and the number of hyperedges are both large, it is necessary to use analytical methods instead of relying only on Monte Carlo simulations.