Algorithm Design: A Fairness-Accuracy Frontier

Algorithm designers increasingly care not only about accuracy but also about fairness across predefined groups. We study the trade-off between these objectives and characterize it by a fairness-accuracy frontier: the set of outcomes that cannot be simultaneously improved in both dimensions. The shape of this frontier is governed by a simple property of the inputs, which we call group skew. In particular, reducing accuracy for both groups to increase fairness is justified if and only if inputs are group skewed. We also study an information design problem in which a designer regulates inputs but another agent chooses the algorithm. We show that, when inputs are not group skewed, banning group identity or other informative inputs is strictly suboptimal.