A Decision Theory for Imprecise Probabilities

Philosophers' Imprint 15 (2015)
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Abstract

Those who model doxastic states with a set of probability functions, rather than a single function, face a pressing challenge: can they provide a plausible decision theory compatible with their view? Adam Elga and others claim that they cannot, and that the set of functions model should be rejected for this reason. This paper aims to answer this challenge. The key insight is that the set of functions model can be seen as an instance of the supervaluationist approach to vagueness more generally. We can then generate our decision theory by applying the general supervaluationist semantics to decision-theoretic claims. The result: if an action is permissible according to all functions in the set, it’s determinately permissible; if impermissible according to all, determinately impermissible; and – crucially – if permissible according to some, but not all, it’s indeterminate whether it’s permissible. This proposal handles with ease some difficult cases ) on which alternative decision theories falter. One reason this view has been overlooked in the literature thus far is that all parties to the debate presuppose that an acceptable decision theory must classify each action as either permissible or impermissible. But I will argue that this thought is misguided. Seeing the set of functions model as an instance of supervaluationism provides a compelling motivation for the claim that there can be indeterminacy in the rationality of some actions.

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Susanna Rinard
Harvard University

Citations of this work

Cluelessness.Hilary Greaves - 2016 - Proceedings of the Aristotelian Society 116 (3):311-339.
Bayesian Cognitive Science, Monopoly, and Neglected Frameworks.Matteo Colombo & Stephan Hartmann - 2015 - British Journal for the Philosophy of Science 68 (2):451–484.
Meditations on Beliefs Formed Arbitrarily.Miriam Schoenfield - 2023 - In Tamar Szabó Gendler, John Hawthorne & Julianne Chung (eds.), Oxford Studies in Epistemology Volume 7. Oxford University Press. pp. 278-305.

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References found in this work

Evidential Symmetry and Mushy Credence.Roger White - 2009 - Oxford Studies in Epistemology 3:161-186.
The possibility of parity.Ruth Chang - 2002 - Ethics 112 (4):659-688.
What conditional probability could not be.Alan Hájek - 2003 - Synthese 137 (3):273--323.
Subjective Probabilities Should be Sharp.Adam Elga - 2010 - Philosophers' Imprint 10.

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