Many organizations use algorithms that have a disparate impact, i.e., the benefits or harms of the algorithm fall disproportionately on certain social groups. Addressing an algorithm's disparate impact can be challenging, however, because it is often unclear whether it is possible to reduce this impact without sacrificing other objectives of the organization, 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 be applied under any exogenous constraint on the algorithm space. We establish the large-sample validity and consistency of our test, and illustrate its practical application by evaluating a healthcare algorithm originally considered by Obermeyer et al. (2019). In this application, we reject the null hypothesis that it is not possible to reduce the algorithm's disparate impact without compromising the accuracy of its predictions.

翻译：许多组织使用的算法会产生差异性影响，即算法的收益或损害不成比例地落在某些社会群体上。然而，解决算法的差异性影响可能具有挑战性，因为通常不清楚是否可以在不牺牲组织其他目标（如准确性或利润）的情况下减少这种影响。建立算法在多个标准下的可改进性具有理论和实践意义：在许多情况下，根据美国联邦法律本应被禁止的差异性影响，若为实现合法商业利益所必需，则是允许的。问题在于政策制定者如何正式证实或反驳这种"必要性"辩护。在本文中，我们提供了一个计量经济学框架，用于检验以下假设：可以在不损害其他预设目标的情况下改进算法的公平性。我们提出的检验方法易于实施，并且可应用于算法空间的任何外生约束条件下。我们证明了该检验的大样本有效性和一致性，并通过评估Obermeyer等人（2019）最初研究的医疗保健算法来说明其实际应用。在该应用中，我们拒绝了原假设，即在不损害预测准确性的情况下不可能减少算法的差异性影响。