  The field of fair machine learning aims to ensure that decisions guided by
algorithms are equitable. Over the last decade, several formal, mathematical
definitions of fairness have gained prominence. Here we first assemble and
categorize these definitions into two broad families: (1) those that constrain
the effects of decisions on disparities; and (2) those that constrain the
effects of legally protected characteristics, like race and gender, on
decisions. We then show, analytically and empirically, that both families of
definitions typically result in strongly Pareto dominated decision policies.
For example, in the case of college admissions, adhering to popular formal
conceptions of fairness would simultaneously result in lower student-body
diversity and a less academically prepared class, relative to what one could
achieve by explicitly tailoring admissions policies to achieve desired
outcomes. In this sense, requiring that these fairness definitions hold can,
perversely, harm the very groups they were designed to protect. In contrast to
axiomatic notions of fairness, we argue that the equitable design of algorithms
requires grappling with their context-specific consequences, akin to the
equitable design of policy. We conclude by listing several open challenges in
fair machine learning and offering strategies to ensure algorithms are better
aligned with policy goals.
