  AI-driven decision-making can lead to discrimination against certain
individuals or social groups based on protected characteristics/attributes such
as race, gender, or age. The domain of fairness-aware machine learning focuses
on methods and algorithms for understanding, mitigating, and accounting for
bias in AI/ML models. Still, thus far, the vast majority of the proposed
methods assess fairness based on a single protected attribute, e.g. only gender
or race. In reality, though, human identities are multi-dimensional, and
discrimination can occur based on more than one protected characteristic,
leading to the so-called ``multi-dimensional discrimination'' or
``multi-dimensional fairness'' problem. While well-elaborated in legal
literature, the multi-dimensionality of discrimination is less explored in the
machine learning community. Recent approaches in this direction mainly follow
the so-called intersectional fairness definition from the legal domain, whereas
other notions like additive and sequential discrimination are less studied or
not considered thus far. In this work, we overview the different definitions of
multi-dimensional discrimination/fairness in the legal domain as well as how
they have been transferred/ operationalized (if) in the fairness-aware machine
learning domain. By juxtaposing these two domains, we draw the connections,
identify the limitations, and point out open research directions.
