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 effects of group dynamics through 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 $\mathcal{A}lnN$, where the prefactor $\mathcal{A}$ 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.

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• Collective behavior in networks
• Social dynamics
• Voter model