Higher-Order Interactions in ABM: A Case Study Using Topologically-Perturbed Voter Models

Using variants of the voter model, and inspired by simulations of such models on networks, we studied a variety of ABM implementations using a random activation scheduler incorporating dyadic and higher-order interactions. Our results provide evidence about the dependency of various observables on whether state updates are simultaneous or staggered per model step (i.e., matrix vs. ABM), if interactions are pairwise or higher-order, or if the underlying topology changes even when the abstract specification of the voter model is the same: simulation features usually thought of as computational—even intuitively innocuous- prove to be phenomenologically impactful. We found that average magnetization is largely modulated by the initial state in dyadic voter models, that exit probability is controlled by network and simulation types, and that interaction types divide consensus times except for 2D regular lattices, which exhibit surprising sensibility to these perturbations. In addition, regular lattices appear to contain spatio-temporal alternating motifs once certain magnetization values are reached, similar to gliders in Conway’s Game of Life. Our findings suggest that ABM simulation workflows must incorporate multiple interaction types and spatial configurations in order to tease our robust findings from either implementation-dependent artifacts or misspecified models, guided by robust statistical physics principles.