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Maximal Domain for Strategy-proof Rules in Allotment Economies

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  • Hideyuki Mizobuchi

    ()

  • Shigehiro Serizawa

    ()

Abstract

We consider the problem of allocating an amount of a perfectly divisible good among a group of n agents. We study how large a preference domain can be to allow for the existence of strategy-proof, symmetric, and efficient allocation rules when the amount of the good is a variable. This question is qualified by an additional requirement that a domain should include a minimally rich domain. We first characterize the uniform rule (Bennasy, 1982) as the unique strategy-proof, symmetric, and efficient rule on a minimally rich domain when the amount of the good is fixed. Then, exploiting this characterization, we establish the following: There is a unique maximal domain that includes a minimally rich domain and allows for the existence of strategy-proof, symmetric, and efficient rules when the amount of good is a variable. It is the single-plateaued domain.
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Suggested Citation

  • Hideyuki Mizobuchi & Shigehiro Serizawa, 2006. "Maximal Domain for Strategy-proof Rules in Allotment Economies," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(1), pages 195-210, August.
  • Handle: RePEc:spr:sochwe:v:27:y:2006:i:1:p:195-210
    DOI: 10.1007/s00355-006-0112-4
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    References listed on IDEAS

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    1. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
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    4. Jordi MassóAuthor-Email: jordi.masso@uab.es & Alejandro Neme, 2002. "A Maximal Domain of Preferences for Tops-only Rules in the Division Problem," UFAE and IAE Working Papers 535.02, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    5. Barbera, Salvador & Sonnenschein, Hugo & Zhou, Lin, 1991. "Voting by Committees," Econometrica, Econometric Society, vol. 59(3), pages 595-609, May.
    6. Serizawa Shigehiro, 1995. "Power of Voters and Domain of Preferences Where Voting by Committees Is Strategy-Proof," Journal of Economic Theory, Elsevier, vol. 67(2), pages 599-608, December.
    7. Ching, Stephen & Serizawa, Shigehiro, 1998. "A Maximal Domain for the Existence of Strategy-Proof Rules," Journal of Economic Theory, Elsevier, vol. 78(1), pages 157-166, January.
    8. Berga, Dolors, 1998. "Strategy-proofness and single-plateaued preferences," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 105-120, March.
    9. repec:ubc:bricol:98-22 is not listed on IDEAS
    10. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    11. Ehlers, Lars, 2002. "Coalitional Strategy-Proof House Allocation," Journal of Economic Theory, Elsevier, vol. 105(2), pages 298-317, August.
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    Cited by:

    1. repec:spr:sochwe:v:49:y:2017:i:2:d:10.1007_s00355-017-1068-2 is not listed on IDEAS
    2. Kentaro Hatsumi & Dolors Berga & Shigehiro Serizawa, 2014. "A maximal domain for strategy-proof and no-vetoer rules in the multi-object choice model," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(1), pages 153-168, February.
    3. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2013. "A characterization of the uniform rule with several commodities and agents," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 871-911, March.
    4. Toyotaka Sakai & Takuma Wakayama, 2012. "Strategy-proofness, tops-only, and the uniform rule," Theory and Decision, Springer, vol. 72(3), pages 287-301, March.
    5. Salvador Barberà, 2010. "Strategy-proof social choice," UFAE and IAE Working Papers 828.10, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    6. Kazuhiko Hashimoto & Takuma Wakayama, 2015. "Fair Reallocation in Economies with Single-Peaked Preferences," ISER Discussion Paper 0947, Institute of Social and Economic Research, Osaka University.
    7. Shuhei Morimoto, 2013. "Maximal domain for strategy-proof probabilistic rules in economies with one public good," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(3), pages 637-669, September.
    8. Kentaro Hatsumi & Shigehiro Serizawa, 2009. "Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 423-447, September.

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