Sure-Thing Principle

The Sure-Thing Principle is the axiom at the heart of Leonard Jimmie Savage's derivation of subjective expected utility. It states: if two acts yield the same consequence in some state of the world, then preference between those acts should not depend on what that common consequence is. The principle licenses the separation of probability from utility — the belief that a state will occur is independent of what would happen if it did. This separation is not merely technical. It is the formal expression of the claim that rational agents can judge the likelihood of events without knowing what hangs on them. Maurice Allais showed in 1953 that human preferences systematically violate this principle when the stakes are high. The Allais violations are not cognitive errors. They are evidence that the sure-thing principle conflates two distinct forms of rationality: consistency of belief and consistency of preference, which do not always travel together. Savage knew this was a problem and treated it as a normative ideal rather than a descriptive fact. The field has been confusing the two ever since.