Global Constraints on Imprecise Credences: Solving Reflection Violations, Belief Inertia, and Other Puzzles

A lot of foundational work in formal epistemology proceeds under the assumption that subjects have precise credences. The traditional requirement of probabilistic coherence presupposes that you have precise credences, for instance, and it says that your precise credence function must satisfy the probability axioms. The traditional rule for updating says that when you get evidence, you should modify your precise credence function by conditionalizing it on the information that you learn. Meanwhile, advocates of imprecise credences challenge the assumption behind these rules. They argue that your partial beliefs are best represented not by a single function, but by a set of functions, or representor.2 The move to imprecise credences leaves many traditional requirements of rationality surprisingly intact, as fans of imprecise credences often simply reinterpret these rules as applying to the individual functions in your representor. In order for your imprecise credences to be rational, each member of your representor must satisfy the probability axioms. In order for you to update rationally, your later representor must contain just those functions that result from conditionalizing each member of your representor on the information you learn.3 However, for agents with imprecise credences, the requirements of rationality needn’t take this form. Whether you are rational might just as easily depend on global