# 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} }

## 164 Citations

### Analysis of Wallace's Decision Theoretic Proof of the Born Rule in Everettian Quantum Mechanics

- Mathematics
- 2015

We analyse Wallace’s adaptation of Decision Theory to formally prove the Born Rule in Everettian Quantum Mechanics. His proof was reorganized with some improvements, and many details were filled in.…

### 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…

### Analysis of Wallace’s Proof of the Born Rule in Everettian Quantum Mechanics II: Concepts and Axioms

- PhilosophyFoundations of Physics
- 2018

Having analyzed the formal aspects of Wallace’s proof of the Born rule, we now discuss the concepts and axioms upon which it is built. Justification for most axioms is shown to be problematic, and at…

### Everettian quantum mechanics and physical probability: Against the principle of “State Supervenience”

- Philosophy
- 2016

### 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…

## References

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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…

### Deutsch on quantum decision theory

- Philosophy
- 2003

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…

### Quantum Probability and Decision Theory, Revisited

- Philosophy
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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…

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- 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

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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:…