Understanding the evolution of collective beliefs is of critical importance to get insights on the political trends as well as on social tastes and opinions. In particular, it is pivotal to develop analytical models that can predict the beliefs dynamics and capture the interdependence of opinions on different subjects. In this article we tackle this issue also accounting for the individual endogenous process of opinion evolution, as well as repulsive interactions between individuals’ opinions that may arise in the presence of an adversarial attitude of the individuals. Using a mean field approach, we characterize the time evolution of opinions of a large population of individuals through a multidimensional Fokker-Planck equation, and we identify the conditions under which stability holds. Finally, we derive the steady-state opinion distribution as a function of the individuals’ personality and of the existing social interactions. Our numerical results show interesting dynamics in the collective beliefs of different social communities, and they highlight the effect of correlated subjects as well as of individuals with an adversarial attitude.

中文翻译：

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社交网络中相关主题的观点动态

了解集体信仰的演变对于深入了解政治趋势以及社会品味和观点至关重要。特别是，开发可以预测信念动态并捕捉不同主题意见的相互依存关系的分析模型至关重要。在本文中，我们解决了这个问题，同时也解释了意见演变的个体内生过程，以及在个体存在对抗态度时可能出现的个体意见之间的排斥相互作用。使用平均场方法，我们通过多维 Fokker-Planck 方程表征大量个人意见的时间演变，并确定稳定性保持的条件。最后，我们将稳态意见分布推导出为个人个性和现有社会互动的函数。我们的数值结果显示了不同社会社区集体信念的有趣动态，它们突出了相关主题以及具有对抗态度的个人的影响。