On the nonexistence of Blackwell's theorem-type results with general preference relations

A well-known theorem of Blackwell states that, when quantity of information is properly defined, every expected utility decision maker prefers more information to less; for more general preferences, however, the theorem is no longer true. In this article, we investigate the extent to which Blackwell's Theorem does not hold and describe conditions, and situations, under which information is still valuable. We also show that, for many types of additions of information, there exists a decision maker who will reject this information.