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Common Knowledge and Consensus with Aggregate Statistics

McKelvey, Richard D. and Page, Talbot (1984) Common Knowledge and Consensus with Aggregate Statistics. Social Science Working Paper, 493. California Institute of Technology , Pasadena, CA. (Unpublished)

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We prove that if n individuals start with the same prior over a probability space, and then each observe private information that for a class of admissible statistics, if a statistic of their posterior probabilities of an event becomes common knowledge, then everyone's posterior probabilities must be the same. The class of admissible statistics includes any statistic which is an invertible function of a stochastically monotone function. We also prove that if information partitions are finite, an iterative procedure of public announcement of the statistic—where the statistic is publicly announced and then individuals recompute posterior probabilities based on their previous information plus the announced value of the statistic—converges in a finite number of steps to the common knowledge situation described above. The result has applications to Delphi type processes for probability assessment, and to economic models in which private information becomes incorporated into an aggregate, publicly observed statistic such as a price or quantity in a market.

Item Type:Report or Paper (Working Paper)
Alternate Title:Common Knowledge, Consensus, and Aggregate Information
Additional Information:Revised. Original dated to October 1983. Published as "Common Knowledge, Consensus, and Aggregate Information," Econometrica 54 (1986):109-127.
Group:Social Science Working Papers
Series Name:Social Science Working Paper
Issue or Number:493
Record Number:CaltechAUTHORS:20170921-144910869
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81702
Deposited By: Jacquelyn Bussone
Deposited On:21 Sep 2017 22:09
Last Modified:03 Oct 2019 18:46

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