Abstract
This paper explores how the Bayesian program benefits from allowing for objective chance as well as subjective degree of belief. It applies David Lewis’s Principal Principle and David Christensen’s principle of informed preference to defend Howard Raiffa’s appeal to preferences between reference lotteries and scaling lotteries to represent degrees of belief. It goes on to outline the role of objective lotteries in an application of rationality axioms equivalent to the existence of a utility assignment to represent preferences in Savage’s famous omelet example of a rational choice problem. An example motivating causal decision theory illustrates the need for representing subjunctive dependencies to do justice to intuitive examples where epistemic and causal independence come apart. We argue to extend Lewis’s account of chance as a guide to epistemic probability to include De Finetti’s convergence results. We explore Diachronic Dutch book arguments as illustrating commitments for treating transitions as learning experiences. Finally, we explore implications for Martingale convergence results for motivating commitment to objective chances.
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References
Anscombe F. J., Aumann R. J. (1963) A definition of subjective probability. Annals of Mathematical Statistics 34(1): 199–205
Arntzenius F., Hall N. (2003) On what we know about chance. British Journal for the Philosophy of Science 54: 171–179
Christensen D. (2001) Preference based arguments for probabilism. Philosophy of Science 68: 356–376
De Finetti, B. (1937). Foresight: Its logical laws, its subjective (Kyburg, Henry E. Jr., sources Trans., In Kyburg & Smokler (Eds.), 1964, pp. 93–158).
Ewens W. J. (2004) Mathematical population genetics. Springer, New York
Freedman D., Pisani R., Purvis R. (1998) Statistics (3rd ed.). W. W. Norton & Company, New York
Gale J. S. (1990) Theoretical population genetics. Unwin Hyman, London
Gibbard A., Harper W. (1980) Counterfactuals and Two Kinds of Expected Utility. In: Harper W., Stalnaker R., Pearce G. (eds) Ifs. D. Reidel Publishing Company, Dordrecht, pp 153–190
Harper W., Kyburg H. E. Jr. (1968) The Jones case. British Journal for the Philosophy of Science 19: 247–258
Harper, W., Wheeler, G. (eds) (2007) Probability and inference: Essays in honour of Henry E. Jr. Kings College Publications, Kyburg
Harper, W. L., Stalnaker, R., & Pearce, G. (1981). Ifs: conditionals, belief, decision, chance, and time. The University of Western Ontario series in philosophy of science, (Vol. 15). Hingham, MA: Kluwer.
Jaynes E. T. (1976) Confidence intervals vs Bayesian intervals. In: Harper W., Hooker C. A. (eds) Foundations of probability theory, statistical inference, and statistical theories of science. D. Reidel Publishing Company, Dordrecht, pp 175–257
Jeffery Richard C. (1965) The logic of decision. McGraw-Hill, New York
Kassen R., Bataillion T. (2006) The distribution of fitness effects among beneficial mutations prior to selection in experimental populations of bacteria. Nature Genetics 38: 484–488
Kyburg H. E. Jr. (1974) Propensities and probabilities. British Journal for the Philosophy of Science 25: 358–375
Kyburg H. E. Jr. (1981) Principle investigation. Journal of Philosophy 78: 772–778
Kyburg, H. E. Jr., Smokler, H. E. (eds) (1964) Studies in subjective probability. Wiley, New York
Levi I. (1983) Review of studies in inductive logic and probability. In: Jeffrey R.C. (eds) 1980’ The philosophical review (Vol. 92, No. 1). University of California Press, Berkeley, pp 116–121
Levi I. (1990) Chance. Philosophical Topics 18(2): 117–149
Lewis D. (1986) Philosophical papers. Oxford University Press, Oxford
Lewis D. (1994) Humean supervenience debugged. Mind 103: 473–490
Luce R.D., Raiffa H. (1967) Games and decision. Wiley, New York
Perfeito L., Fernandes L., Mota C., Gordo I. (2007) Adaptive mutations in bacteria: High rate and small effects. Science 317(5839): 813–815
Quattrone G. A., Tversky A. (1984) Causal versus diagnostic contingencies: On self deception and on the Voter’s illusion. Journal of Personality and Social Psychology 46(2): 237–248
Raiffa H. (1968) Decision analysis: Introductory lectures on choices under uncertainty. Addion-Wesley Publishing Company, Menlo Park
Ramsey, F. P. (1926). Truth and probability. In H. E. Kyburg & H. E. Smokler (Eds.) (Reprinted 1964, pp. 63–92).
Rokyta D. R., Joyce P., Caudle S. B., Wichman H. A. (2005) An empirical test of the mutational landscape model of adaptation using a single-stranded DNA virus. Nature Genetics 37: 441–444
Savage, L. J. (1954/1972). The foundations of statistics. New York: Dover Publications Inc.
Shafir E., Tversky A. (1992) Thinking through uncertainty: Nonconsequential reasoning and choice. Cognitive Psychology 24: 449–474
Sklar L. (1993) Physics and chance: Philosophical issues in the foundations of statistical mechanics. Cambridge University Press, Cambridge
Skyrms B. (1980) Causal necessity. Yale University Press, New Haven
Skyrms B. (1984) Pragmatics and empiricism. Yale University Press, New Haven
Skyrms B. (1997) The structure of radical probabilism. Erkenntnis 45: 285–297
Stalnaker, R. (1972). Letter to David Lewis. In W. Harper, R. Stalnaker, & G. Pearce (Eds.), (1980). Ifs, pp. 151–152.
Teller P. (1976) Conditionalization, observation, and change of preference. In: Harper W., Hooker C.A. (eds) Foundations of probability theory, statistical inference, and statistical theories of science (Vol. I). D. Reidel Publishing Company, Dordrecht, pp 205–253
Tversky A., Shafir E. (1992) The disjunction effect in choice under uncertainty. Psychological Science 3(5): 305–309
Uffink, Jos (2006) Compendium of the foundations of classical statistical physics. Pitt Phil Sci Web site. http://philsci-archive.pitt.edu/archive/00002691/.
van Fraassen B. (1984) Belief and the Will. Journal of Philosophy 81: 235–256
van Fraassen B. (1995) Belief and the problem of Ulysses and the Sirens. Philosophical Studies 77: 7–37
van Fraassen B. (1999) Conditionalization, a new argument for. Topoi 18: 93–96
von Neumann J., Morgenstern O. (1947) Theory of games and economic behavior, second edition. Wiley, New York
Wilson M. (2006) Wandering significance: An essay on conceptual behavior. Clarendon Press, Oxford
Zabell S. L. (2002) It All adds up: The dynamic coherence of radical probabilism. PSA00: Philosophy of Science 69(Suppl 3): S99–S103
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Harper, W., Chow, S.J. & Murray, G. Bayesian chance. Synthese 186, 447–474 (2012). https://doi.org/10.1007/s11229-011-9994-5
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DOI: https://doi.org/10.1007/s11229-011-9994-5