The Born Rule Without a Measurement Postulate

The Born rule governs the probability of outcomes of measurements of quantum systems. Many attempts have been made to derive the Born rule from other postulates. Here we explain that probability is an ill defined concept and that an agent who nevertheless wishes to make approximate predictions will have no alternative measure to weigh the alternatives without subjecting herself to a dutch book. Our proof is complete for projective measurements of pure states without resorting to any measurement postulate and we discuss how it might be applied to generalized measurements. A similar proof is impossible for mixed states. Nevertheless, following the standard convention, probability for mixed states has the same validity and issues as it does in classical physics.