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, especially because it is often unclear whether reducing this impact is possible without sacrificing other important 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 on the accuracy of its predictions.

翻译：许多组织使用的算法具有差异性影响，即算法产生的收益或损害不成比例地落在某些社会群体上。解决算法的差异性影响可能具有挑战性，特别是因为通常不清楚在不牺牲组织其他重要目标（如准确性或利润）的前提下，是否有可能减少这种影响。确立算法在多重标准下的可改进性兼具理论与现实意义：在许多情境下，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，则可能被允许。问题在于政策制定者如何从形式上证实或反驳这种必要性抗辩。本文提出一个计量经济学框架，用于检验以下假设：在算法公平性方面实现改进而不损害其他预设目标是可能的。我们提出的检验方法易于实施，可适用于算法空间上的任何外生约束。我们证明了该检验的大样本有效性及一致性，并通过评估Obermeyer等人2019年最初研究的医疗算法来展示其实际应用。在该应用中，我们拒绝了原假设（即在不降低预测准确性的前提下减少算法差异性影响是不可能的）。