A Measure of Decision-Based Payoff Uncertainty

We introduce decision-based payoff (DBP) uncertainty as a novel measure of informational uncertainty in decision-making. It is defined over an observed sample of nonnegative payoffs from past decisions, evaluated as a fraction of an ex-post optimal payoff benchmark. The resulting distribution of relative payoffs is supported on a subset of the unit interval. DBP uncertainty, taking values between zero and one, quantifies the average deviation from optimality: It vanishes when optimal payoffs are always achieved and reaches one when observed payoffs are consistently zero despite the availability of strictly positive outcomes. The measure is compatible with first- and second-order stochastic dominance and enables meaningful comparisons across decision problems with nonnegative payoffs. It is equal to the average relative regret and vanishes for degenerate problems with singleton action sets, regardless of the observed outcomes. A numerical example involving investment in a call option under uncertain asset prices illustrates the concept's applicability and interpretability.