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This paper analyzes the asymptotic performance of two popular affirmativeaction policies, majority quota and minority reserve, under the immediateacceptance mechanism (IAM) and the top trading cycles mechanism (TTCM) in thecontest of school choice. The matching outcomes of these two affirmativeactions are asymptotically equivalent under the IAM when all students aresincere. Given the possible preference manipulations under the IAM, wecharacterize the asymptotically equivalent sets of Nash equilibrium outcomes ofthe IAM with these two affirmative actions. However, these two affirmativeactions induce different matching outcomes under the TTCM with non-negligibleprobability even in large markets.

On the Asymptotic Performance of Affirmative Actions in School Choice