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-up to 25% of minorities and 55% of majorities can be worse off. 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 allows 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 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. (JEL D47, H75, I21, I28)

We study path-independent choice rules applied to a matching context. We use a classic representation of these choice rules to introduce a powerful technique for matching theory. Using this technique, we provide a deferred acceptance algorithm for many-to-many matching markets with contracts and study its properties. Next, we obtain a compelling comparative static result: if one agent's choice expands, the remaining agents on her side of the market are made worse off, while agents on the other side of the market are made better off. Finally, we establish several results related to path-independent choice rules.