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Probabilistic Assignments of Identical Indivisible Objects and Uniform Probabilistic Rules

  • EHLERS, Lars
  • KLAUS, Bettina

We consider a probabilistic approach to the problem of assigning k indivisible identical objects to a set of agents with single-peaked preferences. Using the ordinal extension of preferences, we characterize the class of uniform probabilistic rules by Pareto efficiency, strategy-proofness, and no-envy. We also show that in this characterization no-envy cannot be replaced by anonymity. When agents are strictly risk averse von-Neumann-Morgenstern utility maximizers, then we reduce the problem of assigning k identical objects to a problem of allocating the amount k of an infinitely divisible commodity.

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File URL: http://hdl.handle.net/1866/366
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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2001-27.

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Length: 25 pages
Date of creation: 2001
Date of revision:
Handle: RePEc:mtl:montde:2001-27
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  1. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-19, March.
  2. Ehlers, Lars & Peters, Hans & Storcken, Ton, 2002. "Strategy-Proof Probabilistic Decision Schemes for One-Dimensional Single-Peaked Preferences," Journal of Economic Theory, Elsevier, vol. 105(2), pages 408-434, August.
  3. Lars Ehlers, 2002. "Probabilistic allocation rules and single-dipped preferences," Social Choice and Welfare, Springer, vol. 19(2), pages 325-348.
  4. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  5. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  6. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer, vol. 19(2), pages 381-413.
  7. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
  8. Ehlers, Lars & Klaus, Bettina, 2001. " Solidarity and Probabilistic Target Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(2), pages 167-84.
  9. Ehlers, Lars, 2000. "Indifference and the uniform rule," Economics Letters, Elsevier, vol. 67(3), pages 303-308, June.
  10. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
  11. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
  12. Crès, Herv� & Moulin, Herv�, 1998. "Random Priority: A Probabilistic Resolution of the Tragedy of the Commons," Working Papers 98-06, Duke University, Department of Economics.
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