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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

Suggested Citation

  • Lars Ehlers & Bettina Klaus, 2003. "Probabilistic assignments of identical indivisible objects and uniform probabilistic rules," Review of Economic Design, Springer;Society for Economic Design, vol. 8(3), pages 249-268, October.
    • Handle: RePEc:spr:reecde:v:8:y:2003:i:3:p:249-268
    DOI: 10.1007/s10058-003-0101-3
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    References listed on IDEAS

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    5. 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.
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    7. Crès, Hervé & Moulin, Hervé, 1998. "Random Priority: A Probabilistic Resolution of the Tragedy of the Commons," Working Papers 98-06, Duke University, Department of Economics.
    8. Ehlers, Lars, 2000. "Indifference and the uniform rule," Economics Letters, Elsevier, vol. 67(3), pages 303-308, June.
    9. Ching, Stephen, 1992. "A simple characterization of the uniform rule," Economics Letters, Elsevier, vol. 40(1), pages 57-60, September.
    10. Moulin, Herve, 1994. "Social choice," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 31, pages 1091-1125, Elsevier.
    11. 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.
    12. Lars Ehlers & Bettina Klaus, 2001. "Solidarity and Probabilistic Target Rules," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 3(2), pages 167-184, April.
    13. 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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    Citations

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    Cited by:

    1. Bochet, Olivier & İlkılıç, Rahmi & Moulin, Hervé, 2013. "Egalitarianism under earmark constraints," Journal of Economic Theory, Elsevier, vol. 148(2), pages 535-562.
    2. 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.
    3. 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.
    4. Yoichi Kasajima, 2013. "Probabilistic assignment of indivisible goods with single-peaked preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(1), pages 203-215, June.
    5. 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.
    6. Toulis, Panos & Parkes, David C., 2015. "Design and analysis of multi-hospital kidney exchange mechanisms using random graphs," Games and Economic Behavior, Elsevier, vol. 91(C), pages 360-382.
    7. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    8. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," 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 2, chapter 21, pages 393-506, Elsevier.
    9. X. Ruiz del Portal, 2012. "Conditions for incentive compatibility in models with multidimensional allocation functions and one-dimensional types," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 311-321, December.
    10. , & Ilkilic, Rahmi & , & ,, 2012. "Balancing supply and demand under bilateral constraints," Theoretical Economics, Econometric Society, vol. 7(3), September.
    11. repec:ebl:ecbull:v:4:y:2007:i:8:p:1-10 is not listed on IDEAS
    12. Kentaro Hatsumi & Shigehiro Serizawa, 2009. "Coalitionally strategy-proof rules in allotment economies with homogeneous indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 423-447, September.

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    More about this item

    Keywords

    Probabilistic rules; single-peaked preferences; strategy-proofness; uniform allocations;
    All these keywords.

    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D60 - Microeconomics - - Welfare Economics - - - General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General

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