  Causal reasoning, in particular, counterfactual reasoning plays a central
role in testing for discrimination. Counterfactual reasoning materializes when
testing for discrimination, what is known as the counterfactual model of
discrimination, when we compare the discrimination comparator with the
discrimination complainant, where the comparator is a similar (or similarly
situated) profile to that of the complainant used for testing the
discrimination claim of the complainant. In this paper, we revisit the
comparator by presenting two kinds of comparators based on the sort of causal
intervention we want to represent. We present the ceteris paribus and the
mutatis mutandis comparator, where the former is the standard and the latter is
a new kind of comparator. We argue for the use of the mutatis mutandis
comparator, which is built on the fairness given the difference notion, for
testing future algorithmic discrimination cases.
