<p>This paper employs epistemic decision theory to explore rational bridge principles between probabilistic beliefs and deductively cogent beliefs. I re-examine Hempel and Levi’s epistemic decision theories and generalize them by introducing a novel rationality norm for belief binarization. This norm posits that an agent ought to have binary beliefs that maximize expected utility in light of their credences. Our findings reveal that the proposed norm implies certain geometrical principles, namely convexity norms. Building upon this framework, I critically evaluate the Humean thesis in Leitgeb’s stability theory of belief and Lin-Kelly’s tracking theory. We establish the impossibility results, demonstrating that those theories violate the proposed norms and consequently fail to do the job of expected utility maximization. In contrast, we discover alternative approaches that align with all of the proposed norms, such as generating beliefs that minimize a Bregman divergence from credences. Our epistemic decision theory for belief binarization can be compared to Dorst’s accuracy argument for the Lockean thesis. We conclude that deductively cogent expected accuracy maximizers are neither Lockean nor Humean.</p>