Economic Comparability of Information Systems

Whether, for a given user, one information system is preferable to another, depends in general on the payoff function characterizing the user, and not only on the probability distributions of channel in and outputs (events and messages) characterizing the information systems. This remains true when information systems are interpreted as statistical experiments used to test hypotheses. Some pairs of information systems are, however, comparable, in the sense that one is preferable to another irrespective of the payoff function. There exists thus a partial ordering of information systems according to their 'informativeness'. The paper states various conditions under which two information systems are comparable: these are certain properties of the distributions of events and messages. Theorems are proved that establish necessity or sufficiency relations between those properties. (Author)