Effectiveness of Equalized Odds for Fair Classification under Imperfect Group Information
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Most approaches for ensuring or improving a model's fairness with respect to a protected attribute (such as race or gender) assume access to the true value of the protected attribute for every data point. In many scenarios, however, perfect knowledge of the protected attribute is unrealistic. In this paper, we ask to what extent fairness interventions can be effective even with imperfect information about the protected attribute. In particular, we study this question in the context of the prominent equalized odds method of Hardt et al. (2016). We claim that as long as the perturbation of the protected attribute is somewhat moderate, one should still run equalized odds if one would run it knowing the true protected attribute: the bias of the classifier that we obtain using the perturbed attribute is smaller than the bias of the original classifier, and its error is not larger than the error of the equalized odds classifier obtained when working with the true protected attribute.
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