Choice with affirmative action
A choice rule with affirmative action decides on the recipients of a limited number of identical objects by reconciling two objectives: respecting a priority ordering over the applicants and supporting a minority group. We extend the standard formulation of a choice problem by incorporating a type function and a priority ordering, and introduce monotonicity axioms on how a choice rule should respond to variations in these parameters. We show that monotonic and substitutable affirmative action rules are the ones that admit a bounded reserve representation. As a prominent class of choice rules that satisfy the monotonicity axioms, we characterize lexicographic affirmative action rules that are prevalent both in the literature and in practice. Our axiomatic approach provides a novel way to think about reserve systems and uncovers choice rules that go beyond lexicographic affirmative action rules.