Affirmative action policies provide a balance between meritocracy and equity in a wide variety of real-life resource allocation problems. We study choice rules where meritocracy is attained by prioritizing individuals based on merit, and equity is attained by reserving positions for target groups of disadvantaged individuals. Focusing on overlapping reserves, the case where an individual can belong to multiple target groups, 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, paired-admissions choice rules are the only ones to satisfy the three axioms. Building on these results, we provide improved mechanisms for implementing a variety of recent reforms, including the 2015 school choice reform in Chile and 2012 college admissions reform in Brazil.

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