Complex problems of social interaction are usually studied within the framework of agent-based models. Some of these problems, such as issue alignment and opinion polarization, are better suited in the framework of $n$-dimensional opinion space. Although this kind of complex problem may be explored by numerical simulations, these simulations can hinder our ability to obtain general results. In this work, we show how, under certain conditions, a classical multidimensional opinion model such as the Axelrod model can give rise to a closed set of master equations in terms of vector similarities between agents. The analytical results fully agree with the simulations on complete networks, accurately predict the similarity distribution of the whole system in sparse topologies, and provide a good approximation of the similarity of physical links that improves when the mean degree of the system increases.

中文翻译：

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基于相似度向量的Axelrod模型解析方法

通常在基于主体的模型框架内研究社会互动的复杂问题。其中一些问题，例如问题一致性和意见分歧，更适合于以下方面的框架：$ñ$维意见空间。尽管可以通过数值模拟来探索这种复杂的问题，但是这些模拟会阻碍我们获得一般结果的能力。在这项工作中，我们展示了在某些条件下，经典的多维意见模型（例如Axelrod模型）如何根据代理之间的向量相似性产生封闭的主方程组。分析结果与完整网络上的仿真完全吻合，可以在稀疏拓扑结构中准确预测整个系统的相似性分布，并且可以很好地近似物理链接的相似性，当系统的平均程度增加时，物理链接的相似性会提高。