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Minimal manipulability: Unanimity and nondictatorship

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  • Maus, Stefan
  • Peters, Hans
  • Storcken, Ton

Abstract

This paper is concerned with the number of profiles at which a nondictatorial social choice function is manipulable. For three or more alternatives the lower bound is derived when the social choice function is nondictatorial and unanimous. In the case of three alternatives the lower bound is also derived when the social choice function is nondictatorial and surjective. In both cases all social choice functions reaching that lower bound are characterized when there are at least three agents. In the case of two agents the characterized social choice functions are only a subset of the set of all social choice functions reaching the minimum.
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Suggested Citation

  • Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Minimal manipulability: Unanimity and nondictatorship," Journal of Mathematical Economics, Elsevier, vol. 43(6), pages 675-691, August.
    • Handle: RePEc:eee:mateco:v:43:y:2007:i:6:p:675-691
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    References listed on IDEAS

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    1. 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.
    2. Arkadii Slinko, 2002. "On Asymptotic Strategy-Proofness of Classical Social Choice Rules," Theory and Decision, Springer, vol. 52(4), pages 389-398, June.
    3. Geoffrey Pritchard & Arkadii Slinko, 2006. "On the Average Minimum Size of a Manipulating Coalition," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 263-277, October.
    4. 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.
    5. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    1. Maus, Stefan & Peters, Hans & Storcken, Ton, 2007. "Anonymous voting and minimal manipulability," Journal of Economic Theory, Elsevier, vol. 135(1), pages 533-544, July.
    2. 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.
    3. Hans Peters & Souvik Roy & Ton Storcken, 2012. "On the manipulability of approval voting and related scoring rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 399-429, July.
    4. Lok, R.B. & Romero Morales, D. & Vermeulen, A.J., 2005. "The agents-are-substitutes property in continuous generalized assignment problems," Research Memorandum 009, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    5. 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.
    6. Bednay, Dezső & Moskalenko, Anna & Tasnádi, Attila, 2019. "Dictatorship versus manipulability," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 72-76.
    7. Stefan Maus & Hans Peters & Ton Storcken, 2007. "Minimal manipulability: anonymity and unanimity," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(2), pages 247-269, September.

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