# Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule

@article{Wallace2003QuantumPF, title={Quantum Probability from Subjective Likelihood: improving on Deutsch's proof of the probability rule}, author={D. Wallace}, journal={Studies in History and Philosophy of Modern Physics}, year={2003}, volume={38}, pages={311-332} }

## 158 Citations

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

- Philosophy
- 2009

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…

Probability in the Everett interpretation

- Mathematics
- 2007

The Everett (many-worlds) interpretation of quantum mechanics faces a prima facie problem concerning quantum probabilities. Research in this area has been fast-paced over the last few years,…

Analysis of Wallace’s Proof of the Born Rule in Everettian Quantum Mechanics: Formal Aspects

- PhysicsFoundations of Physics
- 2018

A new presentation of Wallace’s proof of the Born rule via decision theory is provided, reorganized to simplify some arguments, and analyzed from a formal perspective.

“It from Bit” and the Quantum Probability Rule

- Philosophy
- 2015

I argue that, on the subjective Bayesian interpretation of probability, “it from bit” requires a generalization of probability theory. This does not get us all the way to the quantum probability rule…

On an argument of David Deutsch

- Mathematics
- 2003

We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that…

Probabilities and Shannon's Entropy in the Everett Many-Worlds Theory

- Philosophy
- 2016

Following a controversial suggestion by David Deutsch that decision theory can solve the problem of probabilities in the Everett many-worlds we suggest that the probabilities are induced by Shannon's…

Causation, Decision Theory, and Bell’s Theorem: A Quantum Analogue of the Newcomb Problem

- PhilosophyThe British Journal for the Philosophy of Science
- 2010

It is shown that an agent who acts according to CDT and gives any nonzero credence to some possible causal interpretations underlying quantum phenomena should bet against quantum mechanics in some feasible game scenarios involving entangled systems, no matter what evidence they acquire.

## References

SHOWING 1-10 OF 50 REFERENCES

Quantum probability from decision theory?

- PhilosophyProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2000

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…

Quantum theory of probability and decisions

- Philosophy, PhysicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1999

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…

On an argument of David Deutsch

- Mathematics
- 2003

We analyse an argument of Deutsch, which purports to show that the deterministic part of classical quantum theory together with deterministic axioms of classical decision theory, together imply that…

Derivation of the Born rule from operational assumptions

- MathematicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 2004

The Born rule is derived from operational assumptions, together with assumptions of quantum mechanics that concern only the deterministic development of the state, and provides a probability rule for state spaces that are not Hilbert spaces.

Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation

- Philosophy
- 2003

What is Probability

- Philosophy
- 1969

Probabilities may be subjective or objective; we are concerned with both kinds of probability, and the relationship between them. The fundamental theory of objective probability is quantum mechanics:…

Quantum Theory Needs No ‘Interpretation’

- Physics, Philosophy
- 2000

Purpose of this article is to stress the fact that Quantum Theory does not need an interpretation other than being an algorithm for computing probabilities associated with macroscopic phenomena and…

Implications of quantum theory in the foundations of statistical mechanics

- Physics
- 2001

An investigation is made into how the foundations of statistical mechanics are affected once we treat classical mechanics as an approximation to quantum mechanics in certain domains rather than as a…