The Complete Ordering of Information Alternatives for a Class of Portfolio-Selection Models

Abstract

A well-known result in information economics is that there is no reason to presume decision makers in diverse settings will be unanimous in the selection of an optimal information structure. On its most basic level this negative result follows because different utility functions and/or different actionchoice problems induce rankings of the information alternatives which will not hold uniformly across alternative settings. The only general exception to the above occurs if one deals with costless information and the set of available information alternatives is comprised of increasingly fine information structures in the sense of Blackwell and Girshick (1954). As is wellknown, however, the fineness criterion provides only a partial ordering of the set of all possible information structures. Accordingly, without specification of the circumstances of the decision problem and the decision maker's preferences, it becomes essentially meaningless to make assertions about the usefulness of alternative accounting procedures. A further implication is the impossibility of measuring the value and quality of information. Hence, an important question arising in accounting theory is the identification of conditions such that the concept of usefulness will be meaningful within a class of decision problems. That is, what restrictions on a set of decisioninformation contexts, or settings, are required such that any problem in this set will induce identical orderings on the set of available information structures? On the one extreme, if the set of problems contains only one element, then a solution is, of course, always available; on the other extreme, if the