From Proper Scoring Rules to Max-Min Optimal Forecast Aggregation

Abstract

There are many ways to elicit honest probabilistic forecasts from experts. Once those forecasts are elicited, there are many ways to aggregate them into a single forecast. Should the choice of elicitation method inform the choice of aggregation method? In “From Proper Scoring Rules to Max-Min Optimal Forecast Aggregation,” Neyman and Roughgarden establish a connection between these two problems. To every elicitation method they associate the aggregation method that improves as much as possible upon the forecast of a randomly chosen expert, in the worst case. This association maps the two most widely used elicitation methods (Brier and logarithmic scoring) to the two most well-known aggregation methods (linear and logarithmic pooling). The authors show a number of interesting properties of this connection, including a natural axiomatization of aggregation methods obtained through the connection, as well as an algorithm for efficient no-regret learning of expert weights.