Learning and Pooling, Pooling and Learning
We explore which types of probabilistic updating commute with convex IP pooling (Stewart and Ojea Quintana 2017). Positive results are stated for Bayesian conditionalization (and a mild generalization of it), imaging, and a certain parameterization of Jeffrey conditioning. This last observation is obtained with the help of a slight generalization of a characterization of (precise) externally Bayesian pooling operators due to Wagner (Log J IGPL 18(2):336–345, 2009). These results strengthen the case that pooling should go by imprecise probabilities since no precise pooling method is as versatile.
The bulk of this work was done while we were on a Junior Group Visiting Fellowship at the Munich Center for Mathematical Philosophy. The paper benefited from conversations with Stephan Hartmann and Hannes Leitgeb. We would especially like to thank Greg Wheeler for feedback, numerous relevant discussions, and support. We are grate- ful to Matt Duncan, Robby Finley, Arthur Heller, Isaac Levi, Michael Nielsen, Rohit Parikh, Paul Pedersen, Teddy Seidenfeld, and Reuben Stern for their excellent comments on drafts or presentations of the pa- per. Finally, thanks to an anonymous referee for his or her meticulous and valuable review.
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