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It is natural to think of precise probabilities as being special cases of imprecise probabilities, the special case being when one’s lower and upper probabilities are equal. I argue, however, that it is better to think of the two models as representing two different aspects of our credences, which are often (if not always) vague to some degree. I show that by combining the two models into one model, and understanding that model as a model of vague credence, a natural interpretation arises that suggests a hypothesis concerning how we can improve the accuracy of aggregate credences. I present empirical results in support of this hypothesis. I also discuss how this modeling interpretation of imprecise probabilities bears upon a philosophical objection that has been raised against them, the so-called inductive learning problem.

DOI: 10.1007/s11229-015-0782-5

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