The Wisdom of the Crowd and Higher-Order Beliefs

The classic wisdom-of-the-crowd problem asks how a principal can "aggregate" information about the unknown state of the world from agents without understanding the information structure among them. We propose a new simple procedure "\emph{population mean based aggregation}" to achieve this goal. It only requires eliciting agents' beliefs about the state, and also eliciting some agents' expectations of the average belief in the population. We show that this procedure fully aggregates information: in an infinite population, it always infers the true state of the world. The procedure can accommodate correlation in agents' information, misspecified beliefs, any finite number of possible states of the world, and only requires very weak assumptions on the information structure.