Competition between group interactions and nonlinearity in voter dynamics on hypergraphs

TL;DR

This paper introduces a polyadic voter model on hypergraphs that incorporates group interactions and nonlinearity, demonstrating faster consensus formation and optimal exit times influenced by group size and interaction strength.

Contribution

The study formulates a new group-driven voter model that captures the competition between nonlinearity and group interactions, revealing their impact on consensus dynamics.

Findings

GVM achieves faster consensus than standard voter models.

Exit time scales as A ln N, with A depending on nonlinearity and group constraints.

Optimal conditions minimize the consensus exit time.

Abstract

Social dynamics are often driven by both pairwise (i.e., dyadic) relationships and higher-order (i.e., polyadic) group relationships, which one can describe using hypergraphs. To gain insight into the impact of polyadic relationships on dynamical processes on networks, we formulate and study a polyadic voter process, which we call the group-driven voter model (GVM), that incorporates the effect of group interactions by nonlinear interactions that are subject to a group (i.e., hyperedge) constraint. By examining the competition between nonlinearity and group sizes, we show that the GVM achieves consensus faster than standard voter-model dynamics, with an optimal minimizing exit time. We substantiate this finding by using mean-field theory on annealed uniform hypergraphs with $N$ nodes, for which the exit time scales as ${\cal A}\ln N$, where the prefactor ${\cal A}$ depends both on the nonlinearity and on group-constraint factors. Our results reveal how competition between group interactions and nonlinearity shapes GVM dynamics. We thereby highlight the importance of such competing effects in complex systems with polyadic interactions.