  We turn the definition of individual fairness on its head---rather than
ascertaining the fairness of a model given a predetermined metric, we find a
metric for a given model that satisfies individual fairness. This can
facilitate the discussion on the fairness of a model, addressing the issue that
it may be difficult to specify a priori a suitable metric. Our contributions
are twofold: First, we introduce the definition of a minimal metric and
characterize the behavior of models in terms of minimal metrics. Second, for
more complicated models, we apply the mechanism of randomized smoothing from
adversarial robustness to make them individually fair under a given weighted
$L^p$ metric. Our experiments show that adapting the minimal metrics of linear
models to more complicated neural networks can lead to meaningful and
interpretable fairness guarantees at little cost to utility.
