Sample Complexity of Forecast Aggregation

We consider a Bayesian forecast aggregation model where n experts, after observing private signals about an unknown binary event, report th eir posterior beliefs about the event to a principal, who then aggregates the repor ts into a single prediction for the event. The signals of the experts and the outcome of the event follow a joint distribution that is unknown to the principal, but th e principal has access to i.i.d. "samples" from the distribution, where each sampl e is a tuple of the experts' reports (not signals) and the realization of the even t. Using these samples, the principal aims to find an ε -approximately optimal aggregator, where optimal-ity is measured in terms of the expected squared distance bet ween the aggregated prediction and the realization of the event.