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.JEL C78, D61, D78, I20. * An earlier version (Ehlers, 2010) of this paper emerged from a joint project of the first author with Atila Abdulkadiroglu. We are grateful for his extensive comments and contribution to that paper. Ehlers acknowledges financial support from the SSHRC (Canada).

Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. The prevalent affirmative action policy in school choice limits the number of admitted majority students to give minority students higher chances to attend their desired schools. There have been numerous efforts to reconcile affirmative action policies with celebrated matching mechanisms such as the deferred acceptance and top trading cycles algorithms. Nevertheless, it is theoretically shown that under these algorithms, the policy based on majority quotas may be detrimental to minorities. Using simulations, we find that this is a more common phenomenon rather than a peculiarity. To circumvent the inefficiency caused by majority quotas, we offer a different interpretation of the affirmative action policies based on minority reserves. With minority reserves, schools give higher priority to minority students up to the point that the minorities fill the reserves. We compare the welfare effects of these policies. The deferred acceptance algorithm with minority reserves Pareto dominates the one with majority quotas. Our simulations, which allow for correlations between student preferences and school priorities, indicate that minorities are, on average, better off with minority reserves while adverse effects on majorities are mitigated. Terms of use: Documents in

We characterize choice rules for schools that regard students as substitutes while expressing preferences for a diverse student body. The stable (or fair) assignment of students to schools requires the latter to regard the former as substitutes. Such a requirement is in conflict with the reality of schools' preferences for diversity. We show that the conflict can be useful, in the sense that certain unique rules emerge from imposing both considerations. We also provide welfare comparisons for students when different choice rules are employed.

The prevalent affirmative action policy in school choice limits the number of admitted majority students to give minority students higher chances to attend their desired schools. There have been numerous efforts to reconcile affirmative action policies with celebrated matching mechanisms such as the deferred acceptance and top trading cycles algorithms. Nevertheless, it is theoretically shown that under these algorithms, the policy based on majority quotas may be detrimental to minorities. Using simulations, we find that this is a more common phenomenon rather than a peculiarity. To circumvent the inefficiency caused by majority quotas, we offer a different interpretation of the affirmative action policies based on minority reserves. With minority reserves, schools give higher priority to minority students up to the point that the minorities fill the reserves. We compare the welfare effects of these policies. The deferred acceptance algorithm with minority reserves Pareto dominates the one with majority quotas. Our simulations, which allow for correlations between student preferences and school priorities, indicate that minorities are, on average, better off with minority reserves while adverse effects on majorities are mitigated.

We investigate the testable implications of the theory of stable matchings. We provide a characterization of the matchings that are rationalizable as stable matchings when agents' preferences are unobserved. The characterization is a simple nonparametric test for stability, in the tradition of revealed preference tests. We also characterize the observed stable matchings when monetary transfers are allowed and the stable matchings that are best for one side of the market: extremal stable matchings. We find that the theory of extremal stable matchings is observationally equivalent to requiring that there be a unique stable matching or that the matching be consistent with unrestricted monetary transfers.