Abstract
Under approval voting, each voter can nominate as many candidates as she wishes and the election winners are those candidates that are nominated most often. A voter is said to have voted sincerely if she prefers all those candidates she nominated to all other candidates. As there can be a set of winning candidates rather than just a single winner, a voter’s incentives to vote sincerely will depend on what assumptions we are willing to make regarding the principles by which voters extend their preferences over individual candidates to preferences over sets of candidates. We formulate two such principles, replacement and deletion, and we show that, under approval voting, a voter who accepts those two principles and who knows how the other voters will vote will never have an incentive to vote insincerely. We then discuss the consequences of this result for a number of standard principles of preference extension in view of sincere voting under approval voting.
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Parts of this work have been presented at the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK) in Brussels in June 2007, the Social Choice Colloquium at the University of Tilburg in September 2007, the Dagstuhl Seminar on Computational Issues in Social Choice in October 2007, and the 7th International Meeting on Logic, Game Theory and Social Choice (LGS) in Bucharest in July 2011, as well as local seminars at the Universities of Amsterdam, Padova, and Paris-Dauphine. The insightful feedback received from the participants of these meetings is gratefully acknowledged. Thanks are also due to Steve Brams and an anonymous reviewer for comments on an earlier version of this paper, and to Remzi Sanver and Bill Zwicker for illuminating discussions on preference extensions.
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Endriss, U. Sincerity and manipulation under approval voting. Theory Decis 74, 335–355 (2013). https://doi.org/10.1007/s11238-012-9301-z
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DOI: https://doi.org/10.1007/s11238-012-9301-z