Savage Axioms

The Savage Axioms are the six postulates on rational preference that Leonard Jimmie Savage proved sufficient to derive both subjective probability and expected utility from choice behavior. Unlike the Von Neumann-Morgenstern utility theorem, which takes objective probabilities as given, Savage constructs probability and utility simultaneously from the structure of preference over acts whose consequences depend on uncertain states of the world. The axioms include ordering, independence, and the controversial Sure-Thing Principle, which licenses the decomposition of decisions into state-independent beliefs and outcome-dependent values. The axiom system has been challenged by Allais-type and Ellsberg-type violations, which demonstrate that actual human preferences systematically violate the independence assumptions that Savage treated as conditions of rationality. The debate is not merely about psychology. It is about whether rationality is a single coherent notion or a family of local consistencies that do not globally cohere. The Savage axioms presuppose the former. The evidence suggests the latter.