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The Proportional Random Allocation of Indivisible Units

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  • Moulin, Herve

    (Rice U)

Abstract

Indivisible units are randomly allocated among agents with a claim/demand on the resources. The available resources fall short of the sum of individual claims. The proportional method distributes units sequentially, and the probability of receiving a unit at any step is proportional to the unsatisfied claims. We characterize the family of probabilistic rationing methods meeting the three axioms Consistency, Lower and Upper Composition. It contains the proportional method, all deterministic fixed priority methods, and the priority compositions of proportional methods. The proportional method is the only fair method in the family.

Suggested Citation

  • Moulin, Herve, 2000. "The Proportional Random Allocation of Indivisible Units," Working Papers 2000-02, Rice University, Department of Economics.
  • Handle: RePEc:ecl:riceco:2000-02
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    File URL: http://www.ruf.rice.edu/~econ/papers/2000papers/02Moulin.pdf
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    References listed on IDEAS

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    1. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
    2. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    3. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    4. 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.
    5. Young, H Peyton, 1990. "Progressive Taxation and Equal Sacrifice," American Economic Review, American Economic Association, vol. 80(1), pages 253-266, March.
    6. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
    7. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    8. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    9. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    10. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
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    Cited by:

    1. Lars Ehlers & Bettina Klaus, 2003. "Probabilistic assignments of identical indivisible objects and uniform probabilistic rules," Review of Economic Design, Springer;Society for Economic Design, vol. 8(3), pages 249-268, October.
    2. Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
    3. Hervé Moulin & Richard Stong, 2002. "Fair Queuing and Other Probabilistic Allocation Methods," Mathematics of Operations Research, INFORMS, vol. 27(1), pages 1-30, February.
    4. Ricardo Martínez, 2020. "On how to divide a budget according to population and wealth," ThE Papers 20/10, Department of Economic Theory and Economic History of the University of Granada..
    5. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    6. Moulin, Herve & Stong, Richard, 2003. "Filling a multicolor urn: an axiomatic analysis," Games and Economic Behavior, Elsevier, vol. 45(1), pages 242-269, October.
    7. Vincent Mak & Darryl A. Seale & Eyran J. Gisches & Amnon Rapoport & Meng Cheng & Myounghee Moon & Rui Yang, 2018. "A network ridesharing experiment with sequential choice of transportation mode," Theory and Decision, Springer, vol. 85(3), pages 407-433, October.
    8. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
    9. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357, Elsevier.
    10. Ricardo Martínez & Juan D Moreno Ternero, 2020. "Compensation and sacrifice in the probabilistic rationing of indivisible units," ThE Papers 20/03, Department of Economic Theory and Economic History of the University of Granada..
    11. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
    12. Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.
    13. Tasnadi, Attila, 2002. "On probabilistic rationing methods," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 211-221, November.

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