Inference for an Algorithmic Fairness-Accuracy Frontier

Decision-making processes increasingly rely on the use of algorithms. Yet, algorithms' predictive ability frequently exhibit systematic variation across subgroups of the population. While both fairness and accuracy are desirable properties of an algorithm, they often come at the cost of one another. What should a fairness-minded policymaker do then, when confronted with finite data? In this paper, we provide a consistent estimator for a theoretical fairness-accuracy frontier put forward by Liang, Lu and Mu (2023) and propose inference methods to test hypotheses that have received much attention in the fairness literature, such as (i) whether fully excluding a covariate from use in training the algorithm is optimal and (ii) whether there are less discriminatory alternatives to an existing algorithm. We also provide an estimator for the distance between a given algorithm and the fairest point on the frontier, and characterize its asymptotic distribution. We leverage the fact that the fairness-accuracy frontier is part of the boundary of a convex set that can be fully represented by its support function. We show that the estimated support function converges to a tight Gaussian process as the sample size increases, and then express policy-relevant hypotheses as restrictions on the support function to construct valid test statistics.