On the Asymptotic Performance of Affirmative Actions in School Choice

This paper analyzes the asymptotic performance of two popular affirmative action policies, majority quota and minority reserve, under the immediate acceptance mechanism (IAM) and the top trading cycles mechanism (TTCM) in the contest of school choice. The matching outcomes of these two affirmative actions are asymptotically equivalent under the IAM when all students are sincere. Given the possible preference manipulations under the IAM, we characterize the asymptotically equivalent sets of Nash equilibrium outcomes of the IAM with these two affirmative actions. However, these two affirmative actions induce different matching outcomes under the TTCM with non-negligible probability even in large markets.