The value of information (VoI) is a decision analytic method for quantifying the potential benefit of additional information in the face of uncertainty. This paper reviews the prevalence of VoI applications reported in the peer-reviewed literature from the years 1990–2011. We categorize papers’ applications across the types of uncertainties considered, modeling choices, and contexts of social importance (such as health care and environmental science). We obtain and analyze statistics on the range of applications and identify trends and patterns in them, and conclude with an interpretation of what these mean for researchers and practitioners as they pursue new efforts. Key results include a substantial increase over the last 20 years in published papers utilizing VoI, particularly in the medical field. Nineteen trends in VoI applications from the period of 1990–2000 to 2001–2011 were found to be at least weakly significant. Beyond simple trends, some characteristics of VoI usage depend on the area of application, and in some cases, certain sets of characteristics tend to be found together.
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A utility function transforms dollar values or some other nominal values into a scale for which maximizing the expectation is consistent with the axioms of rationality. There is a vast literature on utility theory. Raiffa (1968) is one source that explains utility. We also refer to multi-attribute utility (Keeney and Raiffa 1976) which involves combining utility scores—often as a weighted sum—for a number of individual attributes, where the single-attribute utility scores are often nonlinear functions of the metric for the attribute.
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The authors thank Laure Canis, Kun Zan, Mayank Mohan, Nolan Jones, John Vogel, Matthew Bates, and Richie Hartz for their assistance. This work was funded in parts by the Dredging Operation Environmental Research (DOER) program by the U.S. Army Corps of Engineers. Permission was granted by the USACE Chief of Engineers to publish this material. The views and opinions expressed in this paper are those of the individual authors and not those of the US Army, or other sponsor organizations.
Electronic supplementary material
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As an example of VoI in use, consider the following case in which a decision maker has two options, to continue passively or to make an investment. Continuing passively has a payoff of $10, while investing has an uncertain payoff, $x. The decision maker believes that if conditions are favorable to the investment, x will be 1,000; if conditions are neutral, x will be 100; and if conditions are unfavorable, x will be −500. Furthermore, the decision maker believes there is a 50 % chance conditions will be unfavorable, a 30 % chance they will be neutral, and only a 20 % chance they will be positive. Without any additional information about conditions, the decision maker will choose to do nothing, because the expected value of the investment is 50 % * (−$500) + 30 % * $100 + 20 % * $1,000 = −$20, which is worse than continuing passively. However, if the decision makers were to obtain perfect information about investment conditions before acting, there is, naturally, a 50 % chance they would be revealed to be negative, a 30 % they would be neutral, and a 20 % chance they would be positive. If conditions were found to be negative, the decision maker would still be passive and receive $10, but if conditions were found to be neutral or positive, the decision maker would invest and receive a payoff of $100 or $1,000, respectively. Thus, with this information, the decision maker has an expected payoff of 50 % * $10 + 30 % * $100 + 20 % * $1,000 = $235, an increase of $225 over the original situation. The increase in expected value from $10 (by continuing passively in all cases) to $235 (by being passive only when conditions are poor) results from having information prior to the decision. If the decision maker is concerned with expected monetary value, we call this increase, $225 in this case, the “expected value of perfect information.”
Appendix 2: Articles surveyed
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Keisler, J.M., Collier, Z.A., Chu, E. et al. Value of information analysis: the state of application. Environ Syst Decis 34, 3–23 (2014). https://doi.org/10.1007/s10669-013-9439-4
- Value of information
- Literature review
- Loss avoidance
- Information cost