Inference for an Algorithmic Fairness-Accuracy Frontier
Abstract
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 lia:lu:mu23 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.
keywords:
PRT18PRT \endlocaldefs
This draft: February 2024. We thank seminar participants at Cornell University and especially José Montiel-Olea for helpful comments.
1 Introduction
Algorithms are increasingly used in many aspects of life, often to guide or support high stake decisions. For example, algorithms are used to predict criminal re-offense risk, and this prediction feeds into the determination of which defendants should receive bail; to predict a job market candidate’s productivity, and this prediction feeds into hiring decisions; to predict an applicant’s likelihood of default on a loan, and this prediction feeds into the decision of who should receive the loan; to predict a student’s performance in college, and this prediction feeds into the decision of which students should be admitted to college; and to assign a health risk score to a patient, and this score feeds into the decision of which patients to treat. Yet, a growing body of literature documents that algorithms may exhibit bias against legally protected subgroups of the population, both in terms of their ability to make correct predictions, and in the type of decisions that they lead to