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Published March 2004 | Accepted Version
Journal Article Open

Information is not about measurability


We present a simple example where the use of σ-algebras as a model of information leads to a paradoxical conclusion: a decisionmaker prefers less information to more. We then explain that the problem arises because the use of σ-algebras as the informational content of a signal is inadequate. We provide a characterization of the different models of information in the literature in terms of Blackwell's theorem.

Additional Information

© 2003 Elsevier B.V. Received 1 October 2002; Revised 1 May 2003; accepted 1 June 2003. Available online 10 September 2003. We are grateful to an anonymous referee, David Blackwell, Don Brown, Hector Chade, David Levine, Jim Pitman, Maxwell Stinchcombe, Tarun Sabarwal, Bill Sudderth, Sergio Turner, Bill Zame, and seminar participants at UCLA and Yale for comments. We thank Larry Epstein, Peter Fishburn, Itzak Gilboa, Catherine Huafei Yan, Massimo Marinacci, Ernesto Mordecki, Malempati Rao, Srinivasa Varadhan and Peter Wakker for their kind attention to our questions. Part of this work was done while Juan Dubra visited Yale University, and Federico Echenique visited U.C. Berkeley.

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