Howson, Colin (2019) Beyond Finite Additivity. [Preprint]

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Abstract

Abstract. There is a Dutch Book argument for the axiom of countable additivity for subjective probability functions, but de Finetti famously rejected the axiom, arguing that it wrongly renders a uniform distribution impermissible over a countably infinite lottery. Dubins however showed that rejecting countable additivity has a strongly paradoxical consequence which a much weaker rule than countable additivity blocks. I argue that this rule, which also prohibits the de Finetti lottery itself, has powerful independent support in a desirable closure principle. I leave it as an open question whether countable additivity itself should be adopted.

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Item Type:	Preprint
Creators:	Creators Email ORCID Howson, Colin howson.colin@gmail.com
Keywords:	Countable additivity; de Finetti lottery; probability one; logical consequence.
Subjects:	Specific Sciences > Probability/Statistics
Depositing User:	Dr. Colin Howson
Date Deposited:	31 Dec 2019 22:57
Last Modified:	31 Dec 2019 22:57
Item ID:	16761
Subjects:	Specific Sciences > Probability/Statistics
Date:	30 September 2019
URI:	https://philsci-archive.pitt.edu/id/eprint/16761

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