On the manipulability of approval voting and related scoring rules (original) (raw)

Abstract

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of candidates: by comparison of worst candidates, best candidates, or by comparison based on stochastic dominance. We perform a similar exercise for _k_-approval rules, where voters approve of a fixed number k of candidates. These results can be used to compare (_k_-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the _k_-approval rule is minimally manipulable—has the smallest number of manipulable preference profiles—under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the _k_-approval rule with k around half the number of candidates is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that _k_-approval rules may improve on the approval rule as far as manipulability is concerned.

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Acknowledgments

We thank participants of conferences in Tilburg (May 2009) and Caen (June 2009) for helpful discussions on this subject. We also thank Vincent Merlin and two referees for their informative comments.

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Authors and Affiliations

1. Department of Quantitative Economics, University of Maastricht, PO Box 616, 6200 MD, Maastricht, The Netherlands
   Hans Peters & Ton Storcken
2. University of Caen, Caen, France
   Souvik Roy

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1. Hans Peters
2. Souvik Roy
3. Ton Storcken

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Correspondence toHans Peters.

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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.

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Peters, H., Roy, S. & Storcken, T. On the manipulability of approval voting and related scoring rules.Soc Choice Welf 39, 399–429 (2012). https://doi.org/10.1007/s00355-011-0621-7

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• Received: 15 November 2011
• Accepted: 17 November 2011
• Published: 13 December 2011
• Issue date: July 2012
• DOI: https://doi.org/10.1007/s00355-011-0621-7

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