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A maximal domain of preferences for strategy-proof, efficient, and simple rules in the division problem

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  • Jordi Massó
  • Alejandro Neme

Abstract

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, “tops-onlyness”, and continuity. These domains (called partially single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences. Copyright Springer-Verlag 2004

Suggested Citation

  • Jordi Massó & Alejandro Neme, 2004. "A maximal domain of preferences for strategy-proof, efficient, and simple rules in the division problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(2), pages 187-206, October.
    • Handle: RePEc:spr:sochwe:v:23:y:2004:i:2:p:187-206
    DOI: 10.1007/s00355-003-0245-7
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    Citations

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    Cited by:

    1. Yohei Sekiguchi, 2012. "A Characterization of the Plurality Rule," CIRJE F-Series CIRJE-F-833, CIRJE, Faculty of Economics, University of Tokyo.
    2. Sekiguchi, Yohei, 2012. "A characterization of the plurality rule," Economics Letters, Elsevier, vol. 116(3), pages 330-332.
    3. Bonifacio, Agustín G. & Massó, Jordi & Neme, Pablo, 2023. "Preference restrictions for simple and strategy-proof rules: Local and weakly single-peaked domains," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    4. Bochet, Olivier & Tumennasan, Norovsambuu, 2020. "Dominance of truthtelling and the lattice structure of Nash equilibria," Journal of Economic Theory, Elsevier, vol. 185(C).
    5. Toyotaka Sakai & Takuma Wakayama, 2012. "Strategy-proofness, tops-only, and the uniform rule," Theory and Decision, Springer, vol. 72(3), pages 287-301, March.
    6. Yeh, Chun-Hsien, 2006. "Reduction-consistency in collective choice problems," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 637-652, September.
    7. Roy, Souvik & Sadhukhan, Soumyarup, 2020. "On the structure of division rules," MPRA Paper 104402, University Library of Munich, Germany.
    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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