  The stable matching problem sets the economic foundation of several practical
applications ranging from school choice and medical residency to ridesharing
and refugee placement. It is concerned with finding a matching between two
disjoint sets of agents wherein no pair of agents prefer each other to their
matched partners. The Deferred Acceptance (DA) algorithm is an elegant
procedure that guarantees a stable matching for any input; however, its outcome
may be unfair as it always favors one side by returning a matching that is
optimal for one side (say men) and pessimal for the other side (say women). A
desirable fairness notion is minimizing the sex-equality cost, i.e. the
difference between the total rankings of both sides. Computing such stable
matchings is a strongly NP-hard problem, which raises the question of what
tractable algorithms to adopt in practice. We conduct a series of empirical
evaluations on the properties of sex-equal stable matchings when preferences of
agents on both sides are correlated. Our empirical results suggest that under
correlated preferences, the DA algorithm returns stable matchings with low
sex-equality cost, which further confirms its broad use in many practical
applications.
