Information Is Not Utility: When Probabilistic Forecasts Help and Hurt Decisions

Richer forecasts can change decisions when objectives depend on distributional information unavailable from the predictive mean and a trained rule can use it. We analyze forecast-to-decision interfaces through sufficiency and bounded-reward stability results, with explicit limits on their applicability. In the original two-regime specification, the mean identifies the predictive law and the action penalty ignores variance. A mean-matched market restores a role for distributional information: the true predictive law improves mean–second-moment utility by 2.08 × 10⁻⁵ per day over the point forecast (95% confidence interval [0.42, 3.74] × 10⁻⁵). A linear readout recovers most of that value, a width-16 network matches the plug-in, and the tested policy-gradient procedures do not. On a twenty-cell map fixed before scoring, the preregistered per-cell rule labels eight cells as helps, nine as irrelevant, and three as hurts. Seed resampling preserves those labels; a Holm correction changes them, including on the anchor cell. A newsvendor with matched demand means replicates the objective separation. Chronos interval width on the S&P 500 exchange-traded fund SPY contains volatility information but does not improve the decision over simpler volatility estimates on the primary predeclared fold. Author manuscript submitted to Machine Learning. This repository deposit is a preprint, not an acceptance or a peer-reviewed journal publication. The manuscript contains the author's funding, competing-interest and AI-assistance disclosures.