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Beyond Finite Additivity

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

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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
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

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