We study fairness-accuracy tradeoffs when a single predictive model must serve multiple demographic groups. A useful tool for understanding this tradeoff is the fairness-accuracy (FA) Pareto frontier, which characterizes the set of models that cannot be improved in either fairness or accuracy without worsening the other. While characterizing the FA frontier requires full knowledge of the data distribution, we focus on the finite-sample regime, quantifying how well a designer can approximate any point on the frontier from limited data and bounding the worst-case gap. In particular, we derive worst-case-optimal estimators that depend on the designer's knowledge of the covariate distribution. For each estimator, we characterize how finite-sample effects asymmetrically impact each group's welfare and identify optimal sample allocation strategies. Finally, we provide uniform finite-sample bounds for the entire FA frontier, yielding confidence bands that quantify the reliability of welfare comparisons across alternative fairness-accuracy tradeoffs.

翻译：本文研究当单一预测模型需服务于多个群体时，公平性与准确性之间的权衡关系。理解这种权衡的关键工具是公平性-准确性（FA）帕累托前沿，该前沿刻画了在公平性或准确性任一维度上无法继续改进（而不损害另一维度）的模型集合。虽然完整刻画FA前沿需要掌握数据分布的全部信息，但本文聚焦有限样本场景，量化设计者如何通过有限数据逼近前沿上的任意点，并给出最坏情况下的误差上界。特别地，我们推导了取决于设计者对协变量分布认知的最坏情况最优估计量。针对每个估计量，我们刻画了有限样本效应对不同群体福利的非对称影响，并确定了最优样本分配策略。最后，我们为整个FA前沿提供了统一的有限样本界，构建了可量化不同公平性-准确性权衡方案间福利比较可靠性的置信带。