Forecast Aggregation

Abstract

Bayesian experts with a common prior that are exposed to different evidence possibly make contradicting probabilistic forecasts. A policy maker who receives the forecasts must aggregate them in the best way possible. This is a challenge whenever the policy maker is not familiar with the prior nor the model and evidence available to the experts. We propose a model of non-Bayesian forecast aggregation and adapt the notion of regret as a means for evaluating the policy maker's performance. Whenever experts are Blackwell ordered taking a weighted average of the two forecasts, the weight of which is proportional to its precision (the reciprocal of the variance), is optimal. The resulting regret is equal 1/8(5√ 5-11) approx 0.0225425, which is 3 to 4 times better than naive approaches such as choosing one expert at random or taking the non-weighted average.