New VOI framework handles imprecise probabilities with decision-rule-specific values

Traditional value-of-information (VOI) analysis assumes a single probability measure, but real-world evidence often narrows probabilities only to a set (a credal set). This paper by Rowan Iskandar formalizes two distinct VOI approaches under imprecision. First, decision-rule-specific values fix a rule like Gamma-maximin (maximizing minimal expected utility) and compute what information is worth to a decision-maker using that rule. Second, a fixed-measure envelope evaluates classical VOI over all admissible precise measures, yielding lower and upper bounds.

The paper proves that the expected value of perfect information is concave over the credal set, meaning its lower envelope endpoint is exactly obtained from extreme measures, while the upper endpoint requires solving a finite linear program. Notably, the Gamma-maximin value can exceed the entire envelope, so rule-specific values are not recovered from endpoints alone. A continuity bound limits VOI change as the measure varies, and partial/sample information endpoints may still be computed from generators under certain conditions. The method combines standard VOI estimators with a search over the credal set. A worked decision problem shows how the two quantities separate conclusions that hold across every admissible measure from those that depend on an unidentified choice of measure.