  The field of algorithmic fairness has rapidly emerged over the past 15 years
as algorithms have become ubiquitous in everyday lives. Algorithmic fairness
traditionally considers statistical notions of fairness algorithms might
satisfy in decisions based on noisy data. We first show that these are
theoretically disconnected from welfare-based notions of fairness. We then
discuss two individual welfare-based notions of fairness, envy freeness and
prejudice freeness, and establish conditions under which they are equivalent to
error rate balance and predictive parity, respectively. We discuss the
implications of these findings in light of the recently discovered
impossibility theorem in algorithmic fairness (Kleinberg, Mullainathan, &
Raghavan (2016), Chouldechova (2017)).
