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. We perform such an analysis in an Everett interpretation without any measurement postulates at all. 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 demonstration is complete for projective measurements of pure states in a finite dimensional Hilbert space and we discuss how it might be applied to generalized measurements. A similar demonstration 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.