Discrimination through algorithmic decision making has received considerable attention recently. Prior work on the topic largely focuses on defining conditions for fairness, but does not define proper measures of algorithmic unfairness. In this paper, we focus on the following practically important question: Given two unfair algorithms, how should we determine which of the two is more unfair? Our core idea is to use existing inequality indices from economics to measure how unequally the outcomes of an algorithm benefit different individuals or groups in a population. Our work offers a well-justified and generalizable framework to compare the (un)fairness of a variety of algorithmic predictors against one another. This unifying approach allows us to quantify unfairness both at the individual and the group level. Furthermore, our work reveals previously overlooked tradeoffs between different fairness notions: using our proposed measures, the overall individual-level unfairness of an algorithm can be decomposed into a between-group and a within-group component. Earlier methods are typically designed to tackle only between-group unfairness, which may be justified for legal reasons. However, we demonstrate that minimizing exclusively the between-group component may, in fact, increase the within-group, and hence the overall unfairness. Finally, we characterize and illustrate the existence of tradeoffs between our measures of (un)fairness and the prediction accuracy.

@Article{speicher2018a,
title = {A Unified Approach to Quantifying Algorithmic Unfairness: Measuring Individual and Group Unfairness via Inequality Indices},
author = {Till Speicher and Hoda Heidari and Nina Grgic-Hlaca and Krishna P. Gummadi and Adish Singla and Adrian Weller and Muhammad Bilal Zafar },
journal = {Proceedings of the International Conference on Knowledge Discovery and Data Mining (KDD)},
year = {2018},
month = {August}}