  We present a simple and versatile framework for evaluating ranked lists in
terms of group fairness and relevance, where the groups (i.e., possible
attribute values) can be either nominal or ordinal in nature. First, we
demonstrate that, if the attribute set is binary, our framework can easily
quantify the overall polarity of each ranked list. Second, by utilising an
existing diversified search test collection and treating each intent as an
attribute value, we demonstrate that our framework can handle soft group
membership, and that our group fairness measures are highly correlated with
both adhoc IR and diversified IR measures under this setting. Third, we
demonstrate how our framework can quantify intersectional group fairness based
on multiple attribute sets. We also show that the similarity function for
comparing the achieved and target distributions over the attribute values
should be chosen carefully.
