 Definition 1 is based on the simple observation that one would generally prefer to stake a good outcome on a more rather than less probable event. But the idea that this defines comparative beliefs might seem questionable. We could, for instance, imagine people who are instrumentally irrational, and as a result fail to prefer \(g\) to \(f\), even when the above conditions all hold and they find \(F\) more likely than \(E\). Moreover, this definition raises the question of how to define the comparative beliefs of those who are indifferent between all outcomes (Eriksson and Hájek 2007). Perhaps no such people exist (and Savage’s  axiom P5  indeed makes clear that his result does not pertain to such people). Nevertheless, it seems a definition of comparative beliefs should not preclude that such people, if existent, have strict comparative beliefs. Savage suggests that this definition of comparative beliefs is plausible in light of his axiom P4, which will be stated below. In any case, it turns out that when a person’s preferences satisfy Savage’s axioms, we can read off her preferences a comparative belief relation that can be represented by a (unique) probability function.