  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.
