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Nonmanipulable multi-valued social decision functions

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  • Allan Feldman

Abstract

Logically satisfactory methods for narrowing the range of social choice can be designed. For example, the SDF which transforms (S, R) into P(S, R), that is, the Pareto rule, satisfies all the conditions imposed on C(·) in Theorem 9: The Pareto rule is normal. For if x ∈ P(S, R) and y ∈ S, then y cannot be Pareto superior to x; so x ∈ P({x, y}, R), and α2 is satisfied. If x ∈ S and x ∈ P({x, y}, R) for all y ∈ S, no y in S is Pareto superior to x, and therefore, x ∈ P(S, R); so γ2 is satisfied. The Pareto rule is clearly neutral and anonymous; it is unbiased among the alternatives and among the individuals. The Pareto rule is obviously non-imposed. The Pareto rule is nonmanipulable. For if xP i y, P({x, y}, R) must be either {x} or {x, y}. If P({x, y}, R)={x, y}, there is an individual j ≠ i for whom yR j x. Consequently no misrepresentation by i can force y out of the set of optima, and therefore the rule is cheatproof. The significance of this paper is that any rule which is logically satisfactory (in the sense of the conditions of Theorem 9) must be bracketed between the maximal and Pareto rules. So those rules are especially important: they provide lower and upper bounds for completely satisfactory multi-valued SDFs. Copyright Martinus Nijhoff b.v 1979

Suggested Citation

  • Allan Feldman, 1979. "Nonmanipulable multi-valued social decision functions," Public Choice, Springer, vol. 34(2), pages 177-188, June.
    • Handle: RePEc:kap:pubcho:v:34:y:1979:i:2:p:177-188
    DOI: 10.1007/BF00129525
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    References listed on IDEAS

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    1. Kelly, Jerry S, 1977. "Strategy-Proofness and Social Choice Functions without Singlevaluedness," Econometrica, Econometric Society, vol. 45(2), pages 439-446, March.
    2. Sen, Amartya K, 1977. "Social Choice Theory: A Re-examination," Econometrica, Econometric Society, vol. 45(1), pages 53-89, January.
    3. Blau, Julian H & Deb, Rajat, 1977. "Social Decision Functions and the Veto," Econometrica, Econometric Society, vol. 45(4), pages 871-879, May.
    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.
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    1. Amílcar Mata Díaz & Ramón Pino Pérez & Jahn Franklin Leal, 2023. "Taxonomy of powerful voters and manipulation in the framework of social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 61(2), pages 277-309, August.
    2. Bochet, Olivier & Sakai, Toyotaka, 2007. "Strategic manipulations of multi-valued solutions in economies with indivisibilities," Mathematical Social Sciences, Elsevier, vol. 53(1), pages 53-68, January.
    3. Eraslan, H.Hulya & McLennan, Andrew, 2004. "Strategic candidacy for multivalued voting procedures," Journal of Economic Theory, Elsevier, vol. 117(1), pages 29-54, July.
    4. Barbera, Salvador & Dutta, Bhaskar & Sen, Arunava, 2005. "Corrigendum to "Strategy-proof social choice correspondences" [J. Econ. Theory 101 (2001) 374-394]," Journal of Economic Theory, Elsevier, vol. 120(2), pages 275-275, February.
    5. Özyurt, Selçuk & Sanver, M. Remzi, 2009. "A general impossibility result on strategy-proof social choice hyperfunctions," Games and Economic Behavior, Elsevier, vol. 66(2), pages 880-892, July.
    6. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    7. Alexander Reffgen, 2011. "Generalizing the Gibbard–Satterthwaite theorem: partial preferences, the degree of manipulation, and multi-valuedness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 37(1), pages 39-59, June.

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