Abstract
AbstractThere 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 that a much weaker rule than countable additivity blocks. I argue that this rule, which also prohibits the de Finetti lottery, has powerful independent support in a desirable closure principle. I leave it as an open question whether countable additivity should be adopted.
Publisher
Cambridge University Press (CUP)
Reference22 articles.
1. The extent of non-conglomerability of finitely additive probabilities
2. Bell, John L. 2000. “Infinitary Logic.” In the Stanford Encyclopedia of Philosophy, edited by Edward N. Zalta. https://plato.stanford.edu/entries/logic-infinitary/
3. Reasoning to a Foregone Conclusion
4. The constraint rule of the maximum entropy principle