Variance and the Value of Information

Abstract

A simple way to approximate the value of information is proposed. This approximation suggests that two kinds of quantities are important in determining the value of information: (1) the optimal behaviors that would be chosen if the decision maker knew which subtype (or state) of the resource it faced; and (2) the costs of small deviations from these subtype optima. I show that the value of information is approximately equal to the product of the mean cost of small deviations from the subtype optima and the variance of a modified distribution of the optimal behaviors. This helps to resolve the conflict between a result from economics, which shows that the value of information does not increase with the variance of subtypes, and results from theoretical behavioral ecology, which show that the effect of adding incomplete information to "conventional" models is greatest when the variance of subtypes is greatest. There is no conflict here as long as an increase in the variance of subtypes results in an increase in the variance of subtype optima, as is often the case. I discuss how changes in a problem's payoff structure change the value of information. The procedure for calculating the value of attending to a partially informative cue is outlined.