Expected value of information

Abstract

The expected value of information (EVI) quantifies the benefit of acquiring new data before making a decision. While colloquially defined as the change in expected value before and after learning, this can be misleading. A precise formulation considers a set of possible worlds, each with a subjective probability, and a set of possible actions, each with a utility conditional on the world. The expected utility of an action is the sum of its utilities across worlds, weighted by world probabilities. Initially, the optimal action maximizes this expected utility. New information k leads to updated probabilities over worlds and revised expected utilities. The value derived from specific information k is the difference between the expected utility of the new optimal action (chosen based on k) and the expected utility of the original optimal action, where both utilities are calculated using the updated probabilities conditional on k. Since the outcome of information gathering is uncertain, the overall EVI is obtained by summing the value derived from each possible information outcome k, weighted by the probability of obtaining that specific information k. This provides a formal measure of the expected gain from seeking information. – AI-generated abstract.