Orthogonal Information Structures : a Model to Evaluate the Information Provided by a Second Opinion

The paper discusses the value of information when a numberof independent sources provide information related to acommon set of states of nature.The starting point is the Information Economic model ofInformation Structures. The model is augmented to representindependence of informational sources by means oforthogonality of the information structures.A new mathematical operator, orthogonal product, is definedand its properties are probed. It is shown that thisoperator maintains some mathematical properties such asclosure, association, unity element, null element, etc. Itis demonstrated how the orthogonal product represents thenotion of multi-source information.The paper proves that an orthogonal product is generallymore informative than its multipliers, namely, if cost isnot considered a constraining factor, then there is a nonnegativevalue to obtaining a second opinion.The paper concludes with a numerical example and adiscussion on the applicability of the model oforthogonality