Machine Learning (ML) based predictive systems are increasingly used to support decisions with a critical impact on individuals' lives such as college admission, job hiring, child custody, criminal risk assessment, etc. As a result, fairness emerged as an important requirement to guarantee that ML predictive systems do not discriminate against specific individuals or entire sub-populations, in particular, minorities. Given the inherent subjectivity of viewing the concept of fairness, several notions of fairness have been introduced in the literature. This paper is a survey of fairness notions that, unlike other surveys in the literature, addresses the question of "which notion of fairness is most suited to a given real-world scenario and why?". Our attempt to answer this question consists in (1) identifying the set of fairness-related characteristics of the real-world scenario at hand, (2) analyzing the behavior of each fairness notion, and then (3) fitting these two elements to recommend the most suitable fairness notion in every specific setup. The results are summarized in a decision diagram that can be used by practitioners and policy makers to navigate the relatively large catalogue of ML fairness notions.

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.

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Machine learning algorithms can produce biased outcome/prediction, typically, against minorities and underrepresented sub-populations. Therefore, fairness is emerging as an important requirement for the safe application of machine learning based technologies. The most commonly used fairness notions (e.g. statistical parity, equalized odds, predictive parity, etc.) are observational and rely on mere correlation between variables. These notions fail to identify bias in case of statistical anomalies such as Simpson's or Berkson's paradoxes. Causalitybased fairness notions (e.g. counterfactual fairness, no-proxy discrimination, etc.) are immune to such anomalies and hence more reliable to assess fairness. The problem of causality-based fairness notions, however, is that they are defined in terms of quantities (e.g. causal, counterfactual, and path-specific effects) that are not always measurable. This is known as the identifiability problem and is the topic of a large body of work in the causal inference literature. The first contribution of this paper is a compilation of the major identifiability results which are of particular relevance for machine learning fairness. To the best of our knowledge, no previous work in the field of ML fairness or causal inference provides such systemization of knowledge. The second contribution is more general and addresses the main problem of using causality in machine learning, that is, how to extract causal knowledge from observational data in real scenarios. This paper shows how this can be achieved using identifiability.