New Perspectives on the Effectiveness of Affirmative Action in School Choice

We revisit the school choice problem with affirmative action policies, or more generally, the controlled school choice problem proposed by Abdulkadiroglu and Sönmez (2003), and furtherly developed by Kojima (2012). The latter investigates the welfare effects of affirmative action policies and shows that certain market situations can hurt minority students. We observe that apart from stable mechanisms and the top trading cycle mechanism, reconciliations between two other celebrated mechanisms, the Boston mechanism and the Serial Dictatorship mechanism, and affirmative action policies, such as the quota-based policy and the priority-based policy, are all detrimental to minorities as well. Nevertheless, we discover that under the priority-based policy with an additional constraint on the priority order of majority students, both the Boston mechanism and the Serial Dictatorship mechanism manage to eliminate adverse consequences. Meanwhile, we also study the reserve-based policy, and demonstrate that it suffers from the same drawback as other mechanisms do unless the flexibility for schools to have majority students when the reserve is not fulfilled is adjusted into a round-concerned form. We also study the Pareto dominance relationship under reserve-based policies, and discover positive results.