Abstract
I have an urn that contains 100 marbles. 30 of those marbles are red. The remain 6 der are yellow. What sort of bets would you be willing to make on the outcome 7 of the next marble drawn from the urn? What odds would you accept on the event 8 “the next marble will be yellow”? A reasonable punter should be willing to accept 9 any betting quotient up to 0.7. I define “betting quotient” as the ratio of the stake 10 to the total winnings. That is the punter should accept a bet that, for an outlay of 11 70 cents, guarantees a return of 1 euro if the next marble is yellow. And the punter 12 should obviously accept bets that cost less for the same return, but what we are 13 really interested in is the most the punter would pay for a bet on an event.
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References
Camerer, C. andWeber,M. (1992). Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty 5, 325–370.
Cozman, F. (n.d.). A brief introduction to the theory of sets of probability measures. http://www.poli.usp.br/p/fabio.cozman/Research/CredalSetsTutorial/quasi-bayesian.html.
Däring, F. (2000). Conditional probability and Dutch books. Philosophy of Science 67, 391–409.
Elga, A. (2010). Subjective probabilities should be sharp. Philosophers’ Imprint 10.
Ellsberg, D. (1961). Risk, ambiguity and the Savage axioms. Quarterly Journal of Economics 75, 643–696.
Hájek, A. (2008). Arguments for—or against—probabilism? British Journal for the Philosophy of Science 59, 793–819.
Halpern, J. Y. (2003). Reasoning about uncertainty. MIT press.
Halpern, J. Y. (2006). Using sets of probability measures to represent uncertainty. arXiv:cs/0608028v1.
Hurwicz, L. (1951). Optimality criteria for decision making under ignorance. Cowles Commission Discussion Paper Statistics 370.
Joyce, J. M. (1998). A nonpragmatic vindication of probabilism. Philosophy of Science 65, 575–603.
Joyce, J. M. (2005). How probabilities reflect evidence. Philosophical Perspectives 19, 153–178.
Joyce, J. M. (2009). Accuracy and coherence: Prospects for an alethic epistemology of partial belief. In F. Huber and C. Schmidt-Petri (Eds.), Degrees of Belief, pp. 263–297. Springer.
Joyce, J. M. (2011). A defense of imprecise credence. Oxford Studies in Epistemology 4. Forthcoming.
Kyburg, H. and Pittarelli, M. (1992). Set-based Bayesianism. Technical Report UR CSD;TR407, University of Rochester, Computer Science Department. http://hdl.handle.net/1802/765.
Levi, I. (1974). On indeterminate probabilities. Journal of Philosophy 71, 391– 418.
Levi, I. (1986). Hard choices: decision making under unresolved conflict. Cambridge University Press.
Paris, J. (1994). The uncertain reasoner’s companion. Cambridge University Press.
Schick, F. (1986). Dutch bookies and money pumps. Journal of Philosophy 83, 112–119.
Seidenfeld, T. and Wasserman, L. (1993). Dilation for sets of probabilities. Annals of Statistics 21, 1139–1154.
Walley, P. (1991). Statistical Reasoning with Imprecise Probabilities, Volume 42 of Monographs on Statistics and Applied Probability. Chapman and Hall.
Walley, P. (2000). Towards a unified theory of imprecise probabilities. International Journal of Approximate Reasoning 24, 125–148.
Weatherson, B. (m.s.). Decision making with imprecise probabilities. Available http://brian.weatherson.org/vdt.pdf.
Wheeler, G. (forthcoming). Dilation demystified. In A. Cullison (Ed.), The Continuum Companion to Epistemology. Continuum.
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Bradley, S. (2012). Dutch Book Arguments and Imprecise Probabilities. In: Dieks, D., Gonzalez, W., Hartmann, S., Stöltzner, M., Weber, M. (eds) Probabilities, Laws, and Structures. The Philosophy of Science in a European Perspective, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-3030-4_1
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