| Sumario: | 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 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.
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