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

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  • 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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Bibliographic Info

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
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Handle: RePEc:cmu:gsiawp:925558684

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Postal: Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890
Web page: http://www.tepper.cmu.edu/

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

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References

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  1. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun S�nmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
  2. José Alcalde Pérez & Antonio Romero-Medina, 2011. "Fair School Placement," Working Papers. Serie AD 2011-22, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  3. 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.
  4. David Card & Jesse Rothstein, 2005. "Racial Segregation and the Black-White Test Score Gap," Working Papers 93, Princeton University, Department of Economics, Center for Economic Policy Studies..
  5. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
  6. Aytek Erdil & Haluk Ergin, 2007. "What`s the Matter with Tie-breaking? Improving Efficiency in School Choice," Economics Series Working Papers 349, University of Oxford, Department of Economics.
  7. EHLERS, Lars, 2010. "School Choice with Control," Cahiers de recherche 13-2010, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  8. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  9. 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, vol. 33(1), pages 115-128, January.
  10. Yenmez, M. Bumin & Yildirim, Muhammed Ali & Hafalir, Isa Emin, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
  11. 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.
  12. Tadenuma, Koichi & Thomson, William, 1991. "No-Envy and Consistency in Economies with Indivisible Goods," Econometrica, Econometric Society, vol. 59(6), pages 1755-67, November.
  13. 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.
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Cited by:
  1. Flip Klijn & Joana Pais & Marc Vorsatz, 2014. "Affirmative Action through Minority Reserves: An Experimental Study on School Choice," Working Papers 752, Barcelona Graduate School of Economics.
  2. Yenmez, M. Bumin & Yildirim, Muhammed Ali & Hafalir, Isa Emin, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
  3. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer, vol. 53(3), pages 561-589, August.
  4. 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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