  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 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 opinion 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 opinion 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.
