IDEAS home Printed from https://ideas.repec.org/p/eca/wpaper/2013-352301.html
   My bibliography  Save this paper

Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?

Author

Listed:
  • Estelle Cantillon
  • Li Chen
  • Juan Sebastian Pereyra Barreiro

Abstract

A classic trade-off that school districts face when deciding which matching algorithm to use is that it is not possible to always respect both priorities and preferences. The student-proposing deferred acceptance algorithm (DA) respects priorities but can lead to inefficient allocations. The top trading cycle algorithm (TTC) respects preferences but may violate priorities. We identify a new condition on school choice markets under which DA is efficient and there is a unique allocation that respects priorities. Our condition generalizes earlier conditions by placing restrictions on how preferences and priorities relate to one another only on the parts that are relevant for the assignment. We discuss how our condition sheds light on existing empirical findings. We show through simulations that our condition significantly expands the range of known environments for which DA is efficient.

Suggested Citation

  • Estelle Cantillon & Li Chen & Juan Sebastian Pereyra Barreiro, 2022. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off ?," Working Papers ECARES 2022-39, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/352301
    as

    Download full text from publisher

    File URL: https://dipot.ulb.ac.be/dspace/bitstream/2013/352301/3/2022-39-CANTILLON_CHEN_PEREYRA-respecting.pdf
    File Function: Full text for the whole work, or for a work part
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Battal Doğan & Lars Ehlers, 2022. "Robust Minimal Instability of the Top Trading Cycles Mechanism," American Economic Journal: Microeconomics, American Economic Association, vol. 14(4), pages 556-582, November.
    2. Yeon-Koo Che & Olivier Tercieux, 2019. "Efficiency and Stability in Large Matching Markets," Journal of Political Economy, University of Chicago Press, vol. 127(5), pages 2301-2342.
    3. Romero-Medina, Antonio & Triossi, Matteo, 2013. "Acyclicity and singleton cores in matching markets," Economics Letters, Elsevier, vol. 118(1), pages 237-239.
    4. Julien Grenet & Yinghua He & Dorothea Kübler, 2022. "Preference Discovery in University Admissions: The Case for Dynamic Multioffer Mechanisms," PSE-Ecole d'économie de Paris (Postprint) hal-04157650, HAL.
    5. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    6. Philip J. Reny, 2021. "A simple sufficient condition for a unique and student-efficient stable matching in the college admissions problem," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 7-9, April.
    7. Ashlagi, Itai & Nikzad, Afshin, 2020. "What matters in school choice tie-breaking? How competition guides design," Journal of Economic Theory, Elsevier, vol. 190(C).
    8. Rustamdjan Hakimov & Onur Kesten, 2018. "The Equitable Top Trading Cycles Mechanism For School Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 2219-2258, November.
    9. Pathak, Parag A. & Shi, Peng, 2021. "How well do structural demand models work? Counterfactual predictions in school choice," Journal of Econometrics, Elsevier, vol. 222(1), pages 161-195.
    10. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    11. Simon Burgess & Ellen Greaves & Anna Vignoles & Deborah Wilson, 2015. "What Parents Want: School Preferences and School Choice," Economic Journal, Royal Economic Society, vol. 125(587), pages 1262-1289, September.
    12. Legros, Patrick & Newman, Andrew, 2010. "Co-ranking mates: Assortative matching in marriage markets," Economics Letters, Elsevier, vol. 106(3), pages 177-179, March.
    13. Atila Abdulkadiroğlu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2020. "Efficiency, Justified Envy, and Incentives in Priority-Based Matching," American Economic Review: Insights, American Economic Association, vol. 2(4), pages 425-442, December.
    14. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    15. Erdil, Aytek & Kumano, Taro, 2019. "Efficiency and stability under substitutable priorities with ties," Journal of Economic Theory, Elsevier, vol. 184(C).
    16. Caterina Calsamiglia & Chao Fu & Maia Güell, 2020. "Structural Estimation of a Model of School Choices: The Boston Mechanism versus Its Alternatives," Journal of Political Economy, University of Chicago Press, vol. 128(2), pages 642-680.
    17. Clark Simon, 2006. "The Uniqueness of Stable Matchings," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 6(1), pages 1-30, December.
    18. 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.
    19. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    20. Chen, Li & Sebastián Pereyra, Juan, 2019. "Self-selection in school choice," Games and Economic Behavior, Elsevier, vol. 117(C), pages 59-81.
    21. Rong, Kang & Tang, Qianfeng & Zhang, Yongchao, 2020. "On stable and efficient mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 187(C).
    22. Cristian Pop-Eleches & Miguel Urquiola, 2013. "Going to a Better School: Effects and Behavioral Responses," American Economic Review, American Economic Association, vol. 103(4), pages 1289-1324, June.
    23. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    24. Monique De Haan & Pieter A. Gautier & Hessel Oosterbeek & Bas van der Klaauw, 2023. "The Performance of School Assignment Mechanisms in Practice," Journal of Political Economy, University of Chicago Press, vol. 131(2), pages 388-455.
    25. Grenet, Julien & He, YingHua & Kübler, Dorothea, 2022. "Preference Discovery in University Admissions: The Case for Dynamic Multioffer Mechanisms," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 130(6), pages 1-1.
    26. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," Working Papers 2009-3, Princeton University. Economics Department..
    27. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    28. Chung-Piaw Teo & Jay Sethuraman & Wee-Peng Tan, 2001. "Gale-Shapley Stable Marriage Problem Revisited: Strategic Issues and Applications," Management Science, INFORMS, vol. 47(9), pages 1252-1267, September.
    29. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    30. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    31. Eun Jeong Heo, 2019. "Preference profiles for efficiency, fairness, and consistency in school choice problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 243-266, March.
    32. Ortega, Josué & Klein, Thilo, 2023. "The cost of strategy-proofness in school choice," Games and Economic Behavior, Elsevier, vol. 141(C), pages 515-528.
    33. Arenas, Andreu & Calsamiglia, Caterina, 2022. "Gender Differences in High-Stakes Performance and College Admission Policies," IZA Discussion Papers 15550, Institute of Labor Economics (IZA).
    34. 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.
    35. Gregory Z. Gutin & Philip R. Neary & Anders Yeo, 2021. "Unique Stable Matchings," Papers 2106.12977, arXiv.org, revised Jul 2023.
    36. Muriel Niederle & Leeat Yariv, 2009. "Decentralized Matching with Aligned Preferences," NBER Working Papers 14840, National Bureau of Economic Research, Inc.
    37. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    38. José Alcalde, 1994. "Exchange-proofness or divorce-proofness? Stability in one-sided matching markets," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 275-287, December.
    39. Salonen, Hannu & Salonen, Mikko A.A., 2018. "Mutually best matches," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 42-50.
    40. Ortega, Josue & Klein, Thilo, 2022. "Improving efficiency and equality in school choice," ZEW Discussion Papers 22-046, ZEW - Leibniz Centre for European Economic Research.
    41. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1269-1282, May.
    42. Gutin, Gregory Z. & Neary, Philip R. & Yeo, Anders, 2023. "Unique stable matchings," Games and Economic Behavior, Elsevier, vol. 141(C), pages 529-547.
    43. 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.
    44. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
    45. Atila Abdulkadiroğlu & Nikhil Agarwal & Parag A. Pathak, 2017. "The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match," American Economic Review, American Economic Association, vol. 107(12), pages 3635-3689, December.
    46. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    47. Julien Grenet & Yinghua He & Dorothea Kübler, 2022. "Preference Discovery in University Admissions: The Case for Dynamic Multioffer Mechanisms," Post-Print hal-04157650, HAL.
    48. Yan Chen & Onur Kesten, 2017. "Chinese College Admissions and School Choice Reforms: A Theoretical Analysis," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 99-139.
    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. Federico Echenique & Joseph Root & Fedor Sandomirskiy, 2024. "Stable matching as transport," Papers 2402.13378, arXiv.org, revised Mar 2025.
    2. Simon Burgess & Estelle Cantillon & Mariagrazia Cavallo & Ellen Greaves & Min Zhang, 2023. "School admissions in England: The rules schools choose on which pupils to admit," ULB Institutional Repository 2013/356676, ULB -- Universite Libre de Bruxelles.
    3. Galichon, Alfred & Ghelfi, Octavia & Henry, Marc, 2023. "Stable and extremely unequal," Economics Letters, Elsevier, vol. 226(C).

    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. Cantillon, Estelle & Chen, Li & Pereyra, Juan S., 2024. "Respecting priorities versus respecting preferences in school choice: When is there a trade-off?," Games and Economic Behavior, Elsevier, vol. 148(C), pages 82-96.
    2. Abdulkadiroglu, Atila & Andersson, Tommy, 2022. "School Choice," Working Papers 2022:4, Lund University, Department of Economics.
    3. Klein, Thilo & Aue, Robert & Ortega, Josué, 2024. "School choice with independent versus consolidated districts," Games and Economic Behavior, Elsevier, vol. 147(C), pages 170-205.
    4. 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.
    5. Gabrielle Fack & Julien Grenet & Yinghua He, 2019. "Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions," American Economic Review, American Economic Association, vol. 109(4), pages 1486-1529, April.
    6. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    7. Hatfield, John William & Kojima, Fuhito & Narita, Yusuke, 2016. "Improving schools through school choice: A market design approach," Journal of Economic Theory, Elsevier, vol. 166(C), pages 186-211.
    8. 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.
    9. Lars Ehlers & Bettina Klaus, 2012. "Strategy-Proofness Makes the Difference : Deferred-Acceptance with Responsive Priorities," Cahiers de recherche 15-2012, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    10. Wu, Binzhen & Zhong, Xiaohan, 2020. "Matching inequality and strategic behavior under the Boston mechanism: Evidence from China's college admissions," Games and Economic Behavior, Elsevier, vol. 123(C), pages 1-21.
    11. Ha, Wei & Kang, Le & Song, Yang, 2020. "College matching mechanisms and matching stability: Evidence from a natural experiment in China," Journal of Economic Behavior & Organization, Elsevier, vol. 175(C), pages 206-226.
    12. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    13. Afacan, Mustafa Oğuz & Dur, Umut & Van der Linden, Martin, 2024. "Capacity design in school choice," Games and Economic Behavior, Elsevier, vol. 146(C), pages 277-291.
    14. Lars Ehlers & Bettina Klaus, 2014. "Strategy-Proofness Makes the Difference: Deferred-Acceptance with Responsive Priorities," Mathematics of Operations Research, INFORMS, vol. 39(4), pages 949-966, November.
    15. Ata Atay & Ana Mauleon & Vincent Vannetelbosch, 2022. "Limited farsightedness in priority-based matching," UB School of Economics Working Papers 2022/438, University of Barcelona School of Economics.
    16. Rodríguez-Álvarez, Carmelo & Romero-Medina, Antonio, 2024. "School choice with transferable student characteristics," Games and Economic Behavior, Elsevier, vol. 143(C), pages 103-124.
    17. Tong Wang & Congyi Zhou, 2020. "High school admission reform in China: a welfare analysis," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 215-269, December.
    18. Han, Xiang, 2024. "On the efficiency and fairness of deferred acceptance with single tie-breaking," Journal of Economic Theory, Elsevier, vol. 218(C).
    19. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    20. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).

    More about this item

    Keywords

    Matching; envyfreeness; efficiency; priorities; preferences; matching algorithms;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:eca:wpaper:2013/352301. 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: Benoit Pauwels (email available below). General contact details of provider: https://edirc.repec.org/data/arulbbe.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.