Abstract
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.
Highlights
In judgement aggregation, a group is faced with a joint decision; frequently, the members of the group disagree about which decision the group should take and/or the grounds for the decision
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
As we already mentioned in the introduction, Young and Levenglick characterize the median rule for such spaces by three assumptions: Condorcet Consistency, Neutrality and Reinforcement
Summary
A group is faced with a joint decision; frequently, the members of the group disagree about which decision the group should take and/or the grounds for the decision. The median rule in judgement aggregation comparison of two admissible views x and y, x agrees with the majority on more issues than y, y is inferior as a group view, and should not be adopted by the group. Theorem 1, characterizes the median rule as the unique judgement aggregation rule satisfying ESME, Reinforcement and Continuity. The main comparison result in the literature is the remarkable characterization of the median rule in the aggregation of linear orderings (“rankings”) by Young and Levenglick (1978). From a compromise perspective, the step from general additive majority rules to the median rule is fundamental From this perspective, Reinforcement is quite compelling, and enables an interpretation of the optimal aggregation rule as minimizing the “aggregate burden of compromise”, as measured by the average distance between individual and group judgments.
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