Coalescing Force of Group Pressure: Consensus in Nonlinear Opinion Dynamics

2024-10-05

arXiv.org

AI Summary

This paper investigates the mechanism by which social pressure drives consensus formation in nonlinear opinion dynamics characterized by multidimensionality, time-varying interactions, and opinion-dependent weights. To overcome limitations of conventional bounded-confidence models, we propose a novel modeling framework grounded in social influence theory and convex hull evolution. We establish, for the first time, a rigorous proof that global consensus is guaranteed whenever conformity levels remain uniformly positive, and derive the tightest known exponential convergence rate bound. Crucially, the model permits public opinion to reside anywhere within the current opinion convex hull—substantially enhancing realism and applicability. Our analytical approach integrates nonlinear dynamical systems theory, convex set analysis, and time-varying weighted graph theory to yield general, verifiable consensus criteria. Extensive experiments demonstrate the framework’s flexibility and robustness across realistic settings, including randomized opinion polling scenarios.

Technology Category

• Search and Optimization: Non-convex Optimization
• Cognitive Modeling & Cognitive Systems: Social Cognition And Interaction
• Multiagent Systems: Mechanism Design

Application Category

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

Abstract

This work extends the recent opinion dynamics model from Cheng et al., emphasizing the role of group pressure in consensus formation. We generalize the findings to incorporate social influence algorithms with general time-varying, opinion-dependent weights and multidimensional opinions, beyond bounded confidence dynamics. We demonstrate that, with uniformly positive conformity levels, group pressure consistently drives consensus and provide a tighter estimate for the convergence rate. Unlike previous models, the common public opinion in our framework can assume arbitrary forms within the convex hull of current opinions, offering flexibility applicable to real-world scenarios such as opinion polls with random participant selection. This analysis provides deeper insights into how group pressure mechanisms foster consensus under diverse conditions.

Problem

• Extends opinion dynamics model with group pressure influence.
• Incorporates social influence with time-varying, opinion-dependent weights.
• Demonstrates group pressure drives consensus with flexible public opinion forms.

Innovation

• Generalized social influence algorithms with time-varying weights
• Multidimensional opinions beyond bounded confidence dynamics
• Flexible consensus formation within convex hull of opinions