Inevitability of Polarization in Geometric Opinion Exchange

Abdou Majeed Alidou, J\'ulia Balig\'acs, Max Hahn-Klimroth, Jan H\k{a}z{\l}a, Lukas Hintze and Olga Scheftelowitsch

Papers from arXiv.org

Abstract: Polarization and unexpected correlations between opinions on diverse topics (including in politics, culture and consumer choices) 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. The opinions are updated according to an update rule belonging to a general class. Our findings are twofold. First, polarization appears to be ubiquitous in the class of models we study, requiring only relatively modest assumptions 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 that are absent in two dimensions.

Date: 2024-02
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://arxiv.org/pdf/2402.08446 Latest version (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2402.08446

Access Statistics for this paper

More papers in Papers from arXiv.org
Bibliographic data for series maintained by arXiv administrators ().