  Recent work has identified a number of formally incompatible operational
measures for the unfairness of a machine learning (ML) system. As these
measures all capture intuitively desirable aspects of a fair system, choosing
"the one true" measure is not possible, and instead a reasonable approach is to
minimize a weighted combination of measures. However, this simply raises the
question of how to choose the weights. Here, we formulate Legally Grounded
Fairness Objectives (LGFO), which uses signals from the legal system to
non-arbitrarily measure the social cost of a specific degree of unfairness. The
LGFO is the expected damages under a putative lawsuit that might be awarded to
those who were wrongly classified, in the sense that the ML system made a
decision different to that which would have be made under the court's preferred
measure. Notably, the two quantities necessary to compute the LGFO, the court's
preferences about fairness measures, and the expected damages, are unknown but
well-defined, and can be estimated by legal advice. Further, as the damages
awarded by the legal system are designed to measure and compensate for the harm
caused to an individual by an unfair classification, the LGFO aligns closely
with society's estimate of the social cost.
