  Disparate treatment occurs when a machine learning model yields different
decisions for individuals based on a sensitive attribute (e.g., age, sex). In
domains where prediction accuracy is paramount, it could potentially be
acceptable to fit a model which exhibits disparate treatment. To evaluate the
effect of disparate treatment, we compare the performance of split classifiers
(i.e., classifiers trained and deployed separately on each group) with
group-blind classifiers (i.e., classifiers which do not use a sensitive
attribute). We introduce the benefit-of-splitting for quantifying the
performance improvement by splitting classifiers. Computing the
benefit-of-splitting directly from its definition could be intractable since it
involves solving optimization problems over an infinite-dimensional functional
space. Under different performance measures, we (i) prove an equivalent
expression for the benefit-of-splitting which can be efficiently computed by
solving small-scale convex programs; (ii) provide sharp upper and lower bounds
for the benefit-of-splitting which reveal precise conditions where a
group-blind classifier will always suffer from a non-trivial performance gap
from the split classifiers. In the finite sample regime, splitting is not
necessarily beneficial and we provide data-dependent bounds to understand this
effect. Finally, we validate our theoretical results through numerical
experiments on both synthetic and real-world datasets.
