  We introduce a method to derive from a characterization of institutional
choice rules (or priority rules), a characterization of the Gale-Shapley
deferred-acceptance (DA) matching rule based on these choice rules. We apply
our method to school choice in Chile, where we design choice rules for schools
that are uniquely compatible with the School Inclusion Law and derive a set of
matching properties, compatible with the law, that characterizes the DA rule
based on the designed choice rules. Our method provides a recipe for
establishing such results and can help policymakers decide on which allocation
rule to use in practice.
