Are Affirmative Action Policies so Impossible

Abstract

Affirmative action policies are a widely used tool for policy makers. One of their objectives is to improve the welfare of a targeted group of students during a school admission procedure. However, it is well-know in the matching literature that these policies can lead to perverse effects: the targeted students can be hurt by the policy intended to help them. In this paper, we take an interim-welfare perspective and show that, in the particular framework of aligned preferences and indifferent schools, the well-known Deferred Acceptance algorithm never hurts the minority students’ welfare once an affirmative action policy is implemented. We also highlight the welfare effects of the ordering defining how the seats of a school are allocated throughout the matching procedure, known as a precedence order. Our main proof elicits two effects of a reinforcement of an affirmative action policy. A direct effect where the policy increases the probability to be assigned to the schools where the policy was reinforced. And an indirect one: in decreasing the competition from other minority students, the policy increases the expected utility of a student, even if this latter has been rejected by the schools where the policy was reinforced. We provide counter examples to show that the environment that we consider is a tight domain for the positive effects on minority students. Last, we perform simulations to study the interim-welfare effects of affirmative actions when we depart from the framework of i) aligned preferences preferences ii) indifferent schools. With indifferent schools, they support that the more correlated are the preferences, the better the affirmative action policy performs. They also show that the rules used to break the indifference of the schools perform differently: a Multiple Tie Breaking rule tends to hurt less the minority students then the Single Tie Breaking rule.