  Across machine learning (ML) sub-disciplines researchers make mathematical
assumptions to facilitate proof-writing. While such assumptions are necessary
for providing mathematical guarantees for how algorithms behave, they also
necessarily limit the applicability of these algorithms to different problem
settings. This practice is known--in fact, obvious--and accepted in ML
research. However, similar attention is not paid to the normative assumptions
that ground this work. I argue such assumptions are equally as important,
especially in areas of ML with clear social impact, such as fairness. This is
because, similar to how mathematical assumptions constrain applicability,
normative assumptions also limit algorithm applicability to certain problem
domains. I show that, in existing papers published in top venues, once
normative assumptions are clarified, it is often possible to get unclear or
contradictory results. While the mathematical assumptions and results are
sound, the implicit normative assumptions and accompanying normative results
contraindicate using these methods in practical fairness applications.
