  Individual fairness, proposed by Dwork et al., is a fairness measure that is
supposed to prevent the unfair treatment of individuals on the subgroup level,
and to overcome the problem that group fairness measures are susceptible to
manipulation, or gerrymandering. The goal of the present paper is to explore
the extent to which it is possible to gerrymander individual fairness itself.
It will be proved that gerrymandering individual fairness in the context of
predicting scores is possible. It will also be argued that individual fairness
provides a very weak notion of fairness for some choices of feature space and
metric. Finally, it will be discussed how the general idea of individual
fairness may be preserved by formulating a notion of fairness that allows us to
overcome some of the problems with individual fairness identified here and
elsewhere.
