Learning and Pooling, Pooling and Learning
- 269 Downloads
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.
- Arló-Costa, H. (2007). The logic of conditionals. In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2014 ed.). Stanford University: Metaphysics Research Lab.Google Scholar
- de Finetti, B. (1964). Foresight: Its logical laws, its subjective sources. In H. E. Kyburg & H. E. Smoklery (Eds.), Studies in Subjective Probability. Hoboken: Wiley.Google Scholar
- Dietrich, F., & List, C. (2014). Probabilistic opinion pooling. In A. Hájek & C. Hitchcock (Eds.), Oxford Handbook of Probability and Philosophy. Oxford: Oxford University Press.Google Scholar
- Good, I. J. (1983). Good Thinking: The Foundations of Probability and Its Applications. Minneapolis: U of Minnesota Press.Google Scholar
- Hájek, A., & Hall, N. (1994). The hypothesis of the conditional construal of conditional probability. In E. Eells & B. Skyrms (Eds.), Probability and conditionals: Belief revision and rational decision (pp. 75–112). Cambridge: Cambridge University Press.Google Scholar
- Hartmann, S. (2014). A new solution to the problem of old evidence. In Philosophy of Science Association 24th Biennial Meeting, Chicago, IL.Google Scholar
- Kyburg, H.E., Pittarelli, M. (1992). Some problems for convex bayesians. In Proceedings of the Eighth International Conference on Uncertainty in Artificial Intelligence, pp. 149–154. Morgan Kaufmann Publishers Inc.Google Scholar
- Leitgeb, H. (2016). Imaging all the people. Episteme. doi: 10.1017/epi.2016.14.
- Levi, I. (1978). Irrelevance. In C. Hooker, J. Leach, & E. McClennen (Eds.), Foundations and Applications of Decision Theory (Vol. 1, pp. 263–273). Boston: Springer.Google Scholar
- Levi, I. (1980). The Enterprise of Knowledge. Cambridge, MA: MIT Press.Google Scholar
- Madansky, A. (1964). Externally Bayesian Groups. Santa Monica, CA: RAND Corporation.Google Scholar
- Raiffa, H. (1968). Decision analysis: Introductory lectures on choices under uncertainty. Random House.Google Scholar
- Ramsey, F. P. (1990). Truth and probability. In D. H. Mellor (Ed.), Philosophical Papers (pp. 52–109). Cambridge University Press.Google Scholar
- Savage, L. (1972, originally published in 1954). The Foundations of Statistics. New York: Wiley.Google Scholar
- Skyrms, B. (1986). Choice and Chance: An Introduction to Inductive Logic (3rd ed.). Belmont: Wadsworth Publishing Company.Google Scholar