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Probabilistic assignments of identical indivisible objects and uniform probabilistic rules

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  • Lars Ehlers

    ()

  • Bettina Klaus

    ()

Abstract

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 maximizer, then we reduce the problem of assigning k identical objects to a problem of allocating the amount k of an infinitely divisible commodity. Copyright Springer-Verlag Berlin/Heidelberg 2003

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Bibliographic Info

Article provided by Springer in its journal Review Economic Design.

Volume (Year): 8 (2003)
Issue (Month): 3 (October)
Pages: 249-268

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Handle: RePEc:spr:reecde:v:8:y:2003:i:3:p:249-268

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Keywords: Probabilistic rules; single-peaked preferences; strategy-proofness; uniform allocations;

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References

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  1. Moulin, Herve, 2000. "The Proportional Random Allocation of Indivisible Units," Working Papers 2000-02, Rice University, Department of Economics.
  2. Lars Ehlers, 2002. "Probabilistic allocation rules and single-dipped preferences," Social Choice and Welfare, Springer, vol. 19(2), pages 325-348.
  3. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
  4. 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.
  5. 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.
  6. 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.
  7. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
  8. 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.
  9. 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.
  10. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
  11. Ehlers, Lars, 2000. "Indifference and the uniform rule," Economics Letters, Elsevier, vol. 67(3), pages 303-308, June.
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Citations

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Cited by:
  1. Kentaro Hatsumi & Shigehiro Serizawa, 2009. "Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods," Social Choice and Welfare, Springer, vol. 33(3), pages 423-447, September.
  2. Wataru KUREISHI & Hideki MIZUKAMI, 2007. "Equal probability for the best and the assignment of identical indivisible objects," Economics Bulletin, AccessEcon, vol. 4(8), pages 1-10.
  3. Bochet, Olivier & Ilkilic, Rahmi & Moulin, Hervé & Sethuraman, Jay, 2012. "Balancing supply and demand under bilateral constraints," Theoretical Economics, Econometric Society, vol. 7(3), September.
  4. Bochet, Olivier & İlkılıç, Rahmi & Moulin, Hervé, 2013. "Egalitarianism under earmark constraints," Journal of Economic Theory, Elsevier, vol. 148(2), pages 535-562.
  5. Adachi, Tsuyoshi, 2010. "The uniform rule with several commodities: A generalization of Sprumont's characterization," Journal of Mathematical Economics, Elsevier, vol. 46(6), pages 952-964, November.
  6. repec:ebl:ecbull:v:4:y:2007:i:8:p:1-10 is not listed on IDEAS
  7. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer, vol. 41(1), pages 203-215, June.
  8. Wataru Kureishi & Hideki Mizukami, 2005. "A Characterization of the Randomized Uniform Rule," Discussion Papers in Economics and Business 05-20, Osaka University, Graduate School of Economics and Osaka School of International Public Policy (OSIPP).

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