Collective decision making with higher-order interactions on d-uniform hypergraphs

Understanding how group interactions influence opinion dynamics is fundamental to the study of collective behavior. In this work, we propose and study a model of opinion dynamics on d-uniform hypergraphs, where individuals interact through group-based (higher-order) structures rather than simple pairwise connections. Each one of the two opinions A and B is characterized by a quality, Q_{A} and Q_{B}, and agents update their opinions according to a general mechanism that takes into account the weighted fraction of agents supporting either opinion and the pooling error, α, a proxy for the information lost during the interaction. Through bifurcation analysis of the mean-field model, we identify two critical thresholds, α_{crit}^{(1)} and α_{crit}^{(2)}, which delimit stability regimes for the consensus states. These analytical predictions are validated through extensive agent-based simulations on both random and scale-free hypergraphs. Moreover, the analytical framework demonstrates that the bifurcation structure and critical thresholds are independent of the underlying topology of the higher-order network, depending solely on the parameters d, i.e., the size of the interaction groups, and the quality ratio. Finally, we bring to the fore a nontrivial effect: The large sizes of the interaction groups could drive the system toward the adoption of the worst option.