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Dynamics of Evolving Social Groups

机译：不断发展的社会群体的动力

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Exclusive social groups are ones in which the group members decide whether or not to admit a candidate to the group. Examples of exclusive social groups include academic departments and fraternal organizations. In this article, we introduce an analytic framework for studying the dynamics of exclusive social groups. In our model, every group member is characterized by his opinion, which is represented as a point on the real line. The group evolves in discrete time steps through a voting process carried out by the group's members. Due to homophily, each member votes for the candidate who is more similar to him (i.e., closer to him on the line). An admission rule is then applied to determine which candidate, if any, is admitted. We consider several natural admission rules including majority and consensus. We ask: How do different admission rules affect the composition of the group in the long run? We study both growing groups (where new members join old ones) and fixed-size groups (where new members replace those who quit). Our analysis reveals intriguing phenomena and phase transitions, some of which are quite counterintuitive.
机译：独家社会团体是小组成员决定是否接纳该小组的候选人的社会团体。独家社会团体的例子包括学术部门和兄弟组织。在本文中，我们介绍了一个分析框架，用于研究独家社会群体的动态。在我们的模型中，每个小组成员的特征都以他的意见为特征，这被表示为真实的观点。该小组在离散的时间中演变，通过该小组成员进行的投票过程。由于同质性，每个成员都投票赞成与他更相似的候选人（即在线上更靠近他）。然后，应用录取规则以确定录取哪个候选人。我们考虑了包括多数和共识在内的几项自然录取规则。我们问：从长远来看，不同的入学规则如何影响小组的组成？我们研究两个成长组（新成员加入旧成员）和固定大小的小组（新成员取代退出的人）。我们的分析揭示了有趣的现象和相变，其中一些非常违反直觉。

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