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Although existing work draws attention to a range of obstacles in realizing fair AI, the field lacks an account that emphasizes how these worries hang together in a systematic way. Furthermore, a review of the fair AI and philosophical literature demonstrates the unsuitability of ‘treat like cases alike’ and other intuitive notions as conceptions of fairness. That review then generates three desiderata for a replacement conception of fairness valuable to AI research: (1) It must provide a meta-theory for understanding tradeoffs, entailing that it must be flexible enough to capture diverse species of objection to decisions. (2) It must not appeal to an impartial perspective (neutral data, objective data, or final arbiter.) (3) It must foreground the way in which judgments of fairness are sensitive to context, i.e., to historical and institutional states of affairs. We argue that a conception of fairness as appropriate concession in the historical iteration of institutional decisions meets these three desiderata. On the basis of this definition, we organize the insights of commentators into a process-structure map of the ethical territory that we hope will bring clarity to computer scientists and ethicists analyzing Fair AI while clearing some ground for further technical and philosophical work. [ABSTRACT FROM AUTHOR]