Journal Article

Countable Additivity and the de Finetti Lottery

Paul Bartha

in The British Journal for the Philosophy of Science

Published on behalf of British Society for the Philosophy of Science

Volume 55, issue 2, pages 301-321
Published in print June 2004 | ISSN: 0007-0882
Published online June 2004 | e-ISSN: 1464-3537 | DOI: http://dx.doi.org/10.1093/bjps/55.2.301
Countable Additivity and the de Finetti Lottery

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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

Journal Article.  0 words. 

Subjects: Philosophy of Science ; Science and Mathematics

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