  We introduce leave-one-out unfairness, which characterizes how likely a
model's prediction for an individual will change due to the inclusion or
removal of a single other person in the model's training data. Leave-one-out
unfairness appeals to the idea that fair decisions are not arbitrary: they
should not be based on the chance event of any one person's inclusion in the
training data. Leave-one-out unfairness is closely related to algorithmic
stability, but it focuses on the consistency of an individual point's
prediction outcome over unit changes to the training data, rather than the
error of the model in aggregate. Beyond formalizing leave-one-out unfairness,
we characterize the extent to which deep models behave leave-one-out unfairly
on real data, including in cases where the generalization error is small.
Further, we demonstrate that adversarial training and randomized smoothing
techniques have opposite effects on leave-one-out fairness, which sheds light
on the relationships between robustness, memorization, individual fairness, and
leave-one-out fairness in deep models. Finally, we discuss salient practical
applications that may be negatively affected by leave-one-out unfairness.
