Testing the Fairness-Improvability of Algorithms

Many algorithms have a disparate impact in that their benefits or harms fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because it is not always clear whether there exists an alternative more-fair algorithm that does not compromise on other key objectives such as accuracy or profit. Establishing the improvability of algorithms with respect to multiple criteria is of both conceptual and practical interest: in many settings, disparate impact that would otherwise be prohibited under US federal law is permissible if it is necessary to achieve a legitimate business interest. The question is how a policy maker can formally substantiate, or refute, this necessity defense. In this paper, we provide an econometric framework for testing the hypothesis that it is possible to improve on the fairness of an algorithm without compromising on other pre-specified objectives. Our proposed test is simple to implement and can incorporate any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and demonstrate its use empirically by evaluating a healthcare algorithm originally considered by Obermeyer et al. (2019). In this demonstration, we find strong statistically significant evidence that it is possible to reduce the algorithm's disparate impact without compromising on the accuracy of its predictions.