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The proportional random allocation of indivisible units

  • Hervé Moulin

    ()

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

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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File URL: http://link.springer.de/link/service/journals/00355/papers/2019002/20190381.pdf
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Article provided by Springer & The Society for Social Choice and Welfare 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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  1. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  2. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
  3. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  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.
  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. Young, H Peyton, 1990. "Progressive Taxation and Equal Sacrifice," American Economic Review, American Economic Association, vol. 80(1), pages 253-66, March.
  7. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  8. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
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