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Trust the Evidence: Two Deference Principles for Imprecise Probabilities

Our intuition that rational agents should value the evidence can be captured by a well-known theorem due to I. J. Good. However, Good's theorem fails when agents have imprecise credences, raising the worry that agents with imprecise credences don't value the evidence. This essay shows a different way to capture our starting intuition, as the claim that rational agents defer to their informed selves. I introduce and motivate two deference principles for imprecise probabilities, and show that rational imprecise agents defer to their informed selves according to these principles. This shows a sense in which imprecise agents value the evidence. I end by comparing the deference principles introduced here with an alternative from the literature.