School choice with controlled choice constraints: Hard bounds versus soft bounds

Controlled choice over public schools attempts giving parents selection options while maintaining diversity of different student types. In practice, diversity constraints are often enforced by setting hard upper bounds and hard lower bounds for each student type. We demonstrate that, with hard bounds, there might not exist assignments that satisfy standard fairness and non-wastefulness properties; and only constrained non-wasteful assignments that are fair for same type students can be guaranteed to exist. We introduce the student exchange algorithm that finds a constrained efficient assignment among such assignments. To achieve fair (across all types) and non-wasteful assignments, we propose control constraints to be interpreted as soft bounds–flexible limits that regulate school priorities dynamically. In this setting, (i) the student-proposing deferred acceptance algorithm produces an assignment that Pareto dominates all other ✩ This paper supersedes Ehlers (2010), which emerged from a joint project of the first author with Atila Abdulkadiroğlu. We are grateful for his extensive comments and contribution to that paper. We are especially grateful to two reviewers and the associate editor for their useful comments and suggestions. We thank Simon Board, Eric Budish, Tayfun Sönmez, the seminar participants at ITAM, Koc University, UCLA, MITRE Auctions and Matching Workshop (University of Michigan), and Measuring and Interpreting Inequality Conference (Becker Friedman Institute). Ehlers acknowledges financial support from the SSHRC (Canada) and the FQRSC (Québec). Hafalir and Yenmez acknowledge financial support from National Science Foundation grant SES-1326584. * Corresponding author. E-mail addresses: [email protected] (L. Ehlers), [email protected] (I.E. Hafalir), [email protected] (M.B. Yenmez), [email protected] (M.A. Yildirim). http://dx.doi.org/10.1016/j.jet.2014.03.004 0022-0531/© 2014 Elsevier Inc. All rights reserved. L. Ehlers et al. / Journal of Economic Theory 153 (2014) 648–683 649 fair assignments while eliciting true preferences and (ii) the school-proposing deferred acceptance algorithm finds an assignment that minimizes violations of controlled choice constraints among fair assignments. © 2014 Elsevier Inc. All rights reserved. JEL classification: C78; D61; D78; I20