In the Sleeping Beauty problem, Beauty is uncertain whether the outcome of a certain coin toss was heads or tails. One argument suggests that her degree of belief in heads should be 1/3, while a second suggests that it should be 1/2. Prima facie, the argument for 1/2 appears to be stronger. I offer a diachronic Dutch Book argument in favor of 1/3. Even for those who are not routinely persuaded by diachronic Dutch Book arguments, this one has some important morals.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Aumann, R., S. Hart, and M. Perry: 1997, ‘The Forgetful Passenger', Games and Economic Behavior 20, 117–120.
Bacchus, F., H. Kyburg, and M. Thalos: 1990, ‘Against Conditionalization', Synthese 85, 475–506.
Bartha, P. and C. Hitchcock: 1999, ‘No One Knows the Date or the Hour: An Unorthodox Application of Rev. Bayes's Theorem', Philosophy of Science 66, S339–S353.
Christensen, D.: 1991, ‘Clever Bookies and Coherent Beliefs', The Philosophical Review 100, 229–247.
Elga, A.: 2000, ‘Self-Locating Belief and the Sleeping Beauty Problem', Analysis 60, 143–147.
Howson, C.: 1993, ‘Dutch Book Arguments and Consistency', in D. Hull, M. Forbes, and K. Okrulik (eds.), PSA 1992,Vol. II, East Lansing, Philosophy of Science Association, pp. 161–168.
Leslie, J.: 1996, The End of the World, New York, Routledge.
Lewis, D.: 1980, ‘A Subjectivist's Guide to Objective Chance', in R. Jeffrey (ed.), Studies in Inductive Logic and Probability, Vol. II. Berkeley: University of California Press, pp. 263-294. Reprinted in D. Lewis, Philosophical Papers, Vol. II, Oxford: Oxford University Press, pp. 83-113.
Lewis, D.: 2001, ‘Sleeping Beauty: Reply to Elga', Analysis 61, 171–176.
Monton, B.: 2001, ‘Sleeping Beauty and the Forgetful Bayesian', Analysis 61, 47–53.
Piccione, M. and A. Rubinstein: 1997, ‘On the Interpretation of Decision Problems with Imperfect Recall', Games and Economic Behavior 20, 3–24.
Quine, W. V. O.: 1969, ‘Propositional Objects', in Ontological Relativity and Other Essays, New York, Columbia University Press, pp. 139–160.
Ramsey, F.: 1926/1990, ‘Truth and Probability', in D. H. Mellor (ed.), Philosophical Papers, Cambridge, Cambridge University Press, pp. 52–94.
Talbott, W.: 1991, ‘Two Principles of Bayesian Epistemology', Philosophical Studies 62, 135–150.
Teller, P.: 1973, ‘Conditionalization and Observation', Synthese 26, 218–258.
van Fraassen, B.: 1984, ‘Belief and the Will', The Journal of Philosophy 81, 235–256.
About this article
Cite this article
Hitchcock, C. Beauty and the Bets. Synthese 139, 405–420 (2004). https://doi.org/10.1023/B:SYNT.0000024889.29125.c0
- Important Moral
- Dutch Book
- Dutch Book Argument
- Sleep Beauty Problem
- Diachronic Dutch Book