IDEAS home Printed from https://ideas.repec.org/p/mtl/montec/13-2011.html
   My bibliography  Save this paper

School Choice with Controlled Choice Constraints: Hard Bounds versus Soft Bounds

Author

Listed:
  • Lars Ehlers
  • Isa E. Hafalir
  • M. Bumin Yenmez
  • Muhammed A. Yildirim

Abstract

Controlled choice over public schools attempts giving options to parents while maintaining diversity, often enforced by setting feasibility constraints with hard upper and lower bounds for each student type. We demonstrate that there might not exist assignments that satisfy standard fairness and non-wastefulness properties; whereas constrained non-wasteful assignments which are fair for same type students always exist. We introduce a "controlled" version of the deferred acceptance algorithm with an improvement stage (CDAAI) that finds a Pareto optimal assignment among such assignments. To achieve fair (across all types) and non-wasteful assignments, we propose the control constraints to be interpreted as soft bounds flexible limits that regulate school priorities. In this setting, a modified version of the deferred acceptance algorithm (DAASB) finds an assignment that is Pareto optimal among fair assignments while eliciting true preferences. CDAAI and DAASB provide two alternative practical solutions depending on the interpretation of the control constraints.

Suggested Citation

  • Lars Ehlers & Isa E. Hafalir & M. Bumin Yenmez & Muhammed A. Yildirim, 2011. "School Choice with Controlled Choice Constraints: Hard Bounds versus Soft Bounds," Cahiers de recherche 13-2011, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  • Handle: RePEc:mtl:montec:13-2011
    as

    Download full text from publisher

    File URL: http://www.cireqmontreal.com/wp-content/uploads/cahiers/13-2011-cah.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    2. Eric A. Hanushek & John F. Kain & Steven G. Rivkin, 2009. "New Evidence about Brown v. Board of Education: The Complex Effects of School Racial Composition on Achievement," Journal of Labor Economics, University of Chicago Press, vol. 27(3), pages 349-383, July.
    3. 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.
    4. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    5. repec:pri:cepsud:109rothstein is not listed on IDEAS
    6. Alkan, Ahmet & Gale, David, 2003. "Stable schedule matching under revealed preference," Journal of Economic Theory, Elsevier, vol. 112(2), pages 289-306, October.
    7. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123, February.
    8. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    9. Federico Echenique & M. Bumin Yenmez, 2015. "How to Control Controlled School Choice," American Economic Review, American Economic Association, vol. 105(8), pages 2679-2694, August.
    10. Card, David & Rothstein, Jesse, 2007. "Racial segregation and the black-white test score gap," Journal of Public Economics, Elsevier, vol. 91(11-12), pages 2158-2184, December.
    11. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(3), pages 561-589, August.
    12. 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.
    13. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
    14. 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.
    15. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    16. Hafalir, Isa Emin & Yenmez, M. Bumin & Yildirim, Muhammed Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    17. Ruth Martínez & Jordi Massó & Alejdanro Neme & Jorge Oviedo, 2004. "On group strategy-proof mechanisms for a many-to-one matching model," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(1), pages 115-128, January.
    18. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2006. "Changing the Boston School Choice Mechanism," Boston College Working Papers in Economics 639, Boston College Department of Economics.
    19. Orhan Aygün & Tayfun Sönmez, 2012. "Matching with Contracts: The Critical Role of Irrelevance of Rejected Contracts," Boston College Working Papers in Economics 804, Boston College Department of Economics.
    20. Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
    21. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
    22. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, vol. 98(3), pages 1189-1194, June.
    23. John William Hatfield & Paul R. Milgrom, 2005. "Matching with Contracts," American Economic Review, American Economic Association, vol. 95(4), pages 913-935, September.
    24. Jonathan Guryan, 2004. "Desegregation and Black Dropout Rates," American Economic Review, American Economic Association, vol. 94(4), pages 919-943, September.
    25. Federico Echenique & Roland G. Fryer, 2007. "A Measure of Segregation Based on Social Interactions," The Quarterly Journal of Economics, Oxford University Press, vol. 122(2), pages 441-485.
    26. Yuichiro Kamada & Fuhito Kojima, 2010. "Efficiency in Matching Markets with Regional Caps: The Case of the Japan Residency Matching Program," Discussion Papers 10-011, Stanford Institute for Economic Policy Research.
    27. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    28. Peter Cramton & Yoav Shoham & Richard Steinberg (ed.), 2006. "Combinatorial Auctions," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262033429, December.
    29. 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.
    30. 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.
    31. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-1767, November.
    32. David Card & Jesse Rothstein, 2005. "Racial Segregation and the Black-White Test Score Gap," Working Papers 879, Princeton University, Department of Economics, Industrial Relations Section..
    33. 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.
    34. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    35. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    36. Kojima, Fuhito, 2012. "School choice: Impossibilities for affirmative action," Games and Economic Behavior, Elsevier, vol. 75(2), pages 685-693.
    37. Federico Echenique & Roland G. Fryer Jr & Alex Kaufman, 2006. "Is School Segregation Good or Bad?," American Economic Review, American Economic Association, vol. 96(2), pages 265-269, May.
    38. David M. Cutler & Edward L. Glaeser, 1997. "Are Ghettos Good or Bad?," The Quarterly Journal of Economics, Oxford University Press, vol. 112(3), pages 827-872.
    39. Scott Duke Kominers & Tayfun Sönmez, 2012. "Designing for Diversity: Matching with Slot-Specific Priorities," Boston College Working Papers in Economics 806, Boston College Department of Economics.
    40. Hatfield, John William & Kojima, Fuhito, 2009. "Group incentive compatibility for matching with contracts," Games and Economic Behavior, Elsevier, vol. 67(2), pages 745-749, November.
    41. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    42. Onur Kesten, 2010. "School Choice with Consent," The Quarterly Journal of Economics, Oxford University Press, 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. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 2010-05, Universite de Montreal, Departement de sciences economiques.
    2. Scott Duke Kominers & Alexander Teytelboym & Vincent P Crawford, 2017. "An invitation to market design," Oxford Review of Economic Policy, Oxford University Press, vol. 33(4), pages 541-571.
    3. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    4. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2018. "Designing matching mechanisms under constraints: An approach from discrete convex analysis," Journal of Economic Theory, Elsevier, vol. 176(C), pages 803-833.
    5. Yuichiro Kamada & Fuhito Kojima, 2020. "Accommodating various policy goals in matching with constraints," The Japanese Economic Review, Springer, vol. 71(1), pages 101-133, January.
    6. Yuen Leng Chow & Isa E. Hafalir & Abdullah Yavas, 2015. "Auction versus Negotiated Sale: Evidence from Real Estate Sales," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 43(2), pages 432-470, June.
    7. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    8. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    9. Braun, Sebastian & Dwenger, Nadja & Kübler, Dorothea & Westkamp, Alexander, 2014. "Implementing quotas in university admissions: An experimental analysis," Games and Economic Behavior, Elsevier, vol. 85(C), pages 232-251.
    10. Umut M. Dur & Scott Duke Kominers & Parag A. Pathak & Tayfun Sönmez, 2013. "The Demise of Walk Zones in Boston: Priorities vs. Precedence in School Choice," NBER Working Papers 18981, National Bureau of Economic Research, Inc.
    11. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202103100800001123, Iowa State University, Department of Economics.
    12. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    13. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    14. Tayfun Sönmez & Tobias B. Switzer, 2013. "Matching With (Branch‐of‐Choice) Contracts at the United States Military Academy," Econometrica, Econometric Society, vol. 81(2), pages 451-488, March.
    15. Bó, Inácio, 2016. "Fair implementation of diversity in school choice," Games and Economic Behavior, Elsevier, vol. 97(C), pages 54-63.
    16. Tomoeda, Kentaro, 2018. "Finding a stable matching under type-specific minimum quotas," Journal of Economic Theory, Elsevier, vol. 176(C), pages 81-117.
    17. Aygün, Orhan & Turhan, Bertan, 2021. "How to De-reserve Reserves," ISU General Staff Papers 202104130700001123, Iowa State University, Department of Economics.
    18. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    19. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    20. Aygün, Orhan & Turhan, Bertan, 2020. "Dynamic reserves in matching markets," Journal of Economic Theory, Elsevier, vol. 188(C).

    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
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • I20 - Health, Education, and Welfare - - Education - - - General

    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:mtl:montec:13-2011. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/cdmtlca.html .

    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: Sharon BREWER (email available below). General contact details of provider: https://edirc.repec.org/data/cdmtlca.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.