The Value of Information and Intensity of Preference

Abstract

Previous research has documented the lack of clear relationships between the value of information and characteristics of the decision problem. This paper shows that the intensity of the decision maker's preference toward the prior choice alternatives can be regarded as the primary determinant of information value. The value of an information source, measured in utility units, is maximal when the decision maker is indifferent vis-à-vis the prior alternatives, and it is lower as the preference for one alternative over the others gets stronger. This holds under quite general conditions, which are made explicit, and for any decision maker's utility function, wealth, and background risks. The maximum buying price of information follows the same pattern for linear utility and, with a restriction, exponential utility, and this may hold approximately for other types of utility functions. The result provides a general, concise, and intuitive explanation for seemingly ill-behaved variations in the value of information. It indicates that nonmonotonic, quasi-concave relationships should generally be expected between value of information and parameters of the decision problem.

Decreasing Marginal Value of Information Under Symmetric Loss

“…This is certainly not the only way to define the value of information or to frame the decision problem. One may frame the problem as that of maximizing expected utility, and measure the value of information as the certain amount that the decision maker would give up to acquire the information (the "buying price") or would require to relinquish the information (the "selling price" of information) (see for example Delquié 2008). For the situation of riskneutral decision makers, these models yield equivalent specifications to ours.…”

“…The underlying uncertainty is represented by a random variable˜and information signals about˜areX 1 X 2 . The information signals have decreasing marginal value if for all n the ex ante 3 A positive comparative statics result is obtained by Delquié (2008), who shows an increase in the value of information with a decrease in the intensity of prior preference for the optimal choice. expected decrease in loss from observingX n (in addition toX 1 X 2 X n−1 ) is less than the expected decrease in loss from observingX n+1 (in addition tõ X 1 X 2 X n ).…”

From the Editors—Group Decisions, Preference Elicitation, Experienced Utility, Survival Probabilities, and Portfolio Value of Information

“…The key contribution of this paper is to dissect the portfolio value of information into two parts: value of information that comes from better prioritization of projects and from ability to exclude projects that do not meet a performance threshold. Other papers in Decision Analysis that relate to this work are Bickel (2006Bickel ( , 2008, Delquié (2008), and Keisler (2004).…”

From the Editors—Games and Decisions in Reliability and Risk

“…Prior papers in Decision Analysis by these authors include Rios and Rios Insua (2009) In a prior related paper, Delquié (2008) examined the value of information and intensity of preference. An earlier Decision Analysis paper related to risk measures is by Denuit and Eeckhoudt (2010) on bivariate stochastic dominance and substitute risk-(in)dependent utilities.…”