Blackwell-Monotone Updating Rules

Mark Whitmeyer

Journal of Political Economy, 2026, vol. 134, issue 8, 2523 - 2554

Abstract: An updating rule specifies how an agent reacts to information. It is Blackwell monotone if more information is always better for an agent in any decision problem and strictly Blackwell monotone if, in addition, every strict information improvement is strictly better in some decision problem. Bayes’s law is strictly Blackwell monotone. Within a broad class of updating rules—those that distort Bayesian posteriors in a signal-independent manner—it is the only strictly Blackwell-monotone updating rule. If decisions are evaluated nonpaternalistically (according to an agent’s beliefs), the Blackwell-monotone updating rules are affine distortions of Bayesian posteriors.

Date: 2026
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