  Savage then gives axioms constraining rational preference, and shows that any set of preferences satisfying those axioms yields an “at least as likely” relation that can be uniquely represented by a probability function. In other words, there is one and only one probability function \(P\) such that for all \(E\) and \(F\), \(P(E) \ge P(F)\) if and only if \(E\) is at least as likely as \(F\). Every preference relation obeying Savage's axioms is represented by this probability function \(P\), together with a utility function which is unique up to positive linear transformation.