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The uniform rule with several commodities: A generalization of Sprumont's characterization

  • Adachi, Tsuyoshi
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    Abstract This paper considers the problem of allocating multiple divisible commodities among a group of agents with single-peaked preferences. We show that the uniform rule is the only allocation rule that satisfies strategy-proofness, envy-freeness, and same-sidedness: the third axiom is a weak efficiency condition that is equivalent to Pareto efficiency in the single-commodity case. Therefore, this result generalizes the characterization of the uniform rule by Sprumont (1991. Econometrica 59 (2), 509-519) in the single-commodity case: it is the only rule satisfying strategy-proofness, envy-freeness, and Pareto efficiency.

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    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 6 (November)
    Pages: 952-964

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:6:p:952-964
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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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 509-19, March.
    2. EHLERS, Lars & KLAUS, Bettina, 2001. "Probabilistic Assignments of Identical Indivisible Objects and Uniform Probabilistic Rules," Cahiers de recherche 2001-27, Universite de Montreal, Departement de sciences economiques.
    3. Michel Le Breton & Arunava Sen, 1999. "Separable Preferences, Strategyproofness, and Decomposability," Econometrica, Econometric Society, vol. 67(3), pages 605-628, May.
    4. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer, vol. 5(2), pages 229-46, March.
    5. Youngsub Chun, 2006. "The Separability Principle in Economies with Single-Peaked Preferences," Social Choice and Welfare, Springer, vol. 26(2), pages 239-253, April.
    6. Sasaki, Hiroo, 2003. "Limitation of Efficiency: Strategy-Proofness and Single-Peaked Preferences with Many Commodities," Working Papers 2003-01, Rice University, Department of Economics.
    7. Kesten, Onur, 2006. "More on the uniform rule: Characterizations without Pareto optimality," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 192-200, March.
    8. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
    9. Thomson William, 1994. "Consistent Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Journal of Economic Theory, Elsevier, vol. 63(2), pages 219-245, August.
    10. Shigehiro Serizawa, 2005. "Pairwise Strategy-Proofness and Self-Enforcing Manipulation," ISER Discussion Paper 0629, Institute of Social and Economic Research, Osaka University.
    11. Bochet, Olivier & Sakai, Toyotaka, 2010. "Secure implementation in allotment economies," Games and Economic Behavior, Elsevier, vol. 68(1), pages 35-49, January.
    12. Shuhei Morimoto & Shigehiro Serizawa & Stephen Ching, 2009. "A Characterization of the Uniform Rule with Several Commodities and Agents," ISER Discussion Paper 0769, Institute of Social and Economic Research, Osaka University.
    13. Border, Kim C & Jordan, J S, 1983. "Straightforward Elections, Unanimity and Phantom Voters," Review of Economic Studies, Wiley Blackwell, vol. 50(1), pages 153-70, January.
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