ABSTRACT
This chapter begins to address questions involving properties of preferences over gambles that are more subtle than those embodied in the concept of an “elementary rational structure” (Def. 2.5.1). Wfe will see how these additional properties can lead to a numerical representa tion, called utility, of preference. As was noted in the Introduction, the entire development is organized into five chapters beginning, here, with the binary case where both of the conse quences are gains. The theory for binary gambles of just losses is formally identical provided one works with “dislike,” i.e., the converse of the preference relation, as the ordering. The binary theory for gains is elaborated in Chapter 4 by adding the binary operation of joint re ceipt This offers alternative ways of axiomatizing possible representations, and it provides considerably more detailed information about the mathematical form of the utility function. In Chapter 5 the binary theory of gains is extended to the nonbinary case, but data recently reported make clear that this generalization is descriptively unsatisfactory in crucial ways. Although there are various proposed representations that currently seem reasonably descrip tive, the development of a descriptively acceptable axiomatic general theory remains open. The situation of binary mixed gains and losses, which is somewhat more complex than that of just binary gains (losses), is covered in Chapters 6 and 7.
