The median rule in judgement aggregation (joint work with Klaus Nehring).

Abstract: I will first briefly introduce social choice theory in general. I will then move onto the subfield of judgement aggregation, and discuss some recent research on this topic. In a judgement aggregation problem, we begin with a set K of logically interconnected propositions, called issues. A view is an assignment of a truth-value to each issue in K. However, not all views are admissible; some may violate the logical relationships between the different issues in K. Suppose that each individual voter has a logically consistent view; we want to aggregate these individual views together to obtain a collective view. A procedure for doing this is called a judgement aggregation rule. The most obvious procedure is to simply agree with the the majority opinion on each issue. But this “majority view” is often logically inconsistent. This raises the question: which (consistent) judgement aggregation rule gives the “best approximation” of the majority view? One plausible candidate is the median rule: this rule chooses the admissible view which minimizes the average Hamming distance to the views of the voters. We have shown that the median rule as the only judgement aggregation rule satisfying three axioms: Ensemble Supermajority Efficiency, Reinforcement, and Upper Hemicontinuity. “Supermajority efficiency” means (roughly) that the rule tries to agree with the majority view in as many issues as possible; furthermore, if it can only agree with a majority in one out of two issues, it will choose the larger majority. Ensemble supermajority efficiency extends this principle to the case where the rule is applied to solve many aggregation problems simultaneously. Reinforcement means that, if two subpopulations independently choose the same view using the rule, then the combined population should also choose this view using this rule. Upper hemicontinuity means that the outcome is invariant under small perturbations; equivalently, it means that an outcome reflecting the will of an “overwhelming majority” of voters cannot be changed by a small minority.

Posted on Jan 13, 2020 in Other Areas, Seminars