IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v162y2016icp1-20.html
   My bibliography  Save this article

Entropy, desegregation, and proportional rationing

Author

Listed:
  • Moulin, Hervé

Abstract

An assignment of students to schools displays zero-segregation if all schools have the same distribution of the different types of students (ethnic, geographical, gender). We axiomatize the choice of an optimally desegregated assignment under arbitrary capacity constraints. The celebrated Consistency axiom, together with standard rational choice requirements, identify the choice rule minimizing a canonical index of proportional fairness: the entropy of the assignment matrix. This is an alternative vindication of the Mutual Information index of segregation recently characterized in Frankel and Volij (2011).

Suggested Citation

  • Moulin, Hervé, 2016. "Entropy, desegregation, and proportional rationing," Journal of Economic Theory, Elsevier, vol. 162(C), pages 1-20.
    • Handle: RePEc:eee:jetheo:v:162:y:2016:i:c:p:1-20
    DOI: 10.1016/j.jet.2015.12.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053115002045
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2015.12.002?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. Frankel, David M. & Volij, Oscar, 2011. "Measuring school segregation," Journal of Economic Theory, Elsevier, vol. 146(1), pages 1-38, January.
    2. H. Peyton Young, 1987. "On Dividing an Amount According to Individual Claims or Liabilities," Mathematics of Operations Research, INFORMS, vol. 12(3), pages 398-414, August.
    3. Bochet, Olivier & İlkılıç, Rahmi & Moulin, Hervé, 2013. "Egalitarianism under earmark constraints," Journal of Economic Theory, Elsevier, vol. 148(2), pages 535-562.
    4. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    5. Gabrielle Demange & Michel L. Balinski, 1989. "An Axiomatic Approach to Proportionality between Matrices," Post-Print halshs-00670952, HAL.
    6. , & Ilkilic, Rahmi & , & ,, 2012. "Balancing supply and demand under bilateral constraints," Theoretical Economics, Econometric Society, vol. 7(3), September.
    7. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
    8. 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.
    9. 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.
    10. Hervé Moulin & Jay Sethuraman, 2013. "The Bipartite Rationing Problem," Operations Research, INFORMS, vol. 61(5), pages 1087-1100, October.
    11. Eric Budish & Yeon-Koo Che & Fuhito Kojima & Paul Milgrom, 2013. "Designing Random Allocation Mechanisms: Theory and Applications," American Economic Review, American Economic Association, vol. 103(2), pages 585-623, April.
    12. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
    13. M. L. Balinski & G. Demange, 1989. "An Axiomatic Approach to Proportionality Between Matrices," Mathematics of Operations Research, INFORMS, vol. 14(4), pages 700-719, November.
    14. Bergantinos, Gustavo & Sanchez, Estela, 2002. "The proportional rule for problems with constraints and claims," Mathematical Social Sciences, Elsevier, vol. 43(2), pages 225-249, March.
    15. Hutchens, Robert, 2001. "Numerical measures of segregation: desirable properties and their implications," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 13-29, July.
    16. Thomson, William, 2012. "On The Axiomatics Of Resource Allocation: Interpreting The Consistency Principle," Economics and Philosophy, Cambridge University Press, vol. 28(3), pages 385-421, November.
    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. Francesco Andreoli & Claudio Zoli, 2023. "Robust dissimilarity comparisons with categorical outcomes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(3), pages 397-437, April.
    2. Péter Csóka & P. Jean-Jacques Herings, 2023. "An Axiomatization of the Pairwise Netting Proportional Rule in Financial Networks," CERS-IE WORKING PAPERS 2301, Institute of Economics, Centre for Economic and Regional Studies.
    3. Gabrielle Demange, 2021. "On the resolution of cross-liabilities," Working Papers halshs-03151128, HAL.
    4. Péter Csóka & P. Jean-Jacques Herings, 2021. "An Axiomatization of the Proportional Rule in Financial Networks," Management Science, INFORMS, vol. 67(5), pages 2799-2812, May.
    5. Csóka, Péter, 2017. "Az arányos csődszabály karakterizációja körbetartozások esetén [The characterization of the proportional rule in the case of circular liabilities]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(9), pages 930-942.
    6. Han, Lining & Juarez, Ruben, 2018. "Free intermediation in resource transmission," Games and Economic Behavior, Elsevier, vol. 111(C), pages 75-84.
    7. Moulin, Herve, 2017. "Consistent bilateral assignment," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 43-55.
    8. Gabrielle Demange, 2020. "Resolution rules in a system of financially linked firms," Working Papers hal-02502413, HAL.
    9. Yoshio Sano & Ping Zhan, 2021. "Extended Random Assignment Mechanisms on a Family of Good Sets," SN Operations Research Forum, Springer, vol. 2(4), pages 1-30, December.

    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, 2017. "Consistent bilateral assignment," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 43-55.
    2. Flores-Szwagrzak, Karol & Østerdal, Lars Peter, 2024. "Rationalizing Sharing Rules," Working Papers 17-2024, Copenhagen Business School, Department of Economics.
    3. 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.
    4. Rahmi İlkılıç & Çağatay Kayı, 2014. "Allocation rules on networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 877-892, December.
    5. Long, Yan & Sethuraman, Jay & Xue, Jingyi, 2021. "Equal-quantile rules in resource allocation with uncertain needs," Journal of Economic Theory, Elsevier, vol. 197(C).
    6. Gabrielle Demange, 2021. "On the resolution of cross-liabilities," PSE Working Papers halshs-03151128, HAL.
    7. Jens Hougaard & Juan Moreno-Ternero & Lars Østerdal, 2013. "Rationing with baselines: the composition extension operator," Annals of Operations Research, Springer, vol. 211(1), pages 179-191, December.
    8. Hervé Moulin & Jay Sethuraman, 2013. "The Bipartite Rationing Problem," Operations Research, INFORMS, vol. 61(5), pages 1087-1100, October.
    9. Giménez-Gómez, José-Manuel & Osório, Antonio, 2015. "Why and how to differentiate in claims problems? An axiomatic approach," European Journal of Operational Research, Elsevier, vol. 241(3), pages 842-850.
    10. Gabrielle Demange, 2020. "Resolution rules in a system of financially linked firms," Working Papers hal-02502413, HAL.
    11. Erlanson, Albin & Szwagrzak, Karol, 2013. "Strategy-Proof Package Assignment," Working Papers 2013:43, Lund University, Department of Economics.
    12. Jingyi Xue, 2018. "Fair division with uncertain needs," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 105-136, June.
    13. William Thomson, 2011. "Consistency and its converse: an introduction," Review of Economic Design, Springer;Society for Economic Design, vol. 15(4), pages 257-291, December.
    14. 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.
    15. Erlanson, Albin & Flores-Szwagrzak, Karol, 2015. "Strategy-proof assignment of multiple resources," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 137-162.
    16. Han, Xiang, 2016. "On the consistency of random serial dictatorship," Economics Letters, Elsevier, vol. 145(C), pages 168-171.
    17. Demange, Gabrielle, 2017. "Mutual rankings," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 35-42.
    18. 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.
    19. Péter Csóka & P. Jean-Jacques Herings, 2018. "Decentralized Clearing in Financial Networks," Management Science, INFORMS, vol. 64(10), pages 4681-4699, October.
    20. 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.

    More about this item

    Keywords

    Assignment; Bipartite rationing; Proportionality; Segregation; Consistency; Entropy;
    All these keywords.

    JEL classification:

    • D - Microeconomics
    • D - Microeconomics

    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:eee:jetheo:v:162:y:2016:i:c:p:1-20. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.