We provide self-contained proof of a theorem relating probabilistic coherence of forecasts to their non-domination by rival forecasts with respect to any proper scoring rule. The theorem recapitulates insights achieved by other investigators, and clarifi es the connection of coherence and proper scoring rules to Bregman divergence.

The pragmatic character of the Dutch book argument makes it unsuitable as an "epistemic" justification for the fundamental probabilist dogma that rational partial beliefs must conform to the axioms of probability. To secure an appropriately epistemic justification for this conclusion, one must explain what it means for a system of partial beliefs to accurately represent the state of the world, and then show that partial beliefs that violate the laws of probability are invariably less accurate than they could be otherwise. (...) The first task can be accomplished once we realize that the accuracy of systems of partial beliefs can be measured on a gradational scale that satisfies a small set of formal constraints, each of which has a sound epistemic motivation. When accuracy is measured in this way it can be shown that any system of degrees of belief that violates the axioms of probability can be replaced by an alternative system that obeys the axioms and yet is more accurate in every possible world. Since epistemically rational agents must strive to hold accurate beliefs, this establishes conformity with the axioms of probability as a norm of epistemic rationality whatever its prudential merits or defects might be. (shrink)

According to Bayesian epistemology, the epistemically rational agent updates her beliefs by conditionalization: that is, her posterior subjective probability after taking account of evidence X, pnew, is to be set equal to her prior conditional probability pold(·|X). Bayesians can be challenged to provide a justification for their claim that conditionalization is recommended by rationality—whence the normative force of the injunction to conditionalize? There are several existing justifications for conditionalization, but none directly addresses the idea that conditionalization will be epistemically rational (...) if and only if it can reasonably be expected to lead to epistemically good outcomes. We apply the approach of cognitive decision theory to provide a justification for conditionalization using precisely that idea. We assign epistemic utility functions to epistemically rational agents; an agent’s epistemic utility is to depend both upon the actual state of the world and on the agent’s credence distribution over possible states. We prove that, under independently motivated conditions, conditionalization is the unique updating rule that maximizes expected epistemic utility. (shrink)