On the manipulability of approval voting and related scoring rules
We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of alternatives: by comparison of worstalternatives, best alternatives, 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 alternatives. 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 alternatives 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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Volume (Year): 39 (2012)
Issue (Month): 2 (July)
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- Donald Campbell & Jerry Kelly, 2009. "Gains from manipulating social choice rules," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 349-371, September.
- Mostapha Diss & Vincent Merlin & Fabrice Valognes, 2010. "On the Condorcet efficiency of approval voting and extended scoring rules for three alternatives," Post-Print halshs-00533124, HAL.
- Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
- Gehrlein, William V. & Lepelley, Dominique, 1998. "The Condorcet efficiency of approval voting and the probability of electing the Condorcet loser," Journal of Mathematical Economics, Elsevier, vol. 29(3), pages 271-283, April.
- Pritchard, Geoffrey & Wilson, Mark C., 2009. "Asymptotics of the minimum manipulating coalition size for positional voting rules under impartial culture behaviour," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 35-57, July.
- Maus, Stefan & Peters, Hans & Storcken, Ton, 2007.
"Minimal manipulability: Unanimity and nondictatorship,"
Journal of Mathematical Economics,
Elsevier, vol. 43(6), pages 675-691, August.
- Maus,Stefan & Peters,Hans & Storcken,Ton, 2004. "Minimal manipulability: Unanimity and Nondictatorship," Research Memorandum 005, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
- Peter Fristrup & Hans Keiding, 1998. "Minimal manipulability and interjacency for two-person social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(3), pages 455-467.
- Saari, Donald G, 1990. "Susceptibility to Manipulation," Public Choice, Springer, vol. 64(1), pages 21-41, January.
- Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July. Full references (including those not matched with items on IDEAS)