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.
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