A judgement aggregation rule takes the views of a collection of voters over a set of interconnected issues and yields a logically consistent collective view. The median rule is a judgement aggregation rule that selects the logically consistent view which minimizes the average distance to the views of the voters (where the “distance” between two views is the number of issues on which they disagree). In the special case of preference aggregation, this is called the Kemeny rule. We show that, under appropriate regularity conditions, the median rule is the unique judgement aggregation rule which satisfies three axioms: Ensemble Supermajority Efficiency, Reinforcement, and Continuity. Our analysis covers aggregation problems in which the consistency restrictions on input and output judgements may differ. We also allow for issues to be weighted, and provide numerous examples in which issue weights arise naturally.

一个判断聚集规则需要选民的集合在一组相互关联的问题的意见，并产生一个逻辑上一致的集体观点。该位规则是判断聚集规则，选择其中最小的逻辑一致的看法平均距离选民的意见（这里的“距离”两种观点之间的问题上，他们不同意的数量）。在偏好聚合的特殊情况下，这称为Kemeny规则。我们证明，在适当的规则性条件下，中位数规则是满足三个公理的唯一判断聚合规则：集合超多数效率，强化和连续性。我们的分析涵盖了聚合问题，在这些问题中，对输入和输出判断的一致性限制可能会有所不同。我们还允许对问题进行加权，并提供众多示例，其中问题的权重自然而然地出现了。