Robust forecast aggregation in large and small markets
In large markets, failure to aggregate information often attributed to strategic behavior on the part of the agents that have private information or to the lack of their expressive power. Using a model of forecast aggregation we demonstrate an additional reason for such failure - the lack of a common prior. In particular we show that observing posterior probabilities reported truthfully by large number of Bayesian naive experts is insufficient for making accurate predictions whenever the aggregator is not privy to the common prior of the experts. In fact, such an aggregator will perform as poor as someone who has seen none of these forecasts.
On the other hand, in small markets, in particular in the case of two experts aggregetor may provide forecasts that are very close to optimal without having any information beside expert's forecasts.
Based on joint works with Itai Arieli and Rann Smorodinsky.