Forecasts That Move Decisions: Truthfulness vs. Influence

A forecaster whose report changes a decision can benefit from misreporting even under a strictly proper score. We study protocols that separate a scored forecast from a bounded request to adjust the executed plan. With an independent identifying audit and plan-only operational routing, we characterize truthfulness for affine protocols and convex operational costs: the best attainable operational value must be minimized at the truthful report. A first-order certificate makes this condition independent of the weight on any differentiable strictly convex score. For quadratic costs, metric projection yields an exact vector solution and bounds on report distortion; in one dimension, truthfulness has a closed-form authority threshold. The principal's preferred authority can nevertheless be smaller, because honest reports may accompany systematically biased plans. We also derive the most informative feasible plan-preserving perturbation for detecting direct message effects. Binding requests prevent symmetric tests but permit one-sided tests, and prescribed symmetric-test power requires an explicit authority margin beyond truthfulness. Finally, we bound the propagation of estimation error through the equilibrium map, separating persistent report distortion from statistical and operational sources of decision loss. Simulations examine these results under bounded authority, censored feedback, and multi-item capacity constraints.