论文标题
对大量选民的随机选举的分析
An Analysis of Random Elections with Large Numbers of Voters
论文作者
论文摘要
在每个选民对所有候选人进行排名的选举中，我们考虑了每对候选人之间的正面结果，并形成一个标记的有向图，称为Margin Graph，其中包含每个候选人比其他每个候选人的胜利余量。开发投票方法的一个核心问题是，在此图中可能会有循环，其中候选$ \ mathsf {a} $打败了候选$ \ Mathsf {b} $，$ \ Mathsf {b} $ tods $ \ m artssf {c} $在本文中，我们应用了中心限制定理，图形同源性和线性代数来分析大量选民发生这种情况的可能性。有很多关于分析获得多数赢家的可能性的文献。我们的分析更加细粒度。我们分析的结果是，在选举数量无限的选举中，从一定精确的意义上讲更循环的保证金图不太可能发生。
In an election in which each voter ranks all of the candidates, we consider the head-to-head results between each pair of candidates and form a labeled directed graph, called the margin graph, which contains the margin of victory of each candidate over each of the other candidates. A central issue in developing voting methods is that there can be cycles in this graph, where candidate $\mathsf{A}$ defeats candidate $\mathsf{B}$, $\mathsf{B}$ defeats $\mathsf{C}$, and $\mathsf{C}$ defeats $\mathsf{A}$. In this paper we apply the central limit theorem, graph homology, and linear algebra to analyze how likely such situations are to occur for large numbers of voters. There is a large literature on analyzing the probability of having a majority winner; our analysis is more fine-grained. The result of our analysis is that in elections with the number of voters going to infinity, margin graphs that are more cyclic in a certain precise sense are less likely to occur.
