© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

A Note on Deutsch’s “Quantum Theory of Probability and Decisions”

Malcolm R. Forster

Published Jan 1, 1999• 0 citations

Abstract

ABSTRACT: David Deutsch has a forthcoming article called “Quantum Theory of Probability and Decisions " in which he claims to derive the standard probabilistic interpretation of the wavefunction from non-probabilistic considerations. In this note, I try to develop his argument in a classical context, to see whether the same ideas can generate probabilistic conclusions from nonprobabilistic assumptions in a more general way. While my answer is negative, the attempt pinpoints the parts of Deutsch’s quantum mechanical argument that must rely on special features of the formalism (assuming that his proof is correct). 1. No Probabilities In, No Probabilities Out? You cannot derive an ‘ought ’ from an ‘is’. And I believe that it was Popper (1959) who once said, in response to those who think that randomness can be defined nonprobabilistically, that one cannot derive a probabilistic conclusion from non-probabilistic premises. Yet this is exactly what Deutsch (to appear) claims for quantum mechanical probabilities. Historically in the development of quantum theory, the Schrödinger

Related papers

Quantum probability from decision theory?

H. Barnum, Carlton M. Caves, J. Finkelstein +2 more

In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical decision theory.’ We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non–probabilistic axioms is already sufficient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason's theorem, relying on fewer assumptions than Deutsch, provides a compelling derivation of the quantum probability law.

arXiv:quant-ph/9907024•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•May 8, 2000•78 citations

Quantum Probability from Decision Theory?

H. Barnum, Carlton M. Caves, J. Finkelstein +2 more

In a recent paper, Deutsch claims to derive the `probabilistic predictions of quan-tum theory ’ from the `non-probabilistic axioms of quantum theory ’ and the `non-probabilistic part of classical decision theory. ’ We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non-probabilistic axioms is already su ¯ cient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason’s theorem, relying on fewer assump-tions than Deutsch, provides a compelling derivation of the quantum probability law.

•Jan 1, 2000•101 citations

Deutsch on quantum decision theory

Peter J. Lewis

A major problem facing no-collapse interpretations of quantum mechanics in the tradition of Everett is how to understand the probabilistic axiom of quantum mechanics (the Born rule) in the context of a deterministic theory in which every outcome of a measurement occurs. Deutsch claims to derive a decision-theoretic analogue of the Born rule from the non-probabilistic part of quantum mechanics and some non-probabilistic axioms of classical decision theory, and hence concludes that no probabilistic axiom is needed. I argue that Deutsch’s derivation begs the question.

•Jan 1, 2003•5 citations

Quantum Probability from Decision Theory?

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.

arXiv:quant-ph/9907004•Jul 1, 1999•0 citations

A formal proof of the Born rule from decision-theoretic assumptions

David Wallace

I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed ``counter-examples'' to show exactly which premises of the argument they violate.

arXiv:0906.2718•Jun 15, 2009•40 citations

How to Prove the Born Rule

David Wallace

Abstract This chapter develops the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett interpreted) quantum mechanics. It sketches the argument informally, then proves it formally, and lastly considers a number of proposed ‘counter-examples’ to show exactly which premises of the argument they violate.

•Jun 24, 2010•68 citations

ABSTRACT: David Deutsch has a forthcoming article called “Quantum Theory of Probability and Decisions " in which he claims to derive the standard probabilistic interpretation of the wavefunction from non-probabilistic considerations. In this note, I try to develop his argument in a classical context, to see whether the same ideas can generate probabilistic conclusions from nonprobabilistic assumptions in a more general way. While my answer is negative, the attempt pinpoints the parts of Deutsch’s quantum mechanical argument that must rely on special features of the formalism (assuming that his proof is correct). 1. No Probabilities In, No Probabilities Out? You cannot derive an ‘ought ’ from an ‘is’. And I believe that it was Popper (1959) who once said, in response to those who think that randomness can be defined nonprobabilistically, that one cannot derive a probabilistic conclusion from non-probabilistic premises. Yet this is exactly what Deutsch (to appear) claims for quantum mechanical probabilities. Historically in the development of quantum theory, the Schrödinger

In a recent paper, Deutsch claims to derive the ‘probabilistic predictions of quantum theory’ from the ‘non–probabilistic axioms of quantum theory’ and the ‘nonprobabilistic part of classical decision theory.’ We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non–probabilistic axioms is already sufficient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason's theorem, relying on fewer assumptions than Deutsch, provides a compelling derivation of the quantum probability law.

In a recent paper, Deutsch claims to derive the `probabilistic predictions of quan-tum theory ’ from the `non-probabilistic axioms of quantum theory ’ and the `non-probabilistic part of classical decision theory. ’ We show that his derivation includes a crucial hidden assumption that vitiates the force of his argument. Furthermore, we point out that in classical decision theory a standard set of non-probabilistic axioms is already su ¯ cient to endow possible outcomes with a natural probability structure. Within that context we argue that Gleason’s theorem, relying on fewer assump-tions than Deutsch, provides a compelling derivation of the quantum probability law.

A major problem facing no-collapse interpretations of quantum mechanics in the tradition of Everett is how to understand the probabilistic axiom of quantum mechanics (the Born rule) in the context of a deterministic theory in which every outcome of a measurement occurs. Deutsch claims to derive a decision-theoretic analogue of the Born rule from the non-probabilistic part of quantum mechanics and some non-probabilistic axioms of classical decision theory, and hence concludes that no probabilistic axiom is needed. I argue that Deutsch’s derivation begs the question.