  We propose a new interpretable measure of unfairness, that allows providing a
quantitative analysis of classifier fairness, beyond a dichotomous fair/unfair
distinction. We show how this measure can be calculated when the classifier's
conditional confusion matrices are known. We further propose methods for
auditing classifiers for their fairness when the confusion matrices cannot be
obtained or even estimated. Our approach lower-bounds the unfairness of a
classifier based only on aggregate statistics, which may be provided by the
owner of the classifier or collected from freely available data. We use the
equalized odds criterion, which we generalize to the multiclass case. We report
experiments on data sets representing diverse applications, which demonstrate
the effectiveness and the wide range of possible uses of the proposed
methodology. An implementation of the procedures proposed in this paper and as
the code for running the experiments are provided in
https://github.com/sivansabato/unfairness.
