On the Asymptotic Performance of Affirmative Actions in School Choice

TL;DR

This paper examines the long-term effects of two affirmative action policies in school choice, comparing their outcomes under different mechanisms and analyzing their stability and strategic behavior in large markets.

Contribution

It provides a theoretical analysis of the asymptotic performance of majority quota and minority reserve policies under IAM and TTCM mechanisms, including equilibrium characterizations.

Findings

Under IAM, the outcomes of both policies are asymptotically equivalent with sincere preferences.

Under TTCM, the policies can lead to different outcomes with non-negligible probability.

The paper characterizes Nash equilibrium outcomes considering strategic preference manipulations.

Abstract

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.