Barrier induced stalemate-consensus transition of self-propelled participants subject to majority rule

TL;DR

This study models how physical barriers influence opinion dynamics among mobile agents, revealing a critical barrier size that causes a transition from opinion stalemate to consensus, with divergence in relaxation times near this transition.

Contribution

It introduces a minimal agent-based model demonstrating how barriers induce a phase transition in opinion states, highlighting the critical barrier size and divergence phenomena.

Findings

Existence of a critical barrier size for opinion transition

Power-law divergence of relaxation time near the critical point

Barriers significantly impact opinion consensus dynamics

Abstract

Natural or artificial barriers, such as the Himalayas, the Berlin Wall, or the Korean Demilitarized Zone, can significantly impede human migration. As a consequence, they may also hinder the dissemination of opinions within society, thereby contributing to divergent geopolitical landscapes and cultural developments. This raises a fundamental question: how do such barriers influence the opinion dynamics of mobile agents, such as human beings? In particular, can a barrier induce transitions in collective opinion states among spatially segregated groups? Here, we investigate the opinion dynamics governed by majority rule in a minimal model comprising self-propelled agents with binary opinions performing random walks within a closed space divided by a barrier. We focus on the conditions under which initially segregated clusters of agents with opposing opinions can reach consensus. Our results reveal the existence of a critical barrier size that marks a transition between stalemate and consensus states. Near this critical point, the relaxation time to reach consensus from an initial stalemate exhibits a power-law divergence. This barrier-induced stalemate-consensus transition in a simple agent-based model offers new insights into the role of physical or social barriers in shaping opinion dynamics and social structures.