  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.
