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

Yan-Wen Xiao; Wei-Chen Guo; Bao-Quan Ai; Liang He

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arXiv · 2505.03464

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

Yan-Wen Xiao·Wei-Chen Guo·Bao-Quan Ai·Liang He

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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.

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Yan-Wen Xiao, Wei-Chen Guo, Bao-Quan Ai, Liang He. 2025-05-08. Barrier induced stalemate-consensus transition of self-propelled participants subject to majority rule. https://arxiv.org/abs/2505.03464

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