A clarification of the nuances in the fairness metrics landscape

In recent years, the problem of addressing fairness in machine learning (ML) and automatic decision making has attracted a lot of attention in the scientific communities dealing with artificial intelligence. A plethora of different definitions of fairness in ML have been proposed, that consider different notions of what is a "fair decision" in situations impacting individuals in the population. The precise differences, implications and "orthogonality" between these notions have not yet been fully analyzed in the literature. In this work, we try to make some order out of this zoo of definitions.