Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability

@article{Pitowsky2002BettingOT,
  title={Betting on the Outcomes of Measurements: A Bayesian Theory of Quantum Probability},
  author={Itamar Pitowsky},
  journal={arXiv: Quantum Physics},
  year={2002}
}
  • I. Pitowsky
  • Published 18 August 2002
  • Philosophy
  • arXiv: Quantum Physics
We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One of the measurements is subsequently chosen and performed and the money placed on the other measurements is returned to the agent. We show how the rules of rational betting imply all the interesting features of quantum probability, even in such finite gambles… 
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References

SHOWING 1-10 OF 67 REFERENCES
Quantum probability from decision theory?
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 probabilities as Bayesian probabilities
In the Bayesian approach to probability theory, probability quantifies a degree of belief for a single trial, without any a priori connection to limiting frequencies. In this paper, we show that,
Quantum Mechanics as Quantum Information (and only a little more)
In this paper, I try once again to cause some good-natured trouble. The issue remains, when will we ever stop burdening the taxpayer with conferences devoted to the quantum foundations? The suspicion
Quantum Theory From Five Reasonable Axioms
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace formula for calculating probabilities). In this paper
Foundations and philosophy of statistical theories in the physical sciences
The Statistics of Non-Boolean Event Structures.- Possibility and Probability.- Some Remarks on Hamiltonian Systems and Quantum Mechanics.- The Possibility Structure of Physical Systems.- Quantum
Bell's theorem, quantum theory and conceptions of the universe
On a Theory of the Collapse of the Wave Function.- On the Measurement Problem of Quantum Mechanics.- A New Characteristic of a Quantum System Between Two Measurements - A "Weak Value".- Can the
Elementary propositions and essentially incomplete knowledge: A framework for the interpretation of quantum mechanics
A central problem in the interpretation of non-relativistic quantum mechanics is to relate the conceptual structure of the theory to the classical idea of the state of a physical system. This paper
Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?
TLDR
Consideration of the problem of making predictions concerning a system on the basis of measurements made on another system that had previously interacted with it leads to the result that one is led to conclude that the description of reality as given by a wave function is not complete.
George Boole's ‘Conditions of Possible Experience’ and the Quantum Puzzle
  • I. Pitowsky
  • Philosophy
    The British Journal for the Philosophy of Science
  • 1994
In the mid-nineteenth century George Boole formulated his ‘conditions of possible experience’. These are equations and ineqaulities that the relative frequencies of (logically connected) events must
...
...