Strategy and the logic of decision

The theory of subjective probability and utility recently proposed by Professor Richard Jeffrey [1 1 [2], [-3] has several unique features and appears to be in some ways distinctly more satisfactory than earlier theories. There is, however, one very important class of decision problems which is not" discussed by Professor Jeffrey problems concerned with decisions about strategies for using information. The principal task of this paper is to point out some questions which arise in attempting to deal with these decision problems within Jeffrey's theory. To do this it will be necessary to examine in some detail Jeffrey's discussion of the relation between his theory and those of Ramsey and Savage [4], [5]. There is some obscurity in this discussion, which must be cleared up before the problem of policy decisions (or strategies) can be discussed. The theory that Jeffrey proposes is unique in at least two respects: (a) Probabilities and utilities (desirabilities in Jeffrey's terminology) are assigned to the same entities propositions. (b) Only truth-functional methods of compounding propositions are employed. In this theory two related measures, P and D, defined on a Boolean algebra of propositions (excluding the null element F), are considered which satisfy the following axioms. For all propositions x and y, not identical with F: