 Decision theory often introduces probability and utility with representation theorems. These theorems show that if preferences among acts meet certain constraints, such as transitivity, then there exist a probability function and a utility function (given a choice of scale) that generate expected utilities agreeing with preferences. David Krantz, R. Duncan Luce, Patrick Suppes, and Amos Tversky (1971) offer a good, general introduction to the purposes and methods of constructing representations theorems. In  Section 3.1,  I discuss the theorems’ function in decision theory.