When is the crowd wise?

 

Consider a setting where many individuals make predictions over the (unknown) state of nature based on signals they receive independently. An outside Bayesian observer, familiar with the common prior shared by the individuals, can aggregate this information and identify correctly the actual state of nature. However, what if the aggregator is ignorant with respect to the common prior? An information structure is said to be identifiable whenever the ignorant aggregator can identify the state. We characterize the set of identifiable information structures and also unveil the fragility of information aggregation in markets with respect to the common prior assumption.

For non-identifiable information structures, aggregator cannot identify the state, thus we turn to the analysis of a setting where aggregtor produces a subjective forecast about the state. We evaluate aggregtor's performance according to the regret: the difference in the accuracies of aggretor's forecast and the forecast of the Baysian aggregtor. We show that for large number of experts an ignorant aggregator expert performs poorly, however for two experts aggregtor can perform surprisingly 

well, and produce forecasts that are very close to optimal Bayesian aggregtion.

 

Based on joint works with Itai Arieli and Rann Smorodinsky.