Normal Bayesian Dialogues

Michael Bacharach

49 citations0/0 files storedJournal of the American Statistical Association

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Game Theory and Applications Probability and Statistical Research Statistical Methods and Bayesian Inference

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.

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References

1976Agreeing to Disagree 1976ON THE EFFICIENCY OF COMPETITIVE STOCK MARKETS WHERE TRADES HAVE DIVERSE INFORMATION 1959Consensus of Subjective Probabilities: The Pari-Mutuel Method 1961The Opinion Pool 1977Combining Expert Judgments: A Bayesian Approach 1964EXTERNALLY BAYESIAN GROUPS 1979A Model of the Jury Decision Process

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1984Asymptotic agreement among communicating decisionmakers 2012Five examples of assessment and expression of measurement uncertainty

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