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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.

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Paper provided by Rice University, Department of Economics in its series Working Papers with number 2000-02.

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Date of creation: Nov 2000
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Handle: RePEc:ecl:riceco:2000-02

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  1. 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.
  2. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  3. Nouweland, C.G.A.M.. van den & Potters, J. & Tijs, S.H. & Zarzuelo, J., 1991. "Cores and related solution concepts for multi-choice games," Research Memorandum 478, Tilburg University, Faculty of Economics and Business Administration.
  4. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
  5. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
  6. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  7. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  8. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  9. Young, H Peyton, 1990. "Progressive Taxation and Equal Sacrifice," American Economic Review, American Economic Association, vol. 80(1), pages 253-66, March.
  10. 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.
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Cited by:
  1. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
  2. Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.
  3. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
  4. Tasnadi, Attila, 2002. "On probabilistic rationing methods," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 211-221, November.
  5. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  6. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  7. Moulin, Herve, 2001. "Filling a Multicolor Urn: An Axiomatic Analysis," Working Papers 2001-01, Rice University, Department of Economics.
  8. 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.
  9. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.

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