We map the recently proposed notions of algorithmic fairness to economic
models of Equality of opportunity (EOP)---an extensively studied ideal of
fairness in political philosophy. We formally show that through our conceptual
mapping, many existing definition of algorithmic fairness, such as predictive
value parity and equality of odds, can be interpreted as special cases of EOP.
In this respect, our work serves as a unifying moral framework for
understanding existing notions of algorithmic fairness. Most importantly, this
framework allows us to explicitly spell out the moral assumptions underlying
each notion of fairness, and interpret recent fairness impossibility results in
a new light. Last but not least and inspired by luck egalitarian models of EOP,
we propose a new family of measures for algorithmic fairness. We illustrate our
proposal empirically and show that employing a measure of algorithmic
(un)fairness when its underlying moral assumptions are not satisfied, can have
devastating consequences for the disadvantaged group's welfare