  To study discrimination in automated decision-making systems, scholars have
proposed several definitions of fairness, each expressing a different fair
ideal. These definitions require practitioners to make complex decisions
regarding which notion to employ and are often difficult to use in practice
since they make a binary judgement a system is fair or unfair instead of
explaining the structure of the detected unfairness. We present an optimal
transport-based approach to fairness that offers an interpretable and
quantifiable exploration of bias and its structure by comparing a pair of
outcomes to one another. In this work, we use the optimal transport map to
examine individual, subgroup, and group fairness. Our framework is able to
recover well known examples of algorithmic discrimination, detect unfairness
when other metrics fail, and explore recourse opportunities.
