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The proportional random allocation of indivisible units

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Author Info
Hervé Moulin () (Rice University, Department of Economics, MS 22, P.O. Box 1892, Houston, TX 77251-1892, USA)

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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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Publisher Info
Article provided by Springer in its journal Social Choice and Welfare.

Volume (Year): 19 (2002)
Issue (Month): 2 ()
Pages: 381-413
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Handle: RePEc:spr:sochwe:v:19:y:2002:i:2:p:381-413

Note: Received: 30 November 1999/Accepted: 15 November 2000
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Young, H Peyton, 1990. "Progressive Taxation and Equal Sacrifice," American Economic Review, American Economic Association, vol. 80(1), pages 253-66, March. [Downloadable!] (restricted)
  2. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August. [Downloadable!] (restricted)
  3. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  4. 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. [Downloadable!] (restricted)
  5. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie). [Downloadable!]
  6. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April. [Downloadable!] (restricted)
  7. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics. [Downloadable!]
  8. 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. [Downloadable!] (restricted)
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  1. 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. [Downloadable!]
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  2. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics. [Downloadable!]
  3. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics. [Downloadable!]
    Other versions:
  4. Moulin, Herve, 2001. "Filling a Multicolor Urn: An Axiomatic Analysis," Working Papers 2001-01, Rice University, Department of Economics. [Downloadable!]
    Other versions:
  5. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics. [Downloadable!]
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