  Algorithmic fairness is receiving significant attention in the academic and
broader literature due to the increasing use of predictive algorithms,
including those based on artificial intelligence. One benefit of this trend is
that algorithm designers and users have a growing set of fairness measures to
choose from. However, this choice comes with the challenge of identifying how
the different fairness measures relate to one another, as well as the extent to
which they are compatible or mutually exclusive. We describe some of the most
widely used fairness metrics using a common mathematical framework and present
new results on the relationships among them. The results presented herein can
help place both specialists and non-specialists in a better position to
identify the metric best suited for their application and goals.
