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Expected Accuracy Supports Conditionalization—and Conglomerability and Reflection

Published online by Cambridge University Press:  01 January 2022

Kenny Easwaran
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Abstract

Expected accuracy arguments have been used by several authors (Leitgeb and Pettigrew and Greaves and Wallace) to support the diachronic principle of conditionalization, in updates where there are only finitely many possible propositions to learn. I show that these arguments can be extended to infinite cases, giving an argument not just for conditionalization but also for principles known as ‘conglomerability’ and ‘reflection’. This shows that the expected accuracy approach is stronger than has been realized. I also argue that we should be careful to distinguish diachronic update principles from related synchronic principles for conditional probability.

Type
Research Article
Information
Philosophy of Science , Volume 80 , Issue 1 , January 2013 , pp. 119 - 142
Copyright
Copyright © The Philosophy of Science Association

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Footnotes

†

I would like to thank the Coalition of Los Angeles Philosophers, audiences at the math department at the University of Southern California and the philosophy department at the University of Konstanz, Richard Pettigrew, and an anonymous referee for this journal, for their helpful comments.

References

Arntzenius, F. 2003. “Some Problems for Conditionalization and Reflection.” Journal of Philosophy 100 (7): 356–70.CrossRefGoogle Scholar
Arntzenius, F., Elga, A., and Hawthorne, J.. 2004. “Bayesianism, Infinite Decisions, and Binding.” Mind 113 (450): 251–83.CrossRefGoogle Scholar
Bradley, D. 2012. “Four Problems about Self-Locating Belief.” Philosophical Review 121 (2): 149–77.CrossRefGoogle Scholar
Christensen, D. 1991. “Clever Bookies and Coherent Beliefs.” Philosophical Review 100 (2): 229–47.CrossRefGoogle Scholar
Dubins, L. 1975. “Finitely Additive Conditional Probabilities, Conglomerability and Disintegrations.” Annals of Probability 3 (1): 89–99.CrossRefGoogle Scholar
Earman, J. 1992. Bayes or Bust? Cambridge, MA: MIT Press.Google Scholar
Easwaran, K. 2008. “The Foundations of Conditional Probability.” PhD thesis, University of California, Berkeley.Google Scholar
Easwaran, K., and Fitelson, B.. 2012. “An ‘Evidentialist’ Worry for Joyce’s Argument for Probabilism.” Dialectica 66 (3): 425–33.Google Scholar
Eriksson, L., and Hájek, A.. 2007. “What Are Degrees of Belief?” Studia Logica 86:185–215.CrossRefGoogle Scholar
Gauthier, D. 1994. “Assure and Threaten.” Ethics 104 (4): 690–721.CrossRefGoogle Scholar
Greaves, H., and Wallace, D.. 2006. “Justifying Conditionalization: Conditionalization Maximizes Expected Epistemic Utility.” Mind 115 (459): 607–32.CrossRefGoogle Scholar
Hájek, A. 2003. “What Conditional Probability Could Not Be.” Synthese 137:273–323.CrossRefGoogle Scholar
Hill, B. M. 1980. “On Some Statistical Paradoxes and Non-disintegrability.” Trabajos de estadística y de investigación operativa 31 (1): 39–66.CrossRefGoogle Scholar
Hill, B. M., and Lane, D.. 1985. “Conglomerability and Countable Additivity.” Sankhyā: Indian Journal of Statistics A 47 (3): 366–79.Google Scholar
Hinchman, E. 2003. “Trust and Diachronic Agency.” Noûs 37 (1): 25–51.CrossRefGoogle Scholar
Joyce, J. 1998. “A Nonpragmatic Vindication of Probabilism.” Philosophy of Science 65 (4): 575–603.CrossRefGoogle Scholar
Joyce, J. 2009. “Accuracy and Coherence: Prospects for an Alethic Epistemology of Partial Belief.” In Degrees of Belief, ed. Huber, F. and Schmidt-Petri, C., 263–97. Berlin: Springer.Google Scholar
Kadane, J. B., Schervish, M. J., and Seidenfeld, T.. 1986. “Statistical Implications of Finitely Additive Probability.” In Bayesian Inference and Decision Techniques: Essays in Honor of Bruno de Finetti, ed. Goel, P. K. and Zellner, A., 59–76. Amsterdam: Elsevier.Google Scholar
Kavka, G. 1983. “The Toxin Puzzle.” Analysis 43:33–36.CrossRefGoogle Scholar
Leitgeb, H., and Pettigrew, R.. 2010a. “An Objective Justification of Bayesianism I: Measuring Inaccuracy.” Philosophy of Science 77 (2): 201–35.Google Scholar
Leitgeb, H., and Pettigrew, R. 2010b. “An Objective Justification of Bayesianism II: The Consequences of Minimizing Inaccuracy.” Philosophy of Science 77 (2): 236–72.Google Scholar
Lindley, D. 1982. “Scoring Rules and the Inevitability of Probability.” International Statistical Review 50 (1): 1–11.CrossRefGoogle Scholar
McClennen, E. 1990. Rationality and Dynamic Choice: Foundational Explorations. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Meacham, C. 2008. “Sleeping Beauty and the Dynamics of De Se Beliefs.” Philosophical Studies 138 (2): 245–69.CrossRefGoogle Scholar
Myrvold, W. 2012. “Epistemic Values and the Value of Learning.” Synthese 187 (2): 547–68.CrossRefGoogle Scholar
Skyrms, B. 1990. The Dynamics of Rational Deliberation. Cambridge, MA: Harvard University Press.Google Scholar
Titelbaum, M. 2008. “The Relevance of Self-Locating Beliefs.” Philosophical Review 117 (4): 555–606.CrossRefGoogle Scholar
van Fraassen, B. 1981. “A Problem for Relative Information Minimizers in Probability Kinematics.” British Journal for the Philosophy of Science 32 (4): 375–79.CrossRefGoogle Scholar
van Fraassen, B. 1984. “Belief and the Will.” Journal of Philosophy 81 (5): 235–56.CrossRefGoogle Scholar
van Fraassen, B. 1995. “Belief and the Problem of Ulysses and the Sirens.” Philosophical Studies 77:7–37.CrossRefGoogle Scholar
Whittle, P. 2000. Probability via Expectation. 4th ed. Berlin: Springer.CrossRefGoogle Scholar