The median rule in judgement aggregation

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. Keywords Judgement aggregation • Majoritarian • Reinforcement • Consistency • Median JEL Classification D71 Versions of the paper have been presented at the 2016 Meeting of Society for Social Choice and Welfare (Lund), the Workshop on Decision Making and Contest Theory (Kibbutz Ein Gedi, 2016), D-TEA (Paris 2017), and various seminars. We are grateful to the participants at these presentations for their valuable suggestions. We also thank Florian Brandl, Jerome Lang and Clemens Puppe for helpful comments. Finally, we thank two reviewers for very perceptive reports and valuable suggestions. M.