  In several matching markets, in order 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.
