Affirmative Action with Overlapping Reserves

In a wide variety of real-life resource allocation problems such as school choice or assignment of public positions, implementation of affirmative action policies rely on choice rules that balance meritocracy with equity. We study choice rules where meritocracy is attained through reliance on a priority list, and equity is attained through reserved positions for target groups of disadvantaged individuals. Focusing on overlapping reserves, the case where an individual can belong to multiple types of reserved positions, we characterize choice rules that satisfy maximal compliance with reservations, elimination of justified envy, and non-wastefulness. When an individual accommodates only one of the reserved positions, the horizontal envelope choice rule is the only rule to satisfy these three axioms. When an individual accommodates each of the reserved positions she qualifies for, there are complementarities between individuals. Under this alternative convention, and assuming there are only two target groups, such as women and minorities, we show that paired-admission choice rules are the only ones to satisfy the three axioms. Building on these results, we provide improved allocation mechanisms for school choice in Chile, public position allocation in India, and college admissions in Brazil.