Blackwell-Monotone Updating Rules

TL;DR

This paper characterizes Blackwell-monotone updating rules, showing that within a broad class, Bayesian updating is uniquely strictly Blackwell monotone, and describes affine distortions of Bayesian posteriors.

Contribution

It identifies the conditions under which Bayesian updating is uniquely strictly Blackwell monotone among a class of distorted updating rules.

Findings

Bayesian law is strictly Blackwell monotone.

Within the class of signal-independent distortions, Bayesian updating is unique.

Blackwell-monotone rules are affine distortions of Bayesian posteriors.

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. If an agent's decisions are evaluated non-paternalistically (according to her beliefs), the Blackwell-monotone updating rules are affine distortions of the Bayesian posteriors.