Polyadic Opinion Formation: The Adaptive Voter Model on a Hypergraph

Abstract

The adaptive voter model is widely used to model opinion dynamics in social complex networks. However, existing adaptive voter models are limited to only pairwise interactions and fail to capture the intricate social dynamics that arises in groups. This paper extends the adaptive voter model to hypergraphs to explore how forces of peer pressure influence collective decision-making. The model consists of two processes: individuals can either consult the group and change their opinion or leave the group and join a different one. The interplay between those two processes gives rise to a two-phase dynamics. In the initial phase, the topology of the hypergraph quickly reaches a new stable state. In the subsequent phase, opinion dynamics plays out on the new topology depending on the mechanism by which opinions spread. If the group always follows the majority, the network rapidly converges to fragmented communities. In contrast, if individuals choose an opinion proportionally to its representation in the group, the system remains in a metastable state for an extended period of time. The results are supported both by stochastic simulations and an analytical mean-field description in terms of hypergraph moments with a moment closure at the pair level.