Analysis 81 (3):479-488 (2021)

Rush T. Stewart
King's College London
Michael Nielsen
University of Sydney
Our aim here is to present a result that connects some approaches to justifying countable additivity. This result allows us to better understand the force of a recent argument for countable additivity due to Easwaran. We have two main points. First, Easwaran’s argument in favour of countable additivity should have little persuasive force on those permissive probabilists who have already made their peace with violations of conglomerability. As our result shows, Easwaran’s main premiss – the comparative principle – is strictly stronger than conglomerability. Second, with the connections between the comparative principle and other probabilistic concepts clearly in view, we point out that opponents of countable additivity can still make a case that countable additivity is an arbitrary stopping point between finite and full additivity.
Keywords Probability  Finite Additivity  Countable Additivity  Conditional Probability  Epistemic Norms  Conglomerability
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DOI 10.1093/analys/anab012
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