The Relationship Between Perfect and Imperfect Information in a Two-Action Risk-Sensitive Problem

The ability to value information is a central feature of decision analysis and one of its most interesting areas of application. Unfortunately, general assertions regarding the drivers of information value or its properties have been difficult to formulate or have been disproved by counterexample. In this paper, we investigate the value of imperfect information relative to perfect information (RVOI). Within the context of a two-action decision problem with normal priors and exponential utility, we derive a closed-form solution for the value of information and demonstrate that the RVOI is maximal when the decision maker is indifferent between the two alternatives. In addition, we determine when the value of an information system providing a normally distributed signal with correlation coefficient ρ is equal to ρ × 100% or ρ² × 100% of the value of perfect information. These results deepen our understanding of information value and enable practitioners to estimate the value of imperfect information in particular settings.