Recent interest in codifying fairness in Automated Decision Systems (ADS) has resulted in a wide range of formulations of what it means for an algorithmic system to be fair. Most of these propositions are inspired by, but inadequately grounded in, political philosophy scholarship. This paper aims to correct that deficit. We introduce a taxonomy of fairness ideals using doctrines of Equality of Opportunity (EOP) from political philosophy, clarifying their conceptions in philosophy and the proposed codification in fair machine learning. We arrange these fairness ideals onto an EOP spectrum, which serves as a useful frame to guide the design of a fair ADS in a given context. We use our fairness-as-EOP framework to re-interpret the impossibility results from a philosophical perspective, as the in-compatibility between different value systems, and demonstrate the utility of the framework with several real-world and hypothetical examples. Through our EOP-framework we hope to answer what it means for an ADS to be fair from a moral and political philosophy standpoint, and to pave the way for similar scholarship from ethics and legal experts.
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