 Savage (1954) likewise derives probabilities and utilities from preferences among options that are constrained by certain putative ‘consistency’ axioms. For a given set of such preferences, he generates a class of utility functions, each a positive linear transformation of the other (i.e. of the form \(U_1 = aU_2 + b\), where \(a \gt 0)\), and a unique probability function. Together these are said to ‘represent’ the agent’s preferences, and the result that they do so is called a ‘representation theorem’.  Jeffrey (1966) refines Savage’s approach. The result is a theory of decision according to which rational choice maximizes ‘expected utility’, a certain probability-weighted average of utilities. (See Buchak 2016 for more discussion.) Some of the difficulties with the behavioristic betting analysis of degrees of belief can now be resolved by moving to an analysis of degrees of belief that is functionalist in spirit. For example, according to Lewis (1986a, 1994a), an agent’s credences are represented by the probability function belonging to a utility function/probability function pair that best rationalizes her behavioral dispositions, rationality being given a decision-theoretic analysis. Representation theorems (in one form or another) underpin representation theorem arguments that rational agents’ credences obey the probability calculus: their preferences obey the requisite axioms, and thus their credences are representable that way. However, as well as being representable probabilistically, such agents’ credences are representable non-probabilistically; why should the probabilistic representation be privileged? See Zynda (2000), Hájek (2008), and Meacham and Weisberg (2011) for this and other objections to representation theorem arguments. 