Risk-Sensitive Accuracy-First Epistemology: Cumulants, Robustness, and Tempered Reporting

Accuracy-first epistemology is often presented as if expected inaccuracy were the uniquely natural evaluation rule. This paper argues that this is a substantive normative choice: expectation is a risk-neutral aggregator of epistemic loss. We develop a risk-sensitive alternative that treats scoring-rule loss as an epistemic gamble and evaluates it with an entropic criterion. Philosophically, this reframes propriety-based sincerity as a special case, yields an endogenous distinction between private belief and public report, and models permissive disagreement as variation in epistemic risk posture rather than a departure from accuracy-first methodology. Technically, the framework delivers a unified structure linking cumulant-sensitive evaluation, a relative-entropy robustness dual, and tempered reporting operators, with an explicit map from private credence to risk-indexed report. We prove general existence and uniqueness results and show how variance appears as the first local correction to expectation. For log score we obtain a closed-form tempered reporting rule with clear limits from sincerity to maximal humility. For Brier score we prove strict convexity, characterize the optimizer by a Gibbs-type fixed point, derive an explicit local flattening direction, and establish the same maximal-humility limit. We also provide an axiomatic characterization of the escort family up to reparameterization, calibrate the canonical parameter map via the entropic log-score problem, and develop initial extensions to social aggregation, polarization, and diachronic consistency.