Forecast aggregation

Just the other day we were planning our weekend activities and looked at the forecast for the weather in Tel-Aviv on Friday, January 27. In particular what interested us was the probability for rain (precipitation). Accuweather's precipitation forecast was 77% while Yahoo! had a forecast of 60% and the Weather Channel was at 90% (all three screenshots are provided in the appendix). It was unclear to us how to aggregate these confliicting forecasts although we knew all three were reputable sources and were using sound weather models and reliable data. Our dilemma was not unique. In fact many of us face such con.icting sources of advice from experts on a daily basis. Forecasts from reliable pollsters on the outcome of the presidential elections, medical prognosis from trusted physicians, investment advice from experienced financial pundits and more. This challenge is in fact the crux of the working of many governing bodies. In the political arena we often see ministers and legislators that are chosen electives and must decide on critical issues and policies with any subject ma.er expertise. Such public electives dictate health care policies, decide on military development and deployment, financial regulation and so on without prior medical / military / financial background. To do so they reach out to experts advices whose information they should aggregate. We consider a model with three agents. .ere are two experts who provide a forecast about the probability over some given future event. .e experts agree on the prior probability, both receive some common information, however, one of them is be.er informed and has access to additional private information1. Both agents form posterior forecasts vis-A-vis Bayes rule. .e two forecasts are shared with the third player, the policy maker (PM), who now aggregates them to form his own subjective forecast. Unfortunately, the identity of the be.er informed expert is not known to the PM.