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

Author Info

Listed author(s):
  • Lars Ehlers
  • Isa Hafalir
  • Bumin Yenmez
  • Muhammed 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.

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File URL: http://www.andrew.cmu.edu/user/isaemin/HardSoftControlFinal.pdf
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Paper provided by Carnegie Mellon University, Tepper School of Business in its series GSIA Working Papers with number 2012-E21.

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Date of creation: Nov 2011
Handle: RePEc:cmu:gsiawp:925558684
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Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890

Web page: http://www.tepper.cmu.edu/

Order Information: Web: http://student-3k.tepper.cmu.edu/gsiadoc/GSIA_WP.asp

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Find related papers by 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

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Cited by:

  1. Goto, Masahiro & Kojima, Fuhito & Kurata, Ryoji & Tamura, Akihisa & Yokoo, Makoto, 2015. "Designing Matching Mechanisms under General Distributional Constraints," MPRA Paper 64000, University Library of Munich, Germany.
  2. Ehlers, Lars & Klaus, Bettina, 2016. "Object allocation via deferred-acceptance: Strategy-proofness and comparative statics," Games and Economic Behavior, Elsevier, vol. 97(C), pages 128-146.
  3. 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.
  4. Kominers, Scott Duke & Sönmez, Tayfun, 2016. "Matching with slot-specific priorities: theory," Theoretical Economics, Econometric Society, vol. 11(2), May.
  5. Klijn, Flip & Pais, Joana & Vorsatz, Marc, 2016. "Affirmative action through minority reserves: An experimental study on school choice," Economics Letters, Elsevier, vol. 139(C), pages 72-75.
  6. 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.
  7. Yenmez, M. Bumin & Yildirim, Muhammed Ali & Hafalir, Isa Emin, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
  8. Kojima, Fuhito & Tamura, Akihisa & Yokoo, Makoto, 2014. "Designing Matching Mechanisms under Constraints: An Approach from Discrete Convex Analysis," MPRA Paper 56189, University Library of Munich, Germany.
  9. Doğan, Battal, 2016. "Responsive affirmative action in school choice," Journal of Economic Theory, Elsevier, vol. 165(C), pages 69-105.
  10. Bó, Inácio, 2016. "Fair implementation of diversity in school choice," Games and Economic Behavior, Elsevier, vol. 97(C), pages 54-63.
  11. Afacan, Mustafa Oğuz & Salman, Umutcan, 2016. "Affirmative actions: The Boston mechanism case," Economics Letters, Elsevier, vol. 141(C), pages 95-97.
  12. Mehmet Ekmekci & M. Bumin Yenmez, "undated". "Integrating Schools for Centralized Admissions," GSIA Working Papers 2014-E20, Carnegie Mellon University, Tepper School of Business.
  13. Duddy, Conal, 2015. "Revising the school choice problem," MPRA Paper 63316, University Library of Munich, Germany.
  14. Kamada, Yuichiro & Kojima, Fuhito, 2017. "Stability concepts in matching under distributional constraints," Journal of Economic Theory, Elsevier, vol. 168(C), pages 107-142.
  15. Goto, Masahiro & Iwasaki, Atsushi & Kawasaki, Yujiro & Yasuda, Yosuke & Yokoo, Makoto, 2014. "Improving Fairness and Efficiency in Matching with Distributional Constraints: An Alternative Solution for the Japanese Medical Residency Match," MPRA Paper 53409, University Library of Munich, Germany.

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