Document Type
Discussion Paper
Publication Date
3-1-2001
CFDP Number
1296
CFDP Pages
11
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.
Recommended Citation
Dubra, Juan and Echenique, Federico, "Measurability Is Not about Information" (2001). Cowles Foundation Discussion Papers. 1550.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1550