On the Value of Information Across Decision Problems

The value of information is an important concept in decision analysis that has been quantified as the buying price (BPI) for the information and the expected utility increase (EUI) obtainable by using the information. These two measures rank information sources identically in a scalar-valued decision problem only when the utility function is linear or exponential. In contrast, this paper focuses on the value of information across scalar-valued decision problems sharing the same utility function such as different divisions within an organization exploring various information sources for their decisions using the same organizational utility function. In this context, it still makes sense to ask which sources are more informative. We show that BPI and EUI rank information sources identically in this context only when the utility function is linear. However, if the certainty equivalent increase is used instead of EUI, then identical ranking with BPI across problems is maintained for the broader class of linear or exponential utility functions. We discuss the importance of these results for distributed decision-making settings, where different departments within an organization may calculate the value of information separately. Our results advise against using EUI to measure information value in this context when risk attitude is important.