External documentation and its quantitative relationship to the internal information state of a decision maker: The information profile

In previous work the basic concepts of a fundamental theory of information flow and analysis were developed. Several important quantities were defined explicitly and quantitatively. The basis of the previous work rested upon the use of a generalized information system, the relating of information to the certainty in making a decision, and the consideration of average decision makers, which permits the development of unique relationships. The earlier‐developed theory is extended in this article to a much wider set of situations for which external documentation plays the dominant information role. This involves the consideration of the way external documentation changes an average decision maker's effectiveness for a particular problem. This leads to the concept of an information profile which is the relationship giving the change in decision‐maker effectiveness as a function of the decision‐maker effectiveness for a specific document. We also develop a model which permits us to define the information profile analytically. Several additional quantities are also defined explicitly and quantitatively. The definition of information developed in earlier work is extended and generalized quantitatively. Information is decision‐maker dependent and is related to the certainty in choosing various courses of action to solve a particular problem. Information is shown to be proportional to the sum of the squares of the probabilities of choice and is defined in terms of binary choice units or BCUs. Many necessary properties of information profiles of documents are developed, and some of their limitations are defined. Finally, examples with appropriate representative curves are presented. The previous work also has been extended to include the situation where the decision maker does not initially know the viable courses of action and must learn them. © 1987 John Wiley & Sons, Inc.