Most approaches aiming to ensure a model's fairness with respect to a
protected attribute (such as gender or race) assume to know the true value of
the attribute for every data point. In this paper, we ask to what extent
fairness interventions can be effective even when only imperfect information
about the protected attribute is available. In particular, we study the
prominent equalized odds postprocessing method of Hardt et al. (2016) under a
perturbation of the attribute. We identify conditions on the perturbation that
guarantee that the bias of a classifier is reduced even by running equalized
odds with the perturbed attribute. We also study the error of the resulting
classifier. We empirically observe that under our identified conditions most
often the error does not suffer from a perturbation of the protected attribute.
For a special case, we formally prove this observation to be true.

本文研究了在只有保护属性的不完美信息的情况下，公平干预是否仍然可行。我们特别研究了 Hardt 等人（2016）的等化几率后处理方法，证明了在属性扰动的情况下，只要符合我们所确定的条件，即使运行等化几率，分类器的偏差也会降低。我们还研究了所得分类器的误差，并实证观察到，在我们确定的条件下，大多数情况下误差不会因保护属性的扰动而受到影响。