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Scoring Imprecise Credences: A Mildly Immodest Proposal

Mayo-Wilson, Conor and Wheeler, Gregory (2016) Scoring Imprecise Credences: A Mildly Immodest Proposal. [Preprint]

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Abstract

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. 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.


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Item Type: Preprint
Creators:
CreatorsEmailORCID
Mayo-Wilson, Conorconormw@gmail.com
Wheeler, Gregorygregory.r.wheeler@gmail.com
Keywords: Imprecise Probability, Proper Scoring Rules, Epistemic Decision Theory
Subjects: General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Depositing User: Gregory Wheeler
Date Deposited: 25 Mar 2016 02:13
Last Modified: 25 Mar 2016 02:13
Item ID: 11989
Official URL: http://onlinelibrary.wiley.com/doi/10.1111/phpr.12...
Subjects: General Issues > Decision Theory
Specific Sciences > Probability/Statistics
Date: January 2016
URI: http://philsci-archive.pitt.edu/id/eprint/11989

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