评分规则下的非收敛选举均衡：超越多元性
Nonconvergent Electoral Equilibria under Scoring Rules: Beyond Plurality
摘要：
我们使用霍特林的空间模型的竞争调查的政治候选人的立场采取的行为下一类的选举制度被称为评分规则。在评分规则选举中，选民对所有竞选公职的候选人进行排名，然后根据非递增分数的向量为候选人分配分数。Cox（1987）描述了所有候选人采取相同政策的收敛纳什均衡。在这里，我们研究非收敛均衡，候选人采取不同的政策。我们确定了一些类别的评分规则表现出一系列不同的平衡属性。对于其中的一些，不收敛的均衡不存在。对于其他人来说，观察到候选人聚集在整个问题空间的位置上的非收敛均衡。特别地，我们证明了这类凸规则除了Borda规则的某些衍生物外，不存在纳什均衡（收敛或非收敛）。最后，我们考察了四名、五名和六名候选人选举的特殊情况.在前两种情况下，我们提供了一个完整的非收敛平衡的特征。
英文摘要：
We use Hotelling's spatial model of competition to investigate the position-taking behaviour of political candidates under a class of electoral systems known as scoring rules. In a scoring rule election, voters rank all the candidates running for office, following which the candidates are assigned points according to a vector of nonincreasing scores. Convergent Nash equilibria in which all candidates adopt the same policy were characterised by Cox (1987). Here, we investigate nonconvergent equilibria, where candidates adopt divergent policies. We identify a number of classes of scoring rules exhibiting a range of different equilibrium properties. For some of these, nonconvergent equilibria do not exist. For others, nonconvergent equilibria in which candidates cluster at positions spread across the issue space are observed. In particular, we prove that the class of convex rules does not have Nash equilibria (convergent or nonconvergent) with the exception of some derivatives of Borda rule. Finally, we examine the special cases of four-, five- and six- candidate elections. In the former two cases, we provide a complete characterisation of nonconvergent equilibria.
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