A New Measure for Decision-Making under Uncertainty

The proposed concept of decision-based payoff (DBP) uncertainty provides a practical way to assess how far real-world decisions deviate, on average, from what could have been achieved with full information. Unlike traditional measures of uncertainty that depend on subjective beliefs or probability models, DBP uncertainty relies purely on realized payoffs. It is defined as the average relative regret, which corresponds to the discrepancy of the optimal to the actual outcome, relative to the optimal outcome, yielding a performance indicator between zero and one. This makes it broadly comparable across different decision problems and application domains.

Importantly, the paper [1] shows that DBP uncertainty is consistent with the standard economic notions of first- and second-order stochastic dominance, which enables the comparison of decision quality across uncertain environments. A numerical application involving investment in a European call option demonstrates how the measure captures the informational limits of decision-making in financial markets.

Beyond its immediate analytical appeal, the new measure provides a decision-centered perspective on uncertainty: Rather than asking how well beliefs describe the world, it asks how well decisions perform given the information available. This approach can be used to evaluate managerial, engineering, or policy decisions made under ambiguity, where probabilistic models are either unavailable or unreliable.

This research builds on earlier work at the Chair of Operations, Economics and Strategy on relatively robust decision-making, which focuses on ensuring reliable performance under incomplete information [2–7].

Abstract: 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.