  In this work we use Equal Oppportunity (EO) doctrines from political
philosophy to make explicit the normative judgements embedded in different
conceptions of algorithmic fairness. We contrast formal EO approaches that
narrowly focus on fair contests at discrete decision points, with substantive
EO doctrines that look at people's fair life chances more holistically over the
course of a lifetime. We use this taxonomy to provide a moral interpretation of
the impossibility results as the incompatibility between different conceptions
of a fair contest -- foward-looking versus backward-looking -- when people do
not have fair life chances. We use this result to motivate substantive
conceptions of algorithmic fairness and outline two plausible procedures based
on the luck-egalitarian doctrine of EO, and Rawls's principle of fair equality
of opportunity.
