Is the pool of fair predictive algorithms fair? It depends, naturally, on both the criteria of fairness and on how we pool. We catalog the relevant facts for some of the most prominent statistical criteria of algorithmic fairness and the dominant approaches to pooling forecasts: linear, geometric, and multiplicative. Only linear pooling, a format at the heart of ensemble methods, preserves any of the central criteria we consider. Drawing on work in the social sciences and social epistemology on the theoretical (...) foundations of the wisdom of crowds, we explain how our observations present an exception to the general trend of finding tradeoffs between the accuracy and fairness of forecasts. (shrink)

We reply to Eva's comment on our "New Possibilities for Fair Algorithms," comparing and contrasting our Spanning criterion with his suggested Spacing criterion.