论文标题
那里有几个共济会？公制空间中的共识投票机制
How Many Freemasons Are There? The Consensus Voting Mechanism in Metric Spaces
论文作者
论文摘要
当接受该群体时，我们研究了一个社会群体的演变，这是通过共识或一致投票确定的。在每个时间段内，两名候选人申请会员资格，并且仅当所有当前小组成员同意时才选择一个候选人。我们应用了投票的空间理论，其中小组成员和候选人位于度量空间中，每个成员都对其最接近（最相似）的候选人进行投票。我们的兴趣集中在$ t $时间段之后的小组中的基数上。为了评估这一点，我们研究了在度量空间上投票的动态共识中固有的几何形状。这使我们能够开发一组技术，用于下限和上限一个组的预期基数。我们将这些方法专门用于二维度量空间。对于单位球，$ t $时间段后集团的预期基数为$θ（t^{1/8}）$。相比之下，对于单位平方，预期的基数至少为$ω（\ ln t）$，但最多$ o（\ ln t \ cdot \ ln \ ln t）$。
We study the evolution of a social group when admission to the group is determined via consensus or unanimity voting. In each time period, two candidates apply for membership and a candidate is selected if and only if all the current group members agree. We apply the spatial theory of voting where group members and candidates are located in a metric space and each member votes for its closest (most similar) candidate. Our interest focuses on the expected cardinality of the group after $T$ time periods. To evaluate this we study the geometry inherent in dynamic consensus voting over a metric space. This allows us to develop a set of techniques for lower bounding and upper bounding the expected cardinality of a group. We specialize these methods for two-dimensional metric spaces. For the unit ball the expected cardinality of the group after $T$ time periods is $Θ(T^{1/8})$. In sharp contrast, for the unit square the expected cardinality is at least $Ω(\ln T)$ but at most $O(\ln T \cdot \ln\ln T )$.
