Mayo-Wilson, Conor, and Gregory Wheeler. “Scoring Imprecise Credences: A Mildly Immodest Proposal.” Philosophy and Phenomenological Research 93 (2016): 55-78.
Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that there is no strictly proper scoring rule for imprecise probabilities.