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Procedurally fair and stable matching

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  • Bettina Klaus
  • Flip Klijn

Abstract

We motivate procedural fairness for matching mechanisms and study two procedurally fair and stable mechanisms: employment by lotto (Aldershof et al. , 1999) and the random order mechanism (Roth and Vande Vate, 1990, Ma, 1996). For both mechanisms we give various examples of probability distributions on the set of stable matchings and discuss properties that differentiate employment by lotto and the random order mechanism. Finally, we consider an adjustment of the random order mechanism, the equitable random order mechanism, that combines aspects of procedural and “endstate” fairness. Copyright Springer-Verlag Berlin/Heidelberg 2006

Suggested Citation

  • Bettina Klaus & Flip Klijn, 2006. "Procedurally fair and stable matching," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 27(2), pages 431-447, January.
    • Handle: RePEc:spr:joecth:v:27:y:2006:i:2:p:431-447
    DOI: 10.1007/s00199-004-0602-5
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    1. Moulin, HervÈ, 1997. "Procedural cum Endstate Justice: An Implementation Viewpoint," Working Papers 97-17, Duke University, Department of Economics.
    2. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541, Elsevier.
    3. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
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    5. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-1480, November.
    6. Antonio Romero-Medina, 2005. "Equitable Selection in Bilateral Matching Markets," Theory and Decision, Springer, vol. 58(3), pages 305-324, May.
    7. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
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    Cited by:

    1. Aziz, Haris & Brandt, Felix & Brill, Markus, 2013. "The computational complexity of random serial dictatorship," Economics Letters, Elsevier, vol. 121(3), pages 341-345.
    2. Elette Boyle & Federico Echenique, 2009. "Sequential entry in many-to-one matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(1), pages 87-99, June.
    3. Li Xiong & Chengwen Wang & Zhaoran Xu, 2022. "Supply and demand matching model of P2P sharing accommodation platforms considering fairness," Electronic Commerce Research, Springer, vol. 22(3), pages 951-978, September.
    4. Sinong Ma & Zvi Safra, 2019. "Fairness and utilitarianism without independence," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(1), pages 29-52, February.
    5. Bettina Klaus & Flip Klijn, 2007. "Corrigendum to “On randomized matching mechanisms” [Economic Theory 8(1996)377–381]," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 32(2), pages 411-416, August.
    6. Bettina Klaus & Flip Klijn, 2009. "Employment By Lotto Revisited," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 11(02), pages 181-198.
    7. Federico Echenique & SangMok Lee & Matthew Shum & M. Bumin Yenmez, 2021. "Stability and Median Rationalizability for Aggregate Matchings," Games, MDPI, vol. 12(2), pages 1-15, April.
    8. Daniela Bubboloni & Michele Gori & Claudia Meo, 2024. "Symmetric mechanisms for two-sided matching problems," Papers 2404.01404, arXiv.org.
    9. Rong Wang & Li Xu & Hashim Zameer & Yasir Ahmed Solangi, 2020. "Modeling Two-Sided Matching Considering Agents’ Psychological Behavior Based on Regret Theory," SAGE Open, , vol. 10(2), pages 21582440209, June.
    10. 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.
    11. Kuvalekar, Aditya Vijay & Romero-Medina, Antonio, 2021. "A fair procedure in a marriage market," UC3M Working papers. Economics 31711, Universidad Carlos III de Madrid. Departamento de Economía.
    12. Zhan Wang & Jinpeng Ma & Hongwei Zhang, 2023. "Object-based unawareness: Theory and applications," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 1-55, December.
    13. Jay Sethuraman & Chung-Piaw Teo & Liwen Qian, 2006. "Many-to-One Stable Matching: Geometry and Fairness," Mathematics of Operations Research, INFORMS, vol. 31(3), pages 581-596, August.
    14. Karla Atkins & Achla Marathe & Chris Barrett, 2007. "A computational approach to modeling commodity markets," Computational Economics, Springer;Society for Computational Economics, vol. 30(2), pages 125-142, September.
    15. Simon Mauras, 2020. "Two-Sided Random Matching Markets: Ex-Ante Equivalence of the Deferred Acceptance Procedures," Papers 2005.08584, arXiv.org.
    16. 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.
    17. Manjunath, Vikram, 2016. "Fractional matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 321-336.
    18. Christian Haas, 2021. "Two-Sided Matching with Indifferences: Using Heuristics to Improve Properties of Stable Matchings," Computational Economics, Springer;Society for Computational Economics, vol. 57(4), pages 1115-1148, April.
    19. Sebastian Montano Correa, 2015. "Compulsory Social Service Matching Market for Physicians in Colombia," Documentos CEDE 12856, Universidad de los Andes, Facultad de Economía, CEDE.
    20. van Basshuysen, Philippe, 2023. "Markets, market algorithms, and algorithmic bias," LSE Research Online Documents on Economics 115694, London School of Economics and Political Science, LSE Library.
    21. Piotr Dworczak, 2021. "Deferred Acceptance with Compensation Chains," Operations Research, INFORMS, vol. 69(2), pages 456-468, March.
    22. Thayer Morrill, 2015. "Two simple variations of top trading cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 123-140, September.

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    More about this item

    Keywords

    Procedural fairness; Random mechanism; Stability; Two-sided matching.;
    All these keywords.

    JEL classification:

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

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