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Wheeler, Gregory; Mayo-Wilson, Conor (January 2016): Scoring Imprecise Credences: A Mildly Immodest Proposal. In: Philosophy and Phenomenological Research, Vol. 93, No. 1: pp. 55-78
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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" (Joyce 1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (Joyce 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. The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption—called strict immodesty—should be rejected, and we prove a representation theorem that characterizes all "mildly" immodest measures of inaccuracy.