Common Knowledge of Summary Statistics
Consider a group of people who are asked to oﬀer their opinions on some issue. “Business conﬁdence” surveys are an example: groups of businessmen are often asked for their predictions of economic indicators such as growth or inflation rates. Each member of the group makes a prediction based on his or her private information, and the average prediction is then publicly announced. If the members of the group are then allowed to revise their opinions, based on whatever information they glean from the public announcement, is there any tendency for the opinions in the group to converge on a common, consensus opinion? In this note we show that under certain conditions the answer to this question is yes.
Brandenburger, Adam and Geanakoplos, John, "Common Knowledge of Summary Statistics" (1988). Cowles Foundation Discussion Papers. 1107.