IDEAS home Printed from https://ideas.repec.org/p/unm/umagsb/2017015.html
   My bibliography  Save this paper

Cost of transformation: a measure on matchings

Author

Listed:
  • Can, Burak

    (Microeconomics & Public Economics, RS: GSBE ETBC)

  • Pourpouneh, Mohsen

    (Quantitative Economics)

  • Storcken, Ton

    (QE Math. Economics & Game Theory, RS: GSBE ETBC)

Abstract

This paper constructs a normative framework to quantify the difference between two matchings in roommate markets. We investigate the “cost of transformation” from one mechanism to another, based on the differences in the outputs of these mechanisms. Several conditions are introduced to ensure this cost reflects the welfare effect of the transformation on individuals. We introduce a measure called the Borda measure, which is fully characterized by these conditions. Several possible applications of this measure under different contexts interpretations are also discussed, such as measuring how unstable, how unfair, or how inefficient a matching is.

Suggested Citation

  • 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).
    • Handle: RePEc:unm:umagsb:2017015
    DOI: 10.26481/umagsb.2017015
    as

    Download full text from publisher

    File URL: https://cris.maastrichtuniversity.nl/ws/files/13734876/RM17015.pdf
    Download Restriction: no
    File URL: https://libkey.io/10.26481/umagsb.2017015?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
    ---><---

    Other versions of this item:

    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. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    3. 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.
    4. Thayer Morrill, 2013. "An alternative characterization of top trading cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 181-197, September.
    5. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    6. 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.
    7. Klaus, Bettina, 2017. "Consistency and its converse for roommate markets," Games and Economic Behavior, Elsevier, vol. 104(C), pages 43-58.
    8. Can, Burak & Storcken, Ton, 2018. "A re-characterization of the Kemeny distance," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 112-116.
    9. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    10. Afacan, Mustafa Oǧuz, 2013. "Alternative characterizations of Boston mechanism," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 176-179.
    11. 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.
    12. Can, Burak, 2014. "Weighted distances between preferences," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 109-115.
    13. Özkal-Sanver, Ipek, 2010. "Impossibilities for roommate problems," Mathematical Social Sciences, Elsevier, vol. 59(3), pages 360-363, May.
    14. 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.
    15. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    16. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    17. Thayer Morrill, 2013. "An alternative characterization of the deferred acceptance algorithm," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(1), pages 19-28, February.
    18. 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.
    19. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    20. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1297-1348.
    21. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    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, 2023. "Distance on matchings: an axiomatic approach," Theoretical Economics, Econometric Society, vol. 18(2), May.
    2. 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.
    3. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    4. Atila Abdulkadiroglu & Tommy Andersson, 2022. "School Choice," NBER Working Papers 29822, National Bureau of Economic Research, Inc.
    5. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    6. Ayoade, Nickesha & Pápai, Szilvia, 2023. "School choice with preference rank classes," Games and Economic Behavior, Elsevier, vol. 137(C), pages 317-341.
    7. Morrill, Thayer, 2015. "Making just school assignments," Games and Economic Behavior, Elsevier, vol. 92(C), pages 18-27.
    8. Afacan, Mustafa Og̃uz & Dur, Umut Mert, 2017. "When preference misreporting is Harm[less]ful?," Journal of Mathematical Economics, Elsevier, vol. 72(C), pages 16-24.
    9. Kesten, Onur & Kurino, Morimitsu, 2019. "Strategy-proof improvements upon deferred acceptance: A maximal domain for possibility," Games and Economic Behavior, Elsevier, vol. 117(C), pages 120-143.
    10. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    11. 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.
    12. Kumano, Taro, 2013. "Strategy-proofness and stability of the Boston mechanism: An almost impossibility result," Journal of Public Economics, Elsevier, vol. 105(C), pages 23-29.
    13. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    14. Pais, Joana & Pintér, Ágnes, 2008. "School choice and information: An experimental study on matching mechanisms," Games and Economic Behavior, Elsevier, vol. 64(1), pages 303-328, September.
    15. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    16. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Levine's Bibliography 122247000000001022, UCLA Department of Economics.
    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. Yajing Chen & Patrick Harless & Zhenhua Jiao, 2021. "The probabilistic rank random assignment rule and its axiomatic characterization," Papers 2104.09165, arXiv.org.
    19. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.
    20. Hakimov, Rustamdjan & Kübler, Dorothea, 2021. "Experiments on centralized school choice and college admissions: a survey," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 24(2), pages 434-488.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:unm:umagsb:2017015. 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: Andrea Willems or Leonne Portz (email available below). General contact details of provider: https://edirc.repec.org/data/meteonl.html .

    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.