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The Division Problem under Constraints

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  • Gustavo Bergantiños

    ()

  • Jordi Massó

    ()

  • Alejandro Neme

    ()

Abstract

The division problem under constraints consists of allocating a given amount of an homogeneous and perfectly divisible good among a subset of agents with single- peaked preferences on an exogenously given interval of feasible allotments. We char- acterize axiomatically the family of extended uniform rules proposed to solve the division problem under constraints. Rules in this family extend the uniform rule used to solve the classical division problem without constraints. We show that the fam- ily of all extended uniform rules coincides with the set of rules satisfying efficiency, strategy-proofness, equal treatment of equals, bound monotonicity, consistency, and independence of irrelevant coalitions.

Suggested Citation

  • Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2013. "The Division Problem under Constraints," UFAE and IAE Working Papers 942.13, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  • Handle: RePEc:aub:autbar:942.13
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    References listed on IDEAS

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    1. Thomson, William, 1997. "The Replacement Principle in Economies with Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 76(1), pages 145-168, September.
    2. Schummer, James & Thomson, William, 1997. "Two derivations of the uniform rule and an application to bankruptcy," Economics Letters, Elsevier, vol. 55(3), pages 333-337, September.
    3. Dagan, Nir, 1996. "A Note on Thomson's Characterizations of the Uniform Rule," Journal of Economic Theory, Elsevier, vol. 69(1), pages 255-261, April.
    4. Ehlers, Lars, 2002. "On Fixed-Path Rationing Methods," Journal of Economic Theory, Elsevier, vol. 106(2), pages 472-477, October.
    5. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
    6. Thomson, William, 1995. "Population-Monotonic Solutions to the Problem of Fair Division When Preferences Are Single-Peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(2), pages 229-246, March.
    7. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with voluntary participation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(3), pages 371-406, March.
    8. 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.
    9. Gustavo Bergantiños & Jordi Massó & Alejandro Neme, 2012. "The division problem with maximal capacity constraints," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 3(1), pages 29-57, March.
    10. 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.
    11. Moulin, Herve, 1999. "Rationing a Commodity along Fixed Paths," Journal of Economic Theory, Elsevier, vol. 84(1), pages 41-72, January.
    12. Manjunath, Vikram, 2012. "When too little is as good as nothing at all: Rationing a disposable good among satiable people with acceptance thresholds," Games and Economic Behavior, Elsevier, vol. 74(2), pages 576-587.
    13. Nash, John, 1950. "The Bargaining Problem," Econometrica, Econometric Society, vol. 18(2), pages 155-162, April.
    14. Sonmez, Tayfun, 1994. "Consistency, monotonicity, and the uniform rule," Economics Letters, Elsevier, vol. 46(3), pages 229-235, November.
    15. William Thomson, 1997. "The replacement principle in economies with indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 15(1), pages 57-66.
    16. 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).
    17. Özgür Kıbrıs, 2003. "Constrained allocation problems with single-peaked preferences: An axiomatic analysis," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 20(3), pages 353-362, June.
    18. Lars Ehlers, 2002. "Resource-monotonic allocation when preferences are single-peaked," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 20(1), pages 113-131.
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    Cited by:

    1. Kim, Sunyoung & Bergantiños, Gustavo & Chun, Youngsub, 2015. "The separability principle in single-peaked economies with participation constraints," Mathematical Social Sciences, Elsevier, vol. 78(C), pages 69-75.
    2. repec:kap:theord:v:84:y:2018:i:1:d:10.1007_s11238-017-9644-6 is not listed on IDEAS

    More about this item

    Keywords

    Division Problem; Single-peaked Preferences.;

    JEL classification:

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

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