A dichotomy theorem on the existence of efficient or neutral sequential voting correspondences

Authors:
Lirong Xia;Jérôme Lang
Affiliations:
Department of Computer Science, Duke University, Durham, NC;LAMSADE, Université Paris-Dauphine, Paris Cedex 16, France
Venue:
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
Year:
2009

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Abstract

Sequential voting rules and correspondences provide a way for agents to make group decisions when the set of available options has a multiissue structure. One important question about sequential voting rules (correspondences) is whether they satisfy two crucial criteria, namely neutrality and efficiency. 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.