Algorithm fairness has started to attract the attention of researchers in AI, Software Engineering and Law communities, with more than twenty different notions of fairness proposed in the last few years. Yet, there is no clear agreement on which definition to apply in each situation. Moreover, the detailed differences between multiple definitions are difficult to grasp. To address this issue, this paper collects the most prominent definitions of fairness for the algorithmic classification problem, explains the rationale behind these definitions, and demonstrates each of them on a single unifying case-study. Our analysis intuitively explains why the same case can be considered fair according to some definitions and unfair according to others.
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