Oscillatory and Excitable Dynamics in an Opinion Model with Group Opinions

2024-08-23

arXiv.org

AI Summary

Conventional opinion dynamics models only capture pairwise interactions, neglecting the independent influence of collective group opinions. Method: We propose a hypergraph-based model that simultaneously represents heterogeneous opinions of individuals and triadic groups, along with their coupled evolutionary dynamics. Contribution/Results: Our framework reveals that group-level opinions can induce two novel non-stationary behaviors—self-sustained oscillations and excitation-driven fluctuations (analogous to social fads). We rigorously prove that oscillations emerge exclusively when pairwise and higher-order interactions are incompletely correlated. Using mean-field theory validated by extensive numerical simulations, we quantitatively characterize the dependencies of oscillation frequency, excitation amplitude, and group coupling strength. These findings demonstrate that higher-order group structures are not merely topological features of networks but constitute a fundamental mechanism driving phase transitions in social dynamics.

Technology Category

• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Game Theory and Economic Paradigms: Social Choice / Voting
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community

Application Category

• Social Networks and Social Media: Media and governance, opinion dynamics, filter bubbles, polarization
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Social networks and social learning

Abstract

In traditional models of opinion dynamics, each agent in a network has an opinion and changes in opinions arise from pairwise (i.e., dyadic) interactions between agents. However, in many situations, groups of individuals can possess a collective opinion that may differ from the opinions of the individuals. In this paper, we study the effects of group opinions on opinion dynamics. We formulate a hypergraph model in which both individual agents and groups of 3 agents have opinions, and we examine how opinions evolve through both dyadic interactions and group memberships. In some parameter regimes, we find that the presence of group opinions can lead to oscillatory and excitable opinion dynamics. In the oscillatory regime, the mean opinion of the agents in a network has self-sustained oscillations. In the excitable regime, finite-size effects create large but short-lived opinion swings (as in social fads). We develop a mean-field approximation of our model and obtain good agreement with direct numerical simulations. We also show, both numerically and via our mean-field description, that oscillatory dynamics occur only when the number of dyadic and polyadic interactions per agent are not completely correlated. Our results illustrate how polyadic structures, such as groups of agents, can have important effects on collective opinion dynamics.

Problem

• Studying group opinions' impact on oscillatory dynamics
• Modeling opinion evolution via dyadic and group interactions
• Exploring conditions for oscillatory and excitable opinion behaviors

Innovation

• Hypergraph model with individual and group opinions
• Mean-field approximation for opinion dynamics
• Dyadic and polyadic interactions analysis