论文标题
Hegselmann-Krause模型的多维扩展
Multi-dimensional extensions of the Hegselmann-Krause model
论文作者
论文摘要
在本文中，我们考虑了两种多维Hagselmann-Krause（HK）模型用于意见动力学。这两个模型描述了个人如何根据同行的影响来调整自己的观点。这些模型在标准方面有所不同，根据该标准，个人决定要受到谁的影响。在基于平均的模型中，个人将他们对各种主题的平均意见与其他人的意见进行了比较，并且仅与那些平均意见在置信区间内的人进行互动。对于此模型，我们为意见范围的合同性提供了替代证明，并表明，当且仅当他们的平均意见这样做时，代理商的意见达成共识/聚类。在统一亲和力模型中，代理比较他们对每个主题的看法，并且只有当主题的情况下，这种观点差异不超过给定的容忍度。我们确定了统一亲和力模型在订单保护属性主题的条件下，我们证明了全球意见范围（因此每个主题的意见范围）是无兴趣的。
In this paper, we consider two multi-dimensional Hagselmann-Krause (HK) models for opinion dynamics. The two models describe how individuals adjust their opinions on multiple topics, based on the influence of their peers. The models differ in the criterion according to which individuals decide whom they want to be influenced from. In the average-based model, individuals compare their average opinions on the various topics with those of the other individuals and interact only with those individuals whose average opinions lie within a confidence interval. For this model, we provide an alternative proof for the contractivity of the range of opinions and show that the agents' opinions reach consensus/clustering if and only if their average opinions do so. In the uniform affinity model agents compare their opinions on every single topic and influence each other only if, topic-wise, such opinions do not differ more than a given tolerance. We identify conditions under which the uniform affinity model enjoys the order-preservation property topic-wise and we prove that the global range of opinions (and hence the range of opinions on every single topic) are nonincreasing.
