Computer Science & AI

A proper scoring rule incentivises a predictor to report their true beliefs, but properness is insufficient to incentivise computation. For any proper scoring rule S and any positive compute cost c, a resource-bounded agent who can cheaply obtain an approximation q to the true probability p has a rational incentive to halt computation strictly before reaching p. We derive the exact equilibrium precision for three canonical scoring rules (log, Brier, spherical), showing the marginal score gain from improving approximation error from epsilon to epsilon-delta is proportional to kappa(p) times epsilon times delta, where kappa(p) is the local curvature of the expected score function. Balancing this against compute cost yields an optimal stopping precision epsilon* = (cT/kappa(p))^(1/3), independent of the initial approximation error. We state necessary and sufficient conditions for a scoring rule to incentivise computation to any target precision, identify when the gap closes (extreme probabilities, high curvature), and discuss implications for AI evaluation systems, prediction markets, and peer review platforms that use scoring rules to elicit accurate reporting from computational agents. All results are proved analytically; no experiments are reported.