  While there has been a flurry of research in algorithmic fairness, what is
less recognized is that modern antidiscrimination law may prohibit the adoption
of such techniques. We make three contributions. First, we discuss how such
approaches will likely be deemed "algorithmic affirmative action," posing
serious legal risks of violating equal protection, particularly under the
higher education jurisprudence. Such cases have increasingly turned toward
anticlassification, demanding "individualized consideration" and barring
formal, quantitative weights for race regardless of purpose. This case law is
hence fundamentally incompatible with fairness in machine learning. Second, we
argue that the government-contracting cases offer an alternative grounding for
algorithmic fairness, as these cases permit explicit and quantitative
race-based remedies based on historical discrimination by the actor. Third,
while limited, this doctrinal approach also guides the future of algorithmic
fairness, mandating that adjustments be calibrated to the entity's
responsibility for historical discrimination causing present-day disparities.
The contractor cases provide a legally viable path for algorithmic fairness
under current constitutional doctrine but call for more research at the
intersection of algorithmic fairness and causal inference to ensure that bias
mitigation is tailored to specific causes and mechanisms of bias.
