  The increasing use of machine learning in high-stakes domains -- where
people's livelihoods are impacted -- creates an urgent need for interpretable,
fair, and highly accurate algorithms. With these needs in mind, we propose a
mixed integer optimization (MIO) framework for learning optimal classification
trees -- one of the most interpretable models -- that can be augmented with
arbitrary fairness constraints. In order to better quantify the "price of
interpretability", we also propose a new measure of model interpretability
called decision complexity that allows for comparisons across different classes
of machine learning models. We benchmark our method against state-of-the-art
approaches for fair classification on popular datasets; in doing so, we conduct
one of the first comprehensive analyses of the trade-offs between
interpretability, fairness, and predictive accuracy. Given a fixed disparity
threshold, our method has a price of interpretability of about 4.2 percentage
points in terms of out-of-sample accuracy compared to the best performing,
complex models. However, our method consistently finds decisions with almost
full parity, while other methods rarely do.
