Blackwell-Monotone Updating Rules

Abstract: An updating rule specifies how an agent reacts to information. An updating rule is Blackwell monotone if more information is always better for an agent in a decision problem and strictly Blackwell monotone if, in addition, there is always a decision problem in which more information is strictly better for an agent. Bayes' law is strictly Blackwell monotone, and I show that within a broad class of updating rules--those that distort the Bayesian posteriors in a signal-independent manner--it is the only strictly Blackwell-monotone updating rule. Moreover, when the state is non-binary, I show that Bayes' law and the trivial updating rule in which an agent dogmatically holds a single belief are the only continuous Blackwell-monotone updating rules.