Information Value Theory

Abstract

The information theory developed by Shannon was designed to place a quantitative measure on the amount of information involved in any communication. The early developers stressed that the information measure was dependent only on the probabilistic structure of the communication process. For example, if losing all your assets in the stock market and having whale steak for supper have the same probability, then the information associated with the occurrence of either event is the same. Attempts to apply Shannon's information theory to problems beyond communications have, in the large, come to grief. The failure of these attempts could have been predicted because no theory that involves just the probabilities of outcomes without considering their consequences could possibly be adequate in describing the importance of uncertainty to a decision maker. It is necessary to be concerned not only with the probabilistic nature of the uncertainties that surround us, but also with the economic impact that these uncertainties will have on us. In this paper the theory of the value of information that arises from considering jointly the probabilistic and economic factors that affect decisions is discussed and illustrated. It is found that numerical values can be assigned to the elimination or reduction of any uncertainty. Furthermore, it is seen that the joint elimination of the uncertainty about a number of even independent factors in a problem can have a value that differs from the sum of the values of eliminating the uncertainty in each factor separately.