A growing body of literature in fairness-aware ML (fairML) aspires to mitigate machine learning (ML)-related unfairness in automated decision-making (ADM) by defining metrics that measure fairness of an ML model and by proposing methods that ensure that trained ML models achieve low values in those metrics. However, the underlying concept of fairness, i.e., the question of what fairness is, is rarely discussed, leaving a considerable gap between centuries of philosophical discussion and recent adoption of the concept in the ML community. In this work, we try to bridge this gap by formalizing a consistent concept of fairness and by translating the philosophical considerations into a formal framework for the training and evaluation of ML models in ADM systems. We derive that fairness problems can already arise without the presence of protected attributes (PAs), pointing out that fairness and predictive performance are not irreconcilable counterparts, but rather that the latter is necessary to achieve the former. Moreover, we argue why and how causal considerations are necessary when assessing fairness in the presence of PAs by proposing a fictitious, normatively desired (FiND) world where the PAs have no causal effects. In practice, this FiND world must be approximated by a warped world, for which the causal effects of the PAs must be removed from the real-world data. Eventually, we achieve greater linguistic clarity for the discussion of fairML. We propose first algorithms for practical applications and present illustrative experiments on COMPAS data.

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