Attitude towards Risk, Prospect Variability, and the Value of Imperfect Information

Abstract

Choice in decision making under uncertainty often includes the option of choosing to utilize an information system, a set of potential messages that may improve current decisions and resulting outcomes. In decision theory the demand price for an information system is defined as the maximum non-stochastic cost, payable from initial wealth prior to the receipt of any message, that makes the decision maker (DM) indifferent between purchasing the system or not. The determinants of the value of information are important to both the buyers and the sellers in the marketplace for information products, and economists study the subject with both theoretical and practical motivations. Theoretical analyses seek to discover the characteristics of the economic and/or statistical environment that allow for definitive qualitative statements about the value of information. The most famous result, Blackwell's Theorem [1; 2], states the necessary and sufficient conditions under which any potential user values one information system more than another. Unfortunately, most results are of the negative variety: there is no general monotonic relationship between the information value and the degree of aversion towards risk [5], the amount of statistical information transmitted [8], the level of initial wealth [6], or the Rothschild-Stiglitz variability of the prior distribution on the state [4]. In practical situations, the buyer or the producer of an information system may desire to utilize quantitative estimates of the value of information. Complete quantitative analysis requires knowledge of the statistical characteristics of the information, identification of the payoff function for the decision problem at hand, and assessment of the information user's utility function for wealth. This last factor, the utility function, is specific to each individual DM and is unlikely to be known by the producer of the information. Unless it can be assumed that all potential buyers are neutral towards risk and hence have an easily assessed linear utility function, the seller of the information product (e.g., a forecasting service with many clients) faces the problem of estimating demand without knowledge of the demanders' utility functions. Policy makers, seeking to assess the value of publicly collected and disseminated information, face a similar problem [12]. Blair and Romano [3], henceforth B-R, recently have introduced a new problem-specific ap-