Venn Predictive Decision-Making

Venn predictors generate multiprobability predictions, which are sets of probability distributions with provable calibration guarantees, quantifying epistemic ambiguity (Knightian uncertainty) rather than providing a single probability estimate. This paper introduces Venn predictive decision-making systems (Venn-PDMSs), a framework that integrates multiprobability predictions with decision-theoretic principles to guide decision-making under uncertainty. As Venn predictors explicitly account for epistemic ambiguity, the resulting Venn-PDMSs possess the capability to “know what they do not know,” thereby facilitating safe human-in-the-loop automation in numerous scenarios. We formalise utility- and regret-based decision criteria, parametrised by an optimism index that allows for interpolation between pessimistic and optimistic subjective stances towards uncertainty. We establish theoretical guarantees, including invariance under affine transformations of the utility function and convergence to Bayes-optimal decisions in certain cases. Through synthetic examples and straightforward applications to mushroom classification and financial credit assessment, we demonstrate that Venn-PDMSs effectively balance epistemic ambiguity and risk (which is probabilistically quantifiable). We also highlight the limitations of aggregating multiprobabilities into point estimates and emphasise the importance of explicitly incorporating ambiguity-aware decision criteria in high-stakes predictive decision-making.