Choice with Affirmative Action

Battal Dogan and Kemal Yildiz   Abstract 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 enrich the standard formulation of a choice problem by incorporating a type function and a priority ordering, and introduce responsiveness axioms that discipline how a choice rule responds to variations in these new parameters. We provide a representation result for the class of responsive and substitutable affirmative action rules, and also show that responsiveness axioms are crucial for substitutable affirmative action. Finally, as a prominent class of choice rules that satisfy our responsiveness axioms, we characterize lexicographic affirmative action rules that are prevalent both in the literature and in practice.