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arXiv 2402.08446cs.SIecon.TH
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几何意见交换中极化的必然性

Inevitability of Polarization in Geometric Opinion Exchange

Abdou Majeed Alidou, Júlia Baligács, Max Hahn-Klimroth, Jan Hązła, Lukas Hintze, Olga Scheftelowitsch

AI总结:

本文研究几何意见交换模型中极化的必然性,证明在仅需适度偏见同化假设下极化普遍存在,并揭示二维与三维及以上动力学在极化表现上的定性差异。

摘要:

不同主题(包括政治、文化和消费者选择)意见之间的极化和意外关联一直备受关注。然而,许多理论模型似乎无法令人信服地解释这些现象。本文受近期一系列工作的启发,这些工作研究用偏见同化和不同主题意见间的几何相互作用来解释极化的模型。智能体意见表示为多维球面上的单位向量,并根据几何规则进行更新。与以往工作不同,我们关注经典的意见交换设置,即智能体在离散时间步更新意见,每步随机一对智能体进行交互。意见根据属于一个一般类别的更新规则进行更新。我们的发现有两方面。首先,在我们研究的模型类别中,极化似乎是普遍存在的,只需反映偏见同化的相对适度假设。其次,二维动力学一方面与三维或更高维动力学之间存在定性差异。相应地,我们证明了二维中一大类更新规则几乎必然出现极化。然后,我们在更有限的情况下证明了三维及更高维的极化,并试图阐明二维中不存在的核心困难。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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