Authors
Paul Bartha
University of British Columbia
Abstract
De Finetti would claim that we can make sense of a draw in which each positive integer has equal probability of winning. This requires a uniform probability distribution over the natural numbers, violating countable additivity. Countable additivity thus appears not to be a fundamental constraint on subjective probability. It does, however, seem mandated by Dutch Book arguments similar to those that support the other axioms of the probability calculus as compulsory for subjective interpretations. These two lines of reasoning can be reconciled through a slight generalization of the Dutch Book framework. Countable additivity may indeed be abandoned for de Finetti's lottery, but this poses no serious threat to its adoption in most applications of subjective probability. Introduction The de Finetti lottery Two objections to equiprobability 3.1 The ‘No random mechanism’ argument 3.2 The Dutch Book argument Equiprobability and relative betting quotients The re-labelling paradox 5.1 The paradox 5.2 Resolution: from symmetry to relative probability Beyond the de Finetti lottery.
Keywords Dutch Book arguments  countable additivity  indifference principle
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DOI 10.1093/bjps/55.2.301
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References found in this work BETA

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Citations of this work BETA

Conditional Probabilities.Kenny Easwaran - 2019 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 131-198.
Fair Infinite Lotteries.Sylvia Wenmackers & Leon Horsten - 2013 - Synthese 190 (1):37-61.
Infinitesimal Probabilities.Sylvia Wenmackers - 2016 - In Richard Pettigrew & Jonathan Weisberg (eds.), The Open Handbook of Formal Epistemology. PhilPapers Foundation. pp. 199-265.
Sleeping Beauty, Countable Additivity, and Rational Dilemmas.J. Ross - 2010 - Philosophical Review 119 (4):411-447.
Challenges to Bayesian Confirmation Theory.John D. Norton - 2011 - In Prasanta S. Bandyopadhyay & Malcolm R. Forster (eds.), Handbook of the Philosophy of Science, Vol. 7: Philosophy of Statistics. Elsevier B.V.. pp. 391-440.

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