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

TL;DR

This paper models opinion dynamics on $d$-uniform hypergraphs, revealing how higher-order group interactions and information loss influence consensus stability and can lead to the adoption of suboptimal opinions.

Contribution

It introduces a mean-field model for opinion dynamics on hypergraphs, identifying critical thresholds and showing topology-independent bifurcation behavior.

Findings

Critical thresholds for opinion stability are analytically derived.

Bifurcation structure depends only on group size and opinion quality, not network topology.

Large group sizes can promote adoption of the less favorable opinion.

Abstract

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, $\alpha$, a proxy for the information lost during the interaction. Through bifurcation analysis of the mean-field model, we identify two critical thresholds, $\alpha_{\text{crit}}^{(1)}$ and $\alpha_{\text{crit}}^{(2)}$, 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.