ORTHOGONAL INFORMATION STRUCTURES—A MODEL TO EVALUATE THE INFORMATION PROVIDED BY A SECOND OPINION

The paper discusses the value of information when a number of independent sources provide information related to a common set of states of nature. The starting point is the information economic model of information structures. The model is augmented to represent independence of informational sources by means of orthogonality of the information structures. A new mathematical operator, orthogonal product, is defined and its properties are probed. It is shown that this operator maintains some mathematical properties such as closure, association, unity element, null element, and so forth. It is demonstrated how the orthogonal product represents the notion of multisource information. The paper proves that an orthogonal product is generally more informative than its multipliers, namely, if cost is not considered a constraining factor, then there is a nonnegative value to obtaining a second opinion. An appendix to the paper expands this result to a case of partially dependent signals. The paper concludes with a numerical example and a discussion of the model's applicability for practical problems such as cost estimates.