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Measurability Is Not about Information

Juan Dubra () and Federico Echenique ()

No 1296, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We comment on the relation between models of information based on signals/partitions, and those based on sigma-algebras. We show that more informative signals need not generate finer sigma-algebras, hence that Blackwell's theorem fails if information is modeled as sigma-algebras. The reason is that the sigma-algebra generated by a partition does not contain all the events that can be known from the information provided by the signal. We also show that there is a non-conventional sigma-algebra that can be associated to a signal which does preserve its information content. Further, expectations and conditional expectations may depend on the choice of sigma-algebra that is associated to a signal. We provide a simple characterization of when the model is robust to changes in the sigma-algebras.

Keywords: Blackwell's theorem; measurability; models of information; partitions; information- preserving sigma-algebras (search for similar items in EconPapers)
JEL-codes: C60 C70 G12 (search for similar items in EconPapers)
Pages: 11 pages
Date: 2001-03
New Economics Papers: this item is included in nep-gth
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