  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.
