Lexicographic choice under variable capacity constraints

In several matching markets, to achieve diversity, agents' priorities are allowed to vary across an institution's available seats, and the institution is let to choose agents in a lexicographic fashion based on a predetermined ordering of the seats, called a (capacity-constrained)lexicographic choice rule. We provide a characterization of lexicographic choice rules and a characterization of deferred acceptance mechanisms that operate based on a lexicographic choice structure under variable capacity constraints. We discuss some implications for the Boston school choice system and show that our analysis can be helpful in applications to select among plausible choice rules.