The Qualitative Grounds of Quantitative Probability

Abstract What is the qualitative basis for deriving meaningful psychological information from probabilistic representations of confidence within decision theory? Conditions on two binary relations—a preference relation $$\succsim $$ ≿ and a comparative confidence relation $$\succsim _c$$ ≿ c —are shown to imply the existence of a probability function and a utility function that jointly represent $$\succsim $$ ≿ under the expected utility rule, where the probability function is unique and also represents $$\succsim _c$$ ≿ c . It is also shown that, under certain conditions, these probabilities contain more meaningful information than can be extracted from the confidence relation on its own. The upshot is that there’s more to what’s meaningful in decision-theoretic representations of confidence than can generally be explained by reference to confidence relations alone.