Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-26T13:11:49.496Z Has data issue: false hasContentIssue false
  • English
  • Français

Bets on Hats: On Dutch Books Against Groups, Degrees of Belief as Betting Rates, and Group-Reflection

Published online by Cambridge University Press:  03 January 2012

Luc Bovens  and
Wlodek Rabinowicz
Get access Rights & Permissions [Opens in a new window]

Abstract

The Story of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable.

Type
Research Article
Information
Episteme , Volume 8 , Issue 3 , October 2011 , pp. 281 - 300
Copyright
Copyright © Cambridge University Press 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bovens, L. 1995. “‘P and I Will Believe that not-P’: Diachronic Constraints on Rational Belief.” Mind 104: 737–60.CrossRefGoogle Scholar
Bovens, L. and Rabinowicz, W.. 2009. “A Dutch Book for Group-Decision Making.” In Löwe, B., Pacuit, E., and Romeijn, J.-W. (eds.), Foundations of the Formal Sciences VI: Reasoning about Probabilities and Probabilistic Reasoning, Studies in Logic, vol. 16, pp. 91–101. London: College Publications.Google Scholar
Bovens, L. and Rabinowicz, W.. 2010. “The Puzzle of the Hats.” Synthese 172: 57–78.Google Scholar
Christensen, D. 1991. “Clever Bookies and Coherent Beliefs.” The Philosophical Review 100: 229–47.Google Scholar
Eriksson, L. and Rabinowicz, W.. Forthcoming. “The Interference Problem for the Betting Interpretation.” Synthese.Google Scholar
Lewis, D. 1980/1986. “A Subjectivist's Guide to Objective Chance.” In Jeffrey, R. (ed.), Studies in Inductive Logic and Probability, vol. II, pp. 263–93. Berkeley, CA: University of California Press. Reprinted with postscripts in Philosophical Papers, vol. II, pp. 83–132. Oxford: Oxford University Press.Google Scholar
Rabinowicz, W. 2008. “Pragmatic Arguments for Rationality Constraints.” In Galavotti, M.-C., Scazzieri, R., and Suppes, P. (eds.), Reasoning, Rationality and Probability, pp. 139–63. Stanford: CSLI Publications; Chicago: University of Chicago Press.Google Scholar
Ramsey, F. 1926/1931. “Truth and Probability.” In The Foundations of Mathematics and Other Logical Essays, Ch. VII, pp. 156–98. Braithwaite, R. B. (ed.). London: Kegan, Paul, Trench, Trubner & Co.; New York: Harcourt, Brace and Co.Google Scholar
Robinson, S. 2001. “Why Mathematicians Now Care About Their Hat Color.” New York Times, April 10, F5.Google Scholar
Selten, R. 1975. “A Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games.” International Journal of Game Theory 4: 25–55.CrossRefGoogle Scholar
van Fraassen, B. 1984. “Belief and the Will.” Journal of Philosophy 81: 235–56.Google Scholar