Inevitability of Polarization in Geometric Opinion Exchange

• 成果类型: Article; Early Access
• 署名作者: Alidou, Abdou Majeed; Hazla, Jan; Baligacs, Julia; Hahn-Klimroth, Max; Hintze, Lukas; Scheftelowitsch, Olga
• 署名单位: University of Oxford; Goethe University Frankfurt; University of Hamburg; Dortmund University of Technology
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0696
• 发表日期: 2026-06-02
• 关键词: opinion exchange; opinion polarization; DYNAMICS

摘要

Polarization and unexpected correlations between opinions on diverse topics are an object of sustained attention. However, numerous theoretical models do not seem to convincingly explain these phenomena. This paper is motivated by a recent line of work, studying models where polarization can be explained in terms of biased assimilation and geometric interplay between opinions on various topics. The agent opinions are represented as unit vectors on a multidimensional sphere and updated according to geometric rules. In contrast to previous work, we focus on the classical opinion exchange setting, where the agents update their opinions in discrete time steps, with a pair of agents interacting randomly at every step. Our findings are twofold. First, polarization appears to be ubiquitous in the class of models we study, requiring only relatively modest assumptions on the update functions, reflecting biased assimilation. Second, there is a qualitative difference between two-dimensional dynamics on the one hand, and three or more dimensions on the other. Accordingly, we prove almost sure polarization for a large class of update rules in two dimensions. Then, we prove polarization in three and more dimensions in more limited cases and try to shed light on central difficulties absent in two dimensions.