Deutsch's quantum probability derivation

From: Robin Hanson (
Date: Fri Jul 27 2001 - 09:22:37 MDT

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.)

   Quantum Theory of Probability and Decisions
   Proc.Roy.Soc.Lond. A455 (1999) 3129-3197.
   by David Deutsch

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.
   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

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.
   Quantum Probability from Decision Theory?
   by J. Finkelstein

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.

Robin Hanson
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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