Coalescing Force of Group Pressure: Consensus in Nonlinear Opinion Dynamics

TL;DR

This paper investigates how group pressure influences consensus in nonlinear opinion dynamics, extending previous models to include social influence with time-varying, opinion-dependent weights and multidimensional opinions, demonstrating that positive conformity leads to consensus.

Contribution

It introduces a generalized opinion dynamics model incorporating diverse social influence mechanisms and proves that group pressure reliably induces consensus under broad conditions.

Findings

Group pressure drives consensus with positive conformity levels.

The model allows arbitrary public opinion forms within the convex hull of current opinions.

Provides tighter convergence rate estimates for opinion consensus.

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.