  Fair inference in supervised learning is an important and active area of
research, yielding a range of useful methods to assess and account for fairness
criteria when predicting ground truth targets. As shown in recent work,
however, when target labels are error-prone, potential prediction unfairness
can arise from measurement error. In this paper, we show that, when an
error-prone proxy target is used, existing methods to assess and calibrate
fairness criteria do not extend to the true target variable of interest. To
remedy this problem, we suggest a framework resulting from the combination of
two existing literatures: fair ML methods, such as those found in the
counterfactual fairness literature on the one hand, and, on the other,
measurement models found in the statistical literature. We discuss these
approaches and their connection resulting in our framework. In a healthcare
decision problem, we find that using a latent variable model to account for
measurement error removes the unfairness detected previously.
