Dutch-Book Arguments against using Conditional Probabilities for Conditional Bets

Open Journal of Philosophy 2 (3):195 (2012)

Abstract
We consider here an important family of conditional bets, those that proceed to settlement if and only if some agreed evidence is received that a condition has been met. Despite an opinion widespread in the literature, we observe that when the evidence is strong enough to generate certainty as to whether the condition has been met or not, using traditional conditional probabilities for such bets will NOT preserve a gambler from having a synchronic Dutch Book imposed upon him. On the contrary (I show) the gambler can be Dutch-Booked if his betting ratios ever depart from a rather different probability, one that involves the probability of the agreed evidence being provided. We note furthermore that this same alternative probability assessment is necessary if the evidence is weaker (i.e. if it fails to provide knowledge whether or not the condition has been met.) By contrast, some of the (rather different) probability assessments proposed by Jeffrey, precisely for such situations, still expose the gambler to a Dutch-Book.
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DOI 10.4236/ojpp.2012.23030
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The Logic of Decision.Richard Jeffrey - 1965 - University of Chicago Press.
Scientific Reasoning: The Bayesian Approach.Colin Howson & Peter Urbach - 1989 - British Journal for the Philosophy of Science 48 (1):126-131.
Philosophical Theories of Probability.Donald Gillies - 2003 - Philosophical Quarterly 53 (210):132-134.

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