IDEAS home Printed from https://ideas.repec.org/a/spr/sochwe/v19y2002i2p381-413.html
   My bibliography  Save this article

The proportional random allocation of indivisible units

Author

Listed:
  • Hervé Moulin

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

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.

Suggested Citation

  • Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 381-413.
    • Handle: RePEc:spr:sochwe:v:19:y:2002:i:2:p:381-413
    Note: Received: 30 November 1999/Accepted: 15 November 2000
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00355/papers/2019002/20190381.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Sprumont, Yves, 1991. "The Division Problem with Single-Peaked Preferences: A Characterization of the Uniform Allocation Rule," Econometrica, Econometric Society, vol. 59(2), pages 509-519, March.
    3. Moulin, Herve, 1995. "On Additive Methods to Share Joint Costs," Mathematical Social Sciences, Elsevier, vol. 30(1), pages 98-99, August.
    4. Carmen Herrero Blanco, 1998. "- Minimal Rights In Claims Problems," Working Papers. Serie AD 1998-20, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    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 253-266, March.
    7. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    8. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    9. 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.
    10. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2006. "Additive rules in discrete allocation problems," European Journal of Operational Research, Elsevier, vol. 172(3), pages 971-978, August.
    2. 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.
    3. Ricardo Martínez, 2020. "On how to divide a budget according to population and wealth," ThE Papers 20/10, Department of Economic Theory and Economic History of the University of Granada..
    4. Moulin, Herve & Stong, Richard, 2003. "Filling a multicolor urn: an axiomatic analysis," Games and Economic Behavior, Elsevier, vol. 45(1), pages 242-269, October.
    5. Martínez, Ricardo & Moreno-Ternero, Juan D., 2022. "Compensation and sacrifice in the probabilistic rationing of indivisible units," European Journal of Operational Research, Elsevier, vol. 302(2), pages 740-751.
    6. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
    7. 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.
    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.
    9. Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.
    10. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    11. Patrick Harless, 2017. "Endowment additivity and the weighted proportional rules for adjudicating conflicting claims," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(3), pages 755-781, March.
    12. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    13. Vincent Mak & Darryl A. Seale & Eyran J. Gisches & Amnon Rapoport & Meng Cheng & Myounghee Moon & Rui Yang, 2018. "A network ridesharing experiment with sequential choice of transportation mode," Theory and Decision, Springer, vol. 85(3), pages 407-433, October.
    14. Moulin, Herve & Stong, Richard, 2001. "Fair Queuing and Other Probabilistic Allocation Methods," Working Papers 2000-09, Rice University, Department of Economics.
    15. Feige, Uriel & Tennenholtz, Moshe, 2014. "On fair division of a homogeneous good," Games and Economic Behavior, Elsevier, vol. 87(C), pages 305-321.
    16. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
    17. Tasnadi, Attila, 2002. "On probabilistic rationing methods," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 211-221, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    3. Boonen, Tim J., 2019. "Equilibrium recoveries in insurance markets with limited liability," Journal of Mathematical Economics, Elsevier, vol. 85(C), pages 38-45.
    4. Ruben Juarez & Rajnish Kumar, 2013. "Implementing efficient graphs in connection networks," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 359-403, October.
    5. Carmen Herrero & Juan Moreno-Ternero & Giovanni Ponti, 2010. "On the adjudication of conflicting claims: an experimental study," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 34(1), pages 145-179, January.
    6. José-Manuel Giménez-Gómez & M. Marco-Gil, 2014. "A new approach for bounding awards in bankruptcy problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(2), pages 447-469, August.
    7. Juarez, Ruben & Ko, Chiu Yu & Xue, Jingyi, 2018. "Sharing sequential values in a network," Journal of Economic Theory, Elsevier, vol. 177(C), pages 734-779.
    8. Koster, Maurice & Boonen, Tim J., 2019. "Constrained stochastic cost allocation," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 20-30.
    9. Moulin, Herve & Stong, Richard, 2003. "Filling a multicolor urn: an axiomatic analysis," Games and Economic Behavior, Elsevier, vol. 45(1), pages 242-269, October.
    10. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    11. Chatterjee, Siddharth & Ertemel, Sinan & Kumar, Rajnish, 2023. "Rationing rules for risky claims," Journal of Mathematical Economics, Elsevier, vol. 108(C).
    12. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2012. "A unifying framework for the problem of adjudicating conflicting claims," Journal of Mathematical Economics, Elsevier, vol. 48(2), pages 107-114.
    13. Jaume García-Segarra & Miguel Ginés-Vilar, 2023. "Additive adjudication of conflicting claims," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(1), pages 93-116, March.
    14. Claudio Zoli, 2012. "Characterizing Inequality Equivalence Criteria," Working Papers 32/2012, University of Verona, Department of Economics.
    15. Satya R. Chakravarty & Palash Sarkar, 2022. "Inequality minimising subsidy and taxation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 10(1), pages 53-67, May.
    16. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    17. José Alcalde & María Marco & José Silva, 2005. "Bankruptcy games and the Ibn Ezra’s proposal," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 103-114, July.
    18. Christopher P. Chambers & Juan D. Moreno-Ternero, 2017. "Taxation and poverty," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 153-175, January.
    19. Bergantinos, Gustavo & Lorenzo, Leticia, 2008. "The equal award principle in problems with constraints and claims," European Journal of Operational Research, Elsevier, vol. 188(1), pages 224-239, July.
    20. Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sochwe:v:19:y:2002:i:2:p:381-413. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.