Qualitative Robust Bayesianism and the Likelihood Principle
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We argue that the likelihood principle (LP) and weak law of likelihood (LL) generalize naturally to settings in which experimenters are justified only in making comparative, non-numerical judgments of the form "A given B is more likely than C given D." To do so, we first formulate qualitative analogs of those theses. Then, using a framework for qualitative conditional probability, just as the characterizes when all Bayesians (regardless of prior) agree that two pieces of evidence are equivalent, so a qualitative/non-numerical version of LP provides sufficient conditions for agreement among experimenters' whose degrees of belief satisfy only very weak "coherence" constraints. We prove a similar result for LL. We conclude by discussing the relevance of results to stopping rules.
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