Quantum probability and decision theory, revisited [2002 online-only paper]


Authors
David Wallace
University of Southern California
Abstract
An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Contact is made with Lewis's Principal Principle linking subjective credence with objective chance: an Everettian Principal Principle is formulated, and shown to be at least as defensible as the usual Principle. Some consequences of (Everettian) quantum mechanics for decision theory itself are also discussed. [NB: this this long (70 pages) and occasionally rambling online-only paper has been almost entirely superseded by material in subsequent; if something is not included in them it usually means that I have had second thoughts. I include it for completeness only.
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References found in this work BETA

Real Patterns.Daniel C. Dennett - 1991 - Journal of Philosophy 88 (1):27-51.
Reasons and Persons.Joseph Margolis - 1984 - Philosophy and Phenomenological Research 47 (2):311-327.
Word and Object.Willard Van Orman Quine - 1960 - Les Etudes Philosophiques 17 (2):278-279.
A Subjectivist’s Guide to Objective Chance.David K. Lewis - 1980 - In Richard C. Jeffrey (ed.), Studies in Inductive Logic and Probability, Volume II. Berkeley: University of California Press. pp. 263-293.

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Citations of this work BETA

Understanding Deutsch's Probability in a Deterministic Universe.Hilary Greaves - 2004 - Studies in History and Philosophy of Modern Physics 35 (3):423-456.
Quantum Probability From Subjective Likelihood: Improving on Deutsch's Proof of the Probability Rule.David Wallace - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):311-332.
Everettian Rationality: Defending Deutsch's Approach to Probability in the Everett Interpretation.David Wallace - 2003 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 34 (3):415-439.
Measurement Outcomes and Probability in Everettian Quantum Mechanics.David J. Baker - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (1):153-169.

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Quantum Probability and Many Worlds.Meir Hemmo - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):333-350.
Probability in the Everett Interpretation.Hilary Greaves - 2006 - Philosophy Compass 2 (1):109–128.
Understanding Deutsch's Probability in a Deterministic Universe.Hilary Greaves - 2004 - Studies in History and Philosophy of Modern Physics 35 (3):423-456.

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