A measure of information value for risk

Information is crucial for risk management; however, no quantified measure to evaluate risk information exists to date. The standard measure of value of factual information is information entropy-that is, the negative logarithm of probability. Despite its applications in various fields, this measure is insufficient for the evaluation of risk information; there are three reasons. First, it requires precise probabilities, which are generally absent in the context of risks. Second, it does not consider the effect of the consequences, which is essential for risks. Third, it does not account for human preferences and subjectivity. This study proposes a quantified measure for the evaluation of factual risk information-that is, observations of occurrence, particularly for binary, unambiguous, and rare phenomena. To develop such a measure, precise probabilities are replaced with updated probabilities, based on the Prospective Reference Theory. Additionally, utility is included as a proxy for the size of consequences. The third challenge-human preferences and subjectivity-is partly addressed by the application of updated perceived probabilities and utility as a measure of human preferences. Such a conventional, quantified measure facilitates the comparison of the potential impact of different messages for a new observation of occurrence for a risk, as well as of messages for different risks. Moreover, it clarifies the factors that systematically affect this impact. More particularly, it indicates the major effects of the perceived number of past occurrences.