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Settling the neutrality and efficiency of decomposable voting rules and correspondences

In this paper, we address the problem of the existence of neutral or efficient decomposable voting rules and correspondences on combinatorial domains, by extending the impossibility theorems about the neutrality and efficiency of seat-by-seat voting rules in a recent paper of Benoit and Kornhauser. Our contributions are the following: we identify the set of neutral rules on two-binary-issue combinatorial domains, which is not covered by their work; and we prove the impossibility theorem for voting correspondences (while Benoit and Kornhauser only consider voting rules). Together with previous work, our work thus completely solves the problem of the existence of neutral or efficient decomposable voting correspondences.