  Efforts to promote equitable public policy with algorithms appear to be
fundamentally constrained by the "impossibility of fairness" (an
incompatibility between mathematical definitions of fairness). This technical
limitation raises a central question about algorithmic fairness: How can
computer scientists and policymakers support equitable policy reforms with
algorithms? In this article, I argue that promoting justice with algorithms
requires reforming the methodology of algorithmic fairness. First, I diagnose
the problems of the current methodology for algorithmic fairness, which I call
"formal algorithmic fairness." Because formal algorithmic fairness restricts
analysis to isolated decision-making procedures, it leads to the impossibility
of fairness and to models that exacerbate oppression despite appearing "fair."
Second, I draw on theories of substantive equality from law and philosophy to
propose an alternative methodology, which I call "substantive algorithmic
fairness." Because substantive algorithmic fairness takes a more expansive
scope of analysis, it enables an escape from the impossibility of fairness and
provides a rigorous guide for alleviating injustice with algorithms. In sum,
substantive algorithmic fairness presents a new direction for algorithmic
fairness: away from formal mathematical models of "fair" decision-making and
toward substantive evaluations of whether and how algorithms can promote
justice in practice.
