Polarization in Attraction-Repulsion Models

TL;DR

This paper presents an extended opinion dynamics model incorporating both attraction and repulsion, demonstrating the emergence of polarization as a stable state and analyzing phase transitions in large populations.

Contribution

It introduces a novel attraction-repulsion model for opinion dynamics and characterizes the conditions leading to polarization versus consensus.

Findings

Total consensus and polarization are the only stable configurations.

The model exhibits a phase transition in large populations.

Analysis extends to higher dimensions with heuristic support.

Abstract

This paper introduces a model for opinion dynamics, where at each time step, randomly selected agents see their opinions - modeled as scalars in [0,1] - evolve depending on a local interaction function. In the classical Bounded Confidence Model, agents opinions get attracted when they are close enough. The proposed model extends this by adding a repulsion component, which models the effect of opinions getting further pushed away when dissimilar enough. With this repulsion component added, and under a repulsion-attraction cleavage assumption, it is shown that a new stable configuration emerges beyond the classical consensus configuration, namely the polarization configuration. More specifically, it is shown that total consensus and total polarization are the only two possible limiting configurations. The paper further provides an analysis of the infinite population regime in dimension 1 and higher, with a phase transition phenomenon conjectured and backed heuristically.