Addressing the problem of fairness is crucial to safely use machine learning
algorithms to support decisions with a critical impact on people's lives such
as job hiring, child maltreatment, disease diagnosis, loan granting, etc.
Several notions of fairness have been defined and examined in the past decade,
such as, statistical parity and equalized odds. The most recent fairness
notions, however, are causal-based and reflect the now widely accepted idea
that using causality is necessary to appropriately address the problem of
fairness. This paper examines an exhaustive list of causal-based fairness
notions, in particular their applicability in real-world scenarios. As the
majority of causal-based fairness notions are defined in terms of
non-observable quantities (e.g. interventions and counterfactuals), their
applicability depends heavily on the identifiability of those quantities from
observational data. In this paper, we compile the most relevant identifiability
criteria for the problem of fairness from the extensive literature on
identifiability theory. These criteria are then used to decide about the
applicability of causal-based fairness notions in concrete discrimination
scenarios