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. 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.
Cite
@article{arxiv.2302.13956,
title = {Blackwell-Monotone Updating Rules},
author = {Mark Whitmeyer},
journal= {arXiv preprint arXiv:2302.13956},
year = {2026}
}
Comments
Previously titled "Bayes = Blackwell, Almost."