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Breadth of loss due to manipulation

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  • Donald Campbell
  • Jerry Kelly

Abstract

We identify the maximal number of people who are harmed when a social choice rule is manipulated. If there are n individuals, then for any $$k$$ greater than 0 and less than n, there is a neutral rule for which the maximal number is $$k$$ , and there is an anonymous rule for which the maximum number is $$k$$ . If the rule selects the majority winner when there is one and satisfies the Pareto criterion, then the maximal number is $$(n-1)/2$$ . Maximal numbers are also calculated for the Borda rule and other scoring rules, and for rules for which the selection depends only on which individuals have which alternatives ranked at the top. We also calculate the maximum number for rules that satisfy the Pareto criterion, but not the Condorcet criterion, and for rules that satisfy the Condorcet criterion, but not the Pareto criterion. Copyright Springer-Verlag Berlin Heidelberg 2014

Suggested Citation

  • Donald Campbell & Jerry Kelly, 2014. "Breadth of loss due to manipulation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(2), pages 393-414, February.
    • Handle: RePEc:spr:joecth:v:55:y:2014:i:2:p:393-414
    DOI: 10.1007/s00199-013-0752-4
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    References listed on IDEAS

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    1. K. J. Arrow & A. K. Sen & K. Suzumura (ed.), 2011. "Handbook of Social Choice and Welfare," Handbook of Social Choice and Welfare, Elsevier, edition 1, volume 2, number 2.
    2. 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.
    3. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    4. William Vickrey, 1960. "Utility, Strategy, and Social Decision Rules," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 74(4), pages 507-535.
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    Cited by:

    1. Herman Demeze & Issofa Moyouwou & Roland Pongou, 2016. "The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis," Working Papers 1611e, University of Ottawa, Department of Economics.
    2. Demeze, Herman & Moyouwou, Issofa & Pongou, Roland, 2016. "The Welfare Economics of Tactical Voting in Democracies: A Partial Identification Equilibrium Analysis," MPRA Paper 70607, University Library of Munich, Germany.

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    More about this item

    Keywords

    Social choice rule; Manipulation; Gains; Losses; D70; D71;
    All these keywords.

    JEL classification:

    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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