Exploring the Impact of Unilateral Affirmative Action on the School Choice Problem

Abstract

Affirmative action in school choice has become a burgeoning area of interest for policymakers and researchers alike. Numerous efforts have sought to characterize the impact of affirmative action on common matching mechanisms for school admissions, such as student-proposing deferred acceptance. Particularly, much work has focused on priority-based affirmative action, or a change in school rankings that uplifts the minority student group while keeping group orderings constant. It has been theoretically shown that deferred acceptance may not necessarily produce outcomes consistent with the intentions of priority-based affirmative action. However, with many elite magnet and exam schools in the U.S. implementing such affirmative action policies independently from the rest of their school district, this popular policy action begs the question of whether such a unilateral change truly improves the outcomes of minority students. Thus, we examine the less well-studied case in which a singular school unilaterally implements affirmative action by changing their preference ordering over students. In order to determine whether and how often a unilateral affirmative action policy produces better admissions outcomes for the intended students, we investigate the impacts of three types of affirmative action ranking changes of different magnitudes – arbitrary, single-swap, and priority-based affirmative action. Through theoretical and simulative analysis, we find that worst cases for several types of student welfare are achievable even through a single school swapping a single pair of students, showing that student-proposing deferred acceptance is highly volatile even under minute changes. We do find that some guarantees of welfare are possible for priority-based affirmative action – however, our simulations show that on average, only a couple minority students will achieve better matches, and that there is high variance in potential outcomes even for students who undergo the same type of change in the affirmative action policy. As such, we cautiously conclude that unilateral affirmative action is not sufficiently beneficial in the average case and is capable of creating severe negative impacts on all students.