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People's opinions evolve over time as they interact with their friends,family, colleagues, and others. In the study of opinion dynamics on networks,one often encodes interactions between people in the form of dyadicrelationships, but many social interactions in real life are polyadic (i.e.,they involve three or more people). In this paper, we extend an asynchronousbounded-confidence model (BCM) on graphs, in which nodes are connected pairwiseby edges, to an asynchronous BCM on hypergraphs, in which arbitrarily manynodes can be connected by a single hyperedge. We show that our hypergraph BCMconverges to consensus under a wide range of initial conditions for theopinions of the nodes, including for non-uniform and asymmetric initial opiniondistributions. We also show that, under suitable conditions, echo chambers canform on hypergraphs with community structure. We demonstrate that the opinionsof individuals can sometimes jump from one opinion cluster to another in asingle time step, a phenomenon (which we call ``opinion jumping'') that is notpossible in standard dyadic BCMs. Additionally, we observe that there is aphase transition in the convergence time on {a complete hypergraph} when thevariance $\sigma^2$ of the initial opinion distribution equals the confidencebound $c$. We prove that the convergence time grows at least exponentially fastwith the number of nodes when $\sigma^2 > c$ and the initial opinions arenormally distributed. Therefore, to determine the convergence properties of ourhypergraph BCM when the variance and the number of hyperedges are both large,it is necessary to use analytical methods instead of relying only on MonteCarlo simulations.

A Bounded-Confidence Model of Opinion Dynamics on Hypergraphs