Gsänger Matthias, Hösel Volker, Mohamad-Klotzbach Christoph, Müller Johannes
Institute of Political Science and Sociology, Julius-Maximilians-University (JMU), 97074 Würzburg, Germany.
School for Computation, Information and Technology, TU München (TUM), 80333 Munich, Germany.
Entropy (Basel). 2024 Feb 28;26(3):212. doi: 10.3390/e26030212.
A unifying setup for opinion models originating in statistical physics and stochastic opinion dynamics are developed and used to analyze election data. The results are interpreted in the light of political theory. We investigate the connection between Potts (Curie-Weiss) models and stochastic opinion models in the view of the Boltzmann distribution and stochastic Glauber dynamics. We particularly find that the q-voter model can be considered as a natural extension of the Zealot model, which is adapted by Lagrangian parameters. We also discuss weak and strong effects (also called extensive and nonextensive) continuum limits for the models. The results are used to compare the Curie-Weiss model, two q-voter models (weak and strong effects), and a reinforcement model (weak effects) in explaining electoral outcomes in four western democracies (United States, Great Britain, France, and Germany). We find that particularly the weak effects models are able to fit the data (Kolmogorov-Smirnov test) where the weak effects reinforcement model performs best (AIC). Additionally, we show how the institutional structure shapes the process of opinion formation. By focusing on the dynamics of opinion formation preceding the act of voting, the models discussed in this paper give insights both into the empirical explanation of elections as such, as well as important aspects of the theory of democracy. Therefore, this paper shows the usefulness of an interdisciplinary approach in studying real world political outcomes by using mathematical models.
我们开发了一种源自统计物理学和随机舆论动态的统一意见模型设置，并将其用于分析选举数据。研究结果依据政治理论进行解读。我们从玻尔兹曼分布和随机格劳伯动力学的角度研究了Potts（居里 - 外斯）模型与随机舆论模型之间的联系。我们特别发现，q - 投票者模型可被视为狂热者模型的自然扩展，该扩展由拉格朗日参数适配。我们还讨论了这些模型的弱效应和强效应（也称为广延和非广延）连续极限。研究结果用于比较居里 - 外斯模型、两个q - 投票者模型（弱效应和强效应）以及一个强化模型（弱效应）在解释四个西方民主国家（美国、英国、法国和德国）选举结果方面的情况。我们发现，尤其是弱效应模型能够拟合数据（柯尔莫哥洛夫 - 斯米尔诺夫检验），其中弱效应强化模型表现最佳（AIC）。此外，我们展示了制度结构如何塑造意见形成过程。通过关注投票行为之前的意见形成动态，本文所讨论的模型不仅为选举的实证解释提供了见解，也为民主理论的重要方面提供了见解。因此，本文展示了跨学科方法在运用数学模型研究现实世界政治结果方面的实用性。
