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)).

We propose an online form of the cake cutting problem. This models situations where agents arrive and depart during the process of dividing a resource. We show that well known fair division procedures like cut-and-choose and the Dubins-Spanier moving knife procedure can be adapted to apply to such online problems. We propose some fairness properties that online cake cutting procedures can possess like online forms of proportionality and envy-freeness. We also consider the impact of collusion between agents. Finally, we study theoretically and empirically the competitive ratio of these online cake cutting procedures. Based on its resistance to collusion, and its good performance in practice, our results favour the online version of the cut-and-choose procedure over the online version of the moving knife procedure.