In social systems, the evolution of interpersonal appraisals and individual opinions are not independent processes but intertwine with each other. Despite extensive studies on both opinion dynamics and appraisal dynamics separately, no previous work has ever combined these two processes together. In this paper, we propose a novel and intuitive model on the interplay between homophily-based appraisal dynamics and influence-based opinion dynamics. We assume that individuals' opinions are updated via the influence network constructed from their interpersonal appraisals, which are in turn updated based on the individual opinions via the homophily mechanism. By theoretical analysis, we characterize the set of equilibria and some transient behavior of our model. Moreover, we establish the equivalence among the convergence of the appraisal network to social balance, the modulus consensus of individual opinions, and the non-vanishing appraisals. Monte Carlo validations further show that the non-vanishing appraisals condition holds for generic initial conditions. Compared with previous works that explain the emergence of social balance via person-to-person homophily mechanism, our model provides an alternative explanation in terms of the person-to-entity homophily mechanism. In addition, our model also describes how individuals' opinions on multiple irrelevant issues become correlated and converge to modulus consensus over time-varying influence networks.

中文翻译：

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基于同质性的评价动态和基于影响的意见动态之间的相互作用：建模和分析

在社会系统中，人际评价和个人意见的演变不是独立的过程，而是相互交织的。尽管分别对意见动态和评价动态进行了广泛的研究，但以前的工作从未将这两个过程结合在一起。在本文中，我们针对基于同质性的评估动态和基于影响的意见动态之间的相互作用提出了一种新颖且直观的模型。我们假设个人的意见是通过他们的人际评价构建的影响网络更新的，而影响网络又通过同质机制根据个人意见进行更新。通过理论分析，我们表征了我们模型的一组平衡和一些瞬态行为。而且，我们建立了评价网络对社会平衡的收敛性、个体意见的模数共识和非消失评价之间的等价性。Monte Carlo 验证进一步表明非消失评估条件适用于通用初始条件。与之前通过人对人同质机制解释社会平衡出现的工作相比，我们的模型在人对实体的同质机制方面提供了另一种解释。此外，我们的模型还描述了个人对多个不相关问题的意见如何在时变影响网络上相互关联并收敛到模数共识。Monte Carlo 验证进一步表明非消失评估条件适用于通用初始条件。与之前通过人对人同质机制解释社会平衡出现的工作相比，我们的模型在人对实体的同质机制方面提供了另一种解释。此外，我们的模型还描述了个人对多个不相关问题的意见如何在时变影响网络上相互关联并收敛到模数共识。Monte Carlo 验证进一步表明非消失评估条件适用于通用初始条件。与之前通过人对人同质机制解释社会平衡出现的工作相比，我们的模型在人对实体的同质机制方面提供了另一种解释。此外，我们的模型还描述了个人对多个不相关问题的意见如何在时变影响网络上相互关联并收敛到模数共识。