IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4882.html
   My bibliography  Save this article

Distance on matchings: an axiomatic approach

Author

Listed:
  • Can, Burak

    (Department of Data Analytics and Digitalisation, Maastricht University)

  • Pourpouneh, Mohsen

    (Center for Blockchains and Electronic Markets, University of Copenhagen)

  • Storcken, Ton

    (Department of Quantitative Economics, Maastricht University)

Abstract

Matchings in a market may have varying degrees of compromise from efficiency, fairness, and or stability. A distance function allows to quantify such concepts or the (dis)similarity between any two matchings. There are a few attempts to propose such functions, however these are tailored for specific applications and ignore the individual preferences completely. In this paper, we construct a normative framework to quantify the difference between outcomes of market mechanisms in matching markets, while endogenizing the preferences of the individuals into the distance concept. Several conditions are introduced to capture natural and appealing behavior of such functions. We find a class of distance functions called \textit{scaled Borda distances}, which is the only class of distance functions that satisfies these conditions simultaneously.

Suggested Citation

  • Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.
  • Handle: RePEc:the:publsh:4882
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20230597/36527/1092
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Klaus, Bettina & Klijn, Flip & Walzl, Markus, 2010. "Stochastic stability for roommate markets," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2218-2240, November.
    2. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    3. 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.
    4. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
    5. Bettina Klaus & Flip Klijn, 2006. "Median Stable Matching for College Admissions," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(1), pages 1-11, April.
    6. Klaus, Bettina, 2017. "Consistency and its converse for roommate markets," Games and Economic Behavior, Elsevier, vol. 104(C), pages 43-58.
    7. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    8. Alvin E Roth & Muriel Niederle, 2007. "Making Markets Thick: Designing Rules for Offers and Acceptances," Levine's Bibliography 843644000000000142, UCLA Department of Economics.
    9. Sasaki, Hiroo & Toda, Manabu, 1992. "Consistency and characterization of the core of two-sided matching problems," Journal of Economic Theory, Elsevier, vol. 56(1), pages 218-227, February.
    10. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    11. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
    12. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    13. Chen, Peter & Egesdal, Michael & Pycia, Marek & Yenmez, M. Bumin, 2016. "Median stable matchings in two-sided markets," Games and Economic Behavior, Elsevier, vol. 97(C), pages 64-69.
    14. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    15. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    16. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    Full references (including those not matched with items on IDEAS)

    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. Can, Burak & Pourpouneh, Mohsen & Storcken, Ton, 2017. "Cost of transformation: a measure on matchings," Research Memorandum 015, Maastricht University, Graduate School of Business and Economics (GSBE).
    2. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    3. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    4. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    5. Ding, Tingting & Schotter, Andrew, 2017. "Matching and chatting: An experimental study of the impact of network communication on school-matching mechanisms," Games and Economic Behavior, Elsevier, vol. 103(C), pages 94-115.
    6. Rustamdjan Hakimov & Dorothea Kübler, 2021. "Experiments on centralized school choice and college admissions: a survey," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 434-488, June.
    7. Abdulkadiroglu, Atila & Andersson, Tommy, 2022. "School Choice," Working Papers 2022:4, Lund University, Department of Economics.
    8. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    9. Li, Mengling, 2020. "Ties matter: Improving efficiency in course allocation by allowing ties," Journal of Economic Behavior & Organization, Elsevier, vol. 178(C), pages 354-384.
    10. Dur, Umut & Hammond, Robert G. & Kesten, Onur, 2021. "Sequential school choice: Theory and evidence from the field and lab," Journal of Economic Theory, Elsevier, vol. 198(C).
    11. Featherstone, Clayton R. & Niederle, Muriel, 2016. "Boston versus deferred acceptance in an interim setting: An experimental investigation," Games and Economic Behavior, Elsevier, vol. 100(C), pages 353-375.
    12. Basteck, Christian & Klaus, Bettina & Kübler, Dorothea, 2021. "How lotteries in school choice help to level the playing field," Games and Economic Behavior, Elsevier, vol. 129(C), pages 198-237.
    13. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    14. Flip Klijn & Joana Pais & Marc Vorsatz, 2013. "Preference intensities and risk aversion in school choice: a laboratory experiment," Experimental Economics, Springer;Economic Science Association, vol. 16(1), pages 1-22, March.
    15. James Boudreau & Vicki Knoblauch, 2013. "Preferences and the price of stability in matching markets," Theory and Decision, Springer, vol. 74(4), pages 565-589, April.
    16. Onur Kesten, 2012. "On two kinds of manipulation for school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(3), pages 677-693, November.
    17. Troyan, Peter, 2012. "Comparing school choice mechanisms by interim and ex-ante welfare," Games and Economic Behavior, Elsevier, vol. 75(2), pages 936-947.
    18. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    19. Chen, Yan & Kesten, Onur, 2019. "Chinese college admissions and school choice reforms: An experimental study," Games and Economic Behavior, Elsevier, vol. 115(C), pages 83-100.
    20. Benoit Decerf, 2023. "A modification aimed at reducing the manipulability and inefficiency of the Boston school choice mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 60(1), pages 75-101, January.

    More about this item

    Keywords

    Matching markets; distance function; metrics;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:the:publsh:4882. 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: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    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.