  The definition and implementation of fairness in automated decisions has been
extensively studied by the research community. Yet, there hides fallacious
reasoning, misleading assertions, and questionable practices at the foundations
of the current fair machine learning paradigm. Those flaws are the result of a
failure to understand that the trade-off between statistically accurate
outcomes and group similar outcomes exists as independent, external constraint
rather than as a subjective manifestation as has been commonly argued. First,
we explain that there is only one conception of fairness present in the fair
machine learning literature: group similarity of outcomes based on a sensitive
attribute where the similarity benefits an underprivileged group. Second, we
show that there is, in fact, a trade-off between statistically accurate
outcomes and group similar outcomes in any data setting where group disparities
exist, and that the trade-off presents an existential threat to the equitable,
fair machine learning approach. Third, we introduce a proof-of-concept
evaluation to aid researchers and designers in understanding the relationship
between statistically accurate outcomes and group similar outcomes. Finally,
suggestions for future work aimed at data scientists, legal scholars, and data
ethicists that utilize the conceptual and experimental framework described
throughout this article are provided.
