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Pedersen, Arthur P.; Wheeler, Gregory (2015): Dilation, Disintegrations, and Delayed Decisions. In: Proceedings of the 9th International Symposium on Imprecise Probability: Theories and Applications (ISIPTA 2015): pp. 227-236
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Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call Good's Principle: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although dilation and non-conglomerability share some simularities, some authors, including Walley and Seidenfeld, Schervish and Kadane, maintain that there are important differences between the two that warrant endorsing different normative positions regarding dilation (which is given a pass) and non-conglomerability (which is not). This article reassesses the grounds for treating dilation and non-conglomerability different. Our analysis exploits a new and general characterization result for dilation to draw a closer connection between dilation and non-conglomerability.