Normal Bayesian Dialogues

Abstract Several individuals have the same prior distribution of a parameter W; each makes an observation, then reveals parts of his posterior distribution. All individuals now update, taking due account of the inferences that have led the others to their announcements. The process is iterated. For the case in which W is a multivariate normal mean vector it is shown inter alia that (a) the parts of individuals' distributions that are iteratively revealed converge to a consensus that embodies all private information; (b) under stated conditions the parts withheld also converge to such a consensus; and (c) the speed of convergence is characterized.