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Boundedness of the range of a strategy-proof social choice function

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  • Serizawa, Shigehiro
  • Weymark, John A.

Abstract

For the provision of m≥1 divisible public goods, relatively weak restrictions on the domain of a strategy-proof social choice function are identified that ensure that its range is bounded. Domain restrictions are also identified for which strategy-proofness implies that the range and the option sets of a social choice function are compact. To illustrate the usefulness of these results, it is shown how a theorem about generalized median voter schemes due to Barberà, Massó, and Serizawa can be established without their assumption that the range of a social choice function is compact provided that the tops of the preferences are not restricted to be finite.

Suggested Citation

  • Serizawa, Shigehiro & Weymark, John A., 2025. "Boundedness of the range of a strategy-proof social choice function," Games and Economic Behavior, Elsevier, vol. 149(C), pages 164-169.
    • Handle: RePEc:eee:gamebe:v:149:y:2025:i:c:p:164-169
    DOI: 10.1016/j.geb.2024.11.013
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    References listed on IDEAS

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    1. Barbera, S. & Masso, J. & Serizawa, S., 1998. "Strategy-Proof Voting on Compact Ranges," Games and Economic Behavior, Elsevier, vol. 25(2), pages 272-291, November.
    2. Barbera, Salvador, 1983. "Strategy-Proofness and Pivotal Voters: A Direct Proof of the Gibbard-Satterthwaite Theorem," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(2), pages 413-417, June.
    3. 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.
    4. Lin Zhou, 1991. "Impossibility of Strategy-Proof Mechanisms in Economies with Pure Public Goods," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 107-119.
    5. Barbera, Salvador & Masso, Jordi & Neme, Alejandro, 1997. "Voting under Constraints," Journal of Economic Theory, Elsevier, vol. 76(2), pages 298-321, October.
    6. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    7. Le Breton, Michel & Weymark, John A., 1999. "Strategy-proof social choice with continuous separable preferences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 47-85, August.
    8. Reny, Philip J., 2001. "Arrow's theorem and the Gibbard-Satterthwaite theorem: a unified approach," Economics Letters, Elsevier, vol. 70(1), pages 99-105, January.
    9. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
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    JEL classification:

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

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