According to the Orthodox Bayesian, every rational agent has a belief state that can be represented by a single precise credence function. But this is counter intuitive, and many (the “imprecise probabilists”) have argued that a rational agent’s belief state should instead be represented by a set of precise credence functions. In this paper, I develop an alternative way to represent an agent’s belief state. Informally, the idea is that the agent’s belief state can be represented by facts about his or her betting behaviour in a range of close counterfactual cases. I show how we can extend this idea into a formal account, whereby the agent’s belief state is represented by a set of sets of precise credence functions. I end by showing that this alternative account gives us a new solution to the problem of dilation.
