Probabilities and Beliefs

Choice-theoretic definitions of subjective probabilities originated with the work of Ramsey and de Finetti and attained their definitive form in the work of Savage. These probabilities are intended to provide a numerical representation of decision-maker's beliefs regarding the likely realization of alternative events. In this paper I argue that the choice-theoretic definitions of subjective probabilities involve a tacit convention--namely, state- independent utility functions--that is not implied by the axioms, and as a consequence choice-theoretic subjective probabilities, even when they exist do not necessarily represent the decision-maker's beliefs