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Durham University

Department of Mathematical Sciences


Publication details for Michael Goldstein

Goldstein, Michael (2001). Avoiding foregone conclusions: geometric and foundational analysis of paradoxes of finite additivity. Journal of Statistical Planning and Inference 94(1): 73-87.

Author(s) from Durham


We consider an example in which the use of finitely additive probabilities leads to the seemingly paradoxical conclusion that we may reason to a foregone conclusion. We give an informal treatment of this paradox. We then develop a geometric approach which formalises this treatment, and offers a foundational resolution of the problem. We discuss this approach both in the context of assessing the value of such paradoxical data and also when used for finite approximation.