  Group fairness is achieved by equalising prediction distributions between
protected sub-populations; individual fairness requires treating similar
individuals alike. These two objectives, however, are incompatible when a
scoring model is calibrated through discontinuous probability functions, where
individuals can be randomly assigned an outcome determined by a fixed
probability. This procedure may provide two similar individuals from the same
protected group with classification odds that are disparately different -- a
clear violation of individual fairness. Assigning unique odds to each protected
sub-population may also prevent members of one sub-population from ever
receiving equal chances of a positive outcome to another, which we argue is
another type of unfairness called individual odds. We reconcile all this by
constructing continuous probability functions between group thresholds that are
constrained by their Lipschitz constant. Our solution preserves the model's
predictive power, individual fairness and robustness while ensuring group
fairness.
