Structure, influence, and consensus: Modeling majority-driven dynamics on hypernetworks

Collective behavior in social systems is shaped not only by pairwise individual-level interactions but also by higher-order groupwise interactions. In this study, we investigate majority-driven collective dynamics within a hypernetwork framework that integrates both pairwise and groupwise interactions. Through systematic simulations across four network topologies, we demonstrate that majority dynamics robustly drive systems from disorder to order, ultimately leading to stable global consensus. By varying pairwise structures, groupwise structures, pairwise-groupwise influence weights, and initial system conditions, we find that the speed and stability of convergence depend strongly on pairwise structures: larger and denser networks converge more smoothly and stably, where random connectivity sustains diversity and delays consensus while structured connectivity promotes strong and resilient consensus. Higher-order groupwise interactions further suppress disagreement and reinforce global consensus. We also identify a fundamental trade-off between pairwise and groupwise influence weights. Dominant pairwise influence accelerate consensus, whereas dominant groupwise influence preserves heterogeneity and slows convergence. In addition, collective outcomes are jointly determined by initial state distributions and individual preferences, giving rise to threshold-like transitions that depend on network topology. Together, these findings reveal how higher-order social interactions reshape majority dynamics and provide a unified framework for understanding consensus formation in complex social systems beyond purely dyadic interactions.