We consider preference relations over information that are monotone: more information is preferred to less. We prove that, if a preference relation on information about an uncountable set of states of nature is monotone, then it is not representable by a utility function

We present a simple example where the use of sigma-algebras as a model of information leads to a paradoxical conclusion: a decision maker prefers less information to more. We then explain that the problem arises because the use of sigma-algebras as the informational content of a signal is...