Skip to main content
Log in

Beauty and the Bets

Synthese Aims and scope Submit manuscript

Abstract

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, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

REFERENCES

  • Aumann, R., S. Hart, and M. Perry: 1997, ‘The Forgetful Passenger', Games and Economic Behavior 20, 117–120.

    Google Scholar 

  • Bacchus, F., H. Kyburg, and M. Thalos: 1990, ‘Against Conditionalization', Synthese 85, 475–506.

    Google Scholar 

  • 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.

    Google Scholar 

  • Christensen, D.: 1991, ‘Clever Bookies and Coherent Beliefs', The Philosophical Review 100, 229–247.

    Google Scholar 

  • Elga, A.: 2000, ‘Self-Locating Belief and the Sleeping Beauty Problem', Analysis 60, 143–147.

    Google Scholar 

  • 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.

    Google Scholar 

  • Leslie, J.: 1996, The End of the World, New York, Routledge.

    Google Scholar 

  • 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.

    Google Scholar 

  • Lewis, D.: 2001, ‘Sleeping Beauty: Reply to Elga', Analysis 61, 171–176.

    Google Scholar 

  • Monton, B.: 2001, ‘Sleeping Beauty and the Forgetful Bayesian', Analysis 61, 47–53.

    Google Scholar 

  • Piccione, M. and A. Rubinstein: 1997, ‘On the Interpretation of Decision Problems with Imperfect Recall', Games and Economic Behavior 20, 3–24.

    Google Scholar 

  • Quine, W. V. O.: 1969, ‘Propositional Objects', in Ontological Relativity and Other Essays, New York, Columbia University Press, pp. 139–160.

    Google Scholar 

  • Ramsey, F.: 1926/1990, ‘Truth and Probability', in D. H. Mellor (ed.), Philosophical Papers, Cambridge, Cambridge University Press, pp. 52–94.

    Google Scholar 

  • Talbott, W.: 1991, ‘Two Principles of Bayesian Epistemology', Philosophical Studies 62, 135–150.

    Google Scholar 

  • Teller, P.: 1973, ‘Conditionalization and Observation', Synthese 26, 218–258.

    Google Scholar 

  • van Fraassen, B.: 1984, ‘Belief and the Will', The Journal of Philosophy 81, 235–256.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

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

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:SYNT.0000024889.29125.c0

Keywords

Navigation