The value of cost-free uncertain evidence

Synthese 199 (5-6):13313-13343 (2021)
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Abstract

We explore the question of whether cost-free uncertain evidence is worth waiting for in advance of making a decision. A classical result in Bayesian decision theory, known as the value of evidence theorem, says that, under certain conditions, when you update your credences by conditionalizing on some cost-free and certain evidence, the subjective expected utility of obtaining this evidence is never less than the subjective expected utility of not obtaining it. We extend this result to a type of update method, a variant of Judea Pearl’s virtual conditionalization, where uncertain evidence is represented as a set of likelihood ratios. Moreover, we argue that focusing on this method rather than on the widely accepted Jeffrey conditionalization enables us to show that, under a fairly plausible assumption, gathering uncertain evidence not only maximizes expected pragmatic utility, but also minimizes expected epistemic disutility.

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The Foundations of Statistics.Leonard J. Savage - 1954 - Wiley Publications in Statistics.
Laws and symmetry.Bas C. Van Fraassen - 1989 - New York: Oxford University Press.
The Logic of Decision.Richard C. Jeffrey - 1965 - New York, NY, USA: University of Chicago Press.

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