Bayesian chance

Synthese 186 (2):447-474 (2012)
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
Keywords Objective chance  Subjective degree of belief  Reference lotteries  Utility axioms  Dutch books  Martingale convergence
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References found in this work BETA
Frank Arntzenius & Ned Hall (2003). On What We Know About Chance. British Journal for the Philosophy of Science 54 (2):171-179.
William L. Harper & Henry E. Kyburg (1968). The Jones Case. British Journal for the Philosophy of Science 19 (3):247-251.
Review author[S.]: Henry E. Kyberg (1974). Propensities and Probabilities. British Journal for the Philosophy of Science 25 (4):358-375.
Henry E. Kyburg Jr (1981). Principle Investigation. Journal of Philosophy 78 (12):772-778.

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J. T. Roberts (2013). Chance Without Credence. British Journal for the Philosophy of Science 64 (1):33-59.
Frank Arntzenius & Ned Hall (2003). On What We Know About Chance. British Journal for the Philosophy of Science 54 (2):171-179.
Ned Hall (2004). Two Mistakes About Credence and Chance. Australasian Journal of Philosophy 82 (1):93 – 111.
Ned Hall (2004). Two Mistakes About Credence and Chance. Australasian Journal of Philosophy 82 (1):93 – 111.
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