  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), in
which we incorporate 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 optimum minimizing
exit time {\tau} . We substantiate this finding by using mean-field theory on
annealed uniform hypergraphs with N nodes, for which {\tau} scales as A ln N,
where the prefactor 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.
