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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.

Suggested Citation

  • Lars Ehlers & Isa Hafalir & Bumin Yenmez & Muhammed Yildirim, 2011. "School Choice with Controlled Choice Constraints: Hard Bounds versus Soft Bounds," GSIA Working Papers 2012-E21, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:925558684
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    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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