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I'm excited to finally see a persuasive derivation of the standard "Born rule"

for calculating quantum probabilities. Previous derivations have not seemed

fully persuasive to me and many others. But this one seems solid to me.

Below is Deutsch's paper with his derivation, and two critical replies. The

first critical paper is right that Deutsch implicitly assumes their eqn 13,

but wrong that it is as justified as their eqn 14. Eqn 13 is just switching

the labels "1" and "2", while eqn 14 is vastly stronger. (The second

critical paper balks at this same relabeling eqn.)

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Quantum Theory of Probability and Decisions

Proc.Roy.Soc.Lond. A455 (1999) 3129-3197.

by David Deutsch

http://xxx.lanl.gov/abs/quant-ph/9906015

The probabilistic predictions of quantum theory are conventionally obtained

from a special probabilistic axiom. But that is unnecessary because all the

practical consequences of such predictions follow from the remaining,

non-probabilistic, axioms of quantum theory, together with the

non-probabilistic part of classical decision theory.

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Quantum Probability from Decision Theory?

Proc.Roy.Soc.Lond. A456 (2000) 1175-118.

by H. Barnum, C. M. Caves, J. Finkelstein, C. A. Fuchs, R. Schack

http://xxx.lanl.gov/abs/quant-ph/9907024

In a recent paper (quant-ph/9906015), Deutsch claims to derive the

"probabilistic predictions of quantum theory" from the "non-probabilistic

axioms of quantum theory" and the "non-probabilistic part of classical

decision theory." We show that his derivation fails because it includes

hidden probabilistic assumptions.

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Quantum Probability from Decision Theory?

by J. Finkelstein

http://xxx.lanl.gov/abs/quant-ph/9907004

Deutsch has recently (in quant-ph/9906015) offered a justification, based

only on the non-probabilistic axioms of quantum theory and of classical

decision theory, for the use of the standard quantum probability rules. In

this note, this justification is examined.

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Robin Hanson rhanson@gmu.edu http://hanson.gmu.edu

Asst. Prof. Economics, George Mason University

MSN 1D3, Carow Hall, Fairfax VA 22030-4444

703-993-2326 FAX: 703-993-2323

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