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

2025-11-17

AI Summary

Traditional pairwise-interaction models fail to capture how higher-order interactions—represented by *d*-uniform hypergraphs—influence collective opinion dynamics and decision-making in group settings. Method: We propose a hypergraph-based framework for group opinion dynamics that explicitly incorporates group size *d*, option quality ratio *α*, and information loss in individual updating rules. We analyze the model via mean-field bifurcation theory and agent-based simulations across diverse hypergraph topologies (e.g., random, scale-free). Contribution/Results: We uncover a counterintuitive “majority irrationality” phenomenon: increasing group size *d* can paradoxically favor inferior options. This phase transition is governed solely by *d* and *α*, independent of hypergraph structure. We analytically derive two critical stability thresholds, *α*_tr1 and *α*_tr2, demarcating regimes of consensus on high- versus low-quality options—and confirm their precision through numerical experiments. Theoretical predictions align closely with simulation results across topologies.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Decision/Utility Theory
• Knowledge Representation and Reasoning: Preferences

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution

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

Problem

• Modeling opinion dynamics with group interactions on hypergraphs
• Analyzing how group size affects collective decision-making outcomes
• Identifying critical thresholds for consensus stability in opinion formation

Innovation

• Higher-order interactions modeled on d-uniform hypergraphs
• Bifurcation analysis identifies critical opinion stability thresholds
• Group size drives adoption of suboptimal opinion choices