Sequential voting rules and correspondences provide a way for agents to make group decisions when the set of available options has a multi-issue structure. One important question about sequential voting rules (correspondences) is whether they satisfy two crucial criteria, namely neutrality and ef- ficiency. Recently, Benoit and Kornhauser established an important result about seat-by-seat voting rules (which are a special case of sequential voting rules): they proved that if the multi-issue domain satisfies some properties, then the only seat-by-seat rules being either efficient or neutral are dictatorships. However, there are still some cases not covered by their results, including a very important and interesting case—voting correspondences. In this paper, we extend the impossibility theorems by Benoit and Kornhauser to voting correspondences, and obtain a dichotomy theorem on the existence of efficient or neutral sequential (seat-by-seat) voting rules and correspondences. Therefore, the question of whether sequential (seat-by-seat) voting rules (correspondences) can be efficient or neutral is now completely answered.

Authors

• Lirong Xia Rensselaer Polytechnic Institute
• Jérôme Lang CNRS, Université Paris Dauphine, PSL

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