On the welfare effects of affirmative actions in school choice

Recent evidence, from both academia and practice, indicates that implementing affirmative action policies in school choice problems may induce substantial welfare losses on the intended beneficiaries. This paper addresses the following two questions: what are the causes of such perverse consequences, and when we can effectively implement affirmative action policies without unsatisfactory outcomes. Using the minority reserve policy in the student optimal stable mechanism as an example, I show that two acyclicity conditions, type-specific acyclicity and strongly type-specific acyclicity, are crucial for the effective implementations of minority reserve policies. I further illustrate how restrictive these two acyclicity conditions are, and the intrinsic difficulty of embedding diversity goals into stable matching mechanisms. Under some regularity conditions, I demonstrate that the minority reserve policy is very unlikely to cause welfare losses on any minority students when the number of schools is sufficiently large.