Related papers: Decisions, Decisions, Decisions: Can Savage Salvag…
This note is a somewhat-lighthearted comment on a recent paper by David Wallace, arXiv:0906.2718[quant-ph] entitled "A formal proof of the Born rule from decision-theoretic assumptions".
Although ultimately motivated by quantum theoretical considerations, Everett's many-world idea remains valid, as an approximation, in the classical limit. However to be applicable it must in any case be applied in conjunction with an…
This paper investigates a purely qualitative version of Savage's theory for decision making under uncertainty. Until now, most representation theorems for preference over acts rely on a numerical representation of utility and uncertainty…
I show how probabilities arise in quantum physics by exploring implications of {\it environment - assisted invariance} or {\it envariance}, a recently discovered symmetry exhibited by entangled quantum systems. Envariance of perfectly…
We have recently developed a new understanding of probability in quantum gravity. In this paper we provide an overview of this new approach and its implications. Adopting the de Broglie-Bohm pilot-wave formulation of quantum physics, we…
Probabilistic graphical models such as Bayesian Networks are one of the most powerful structures known by the Computer Science community for deriving probabilistic inferences. However, modern cognitive psychology has revealed that human…
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
The Everett interpretation of quantum mechanics divides naturally into two parts: first, the interpretation of the structure of the quantum state, in terms of branching, and second, the interpretation of this branching structure in terms of…
Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…
The auxiliary rules of quantum mechanics have always included the Born rule that connects probability with square modulus. This need not be the case, for it is possible to introduce probability into the theory through probability current…
The Born rule assigns a probability to any possible outcome of a quantum measurement, but leaves open the question how these probabilities are to be interpreted and, in particular, how they relate to the outcome observed in an actual…
The predictions of quantum mechanics are probabilistic. Quantum probabilities are extracted using a postulate of the theory called the Born rule, the status of which is central to the "measurement problem" of quantum mechanics. Efforts to…
Excluding the concept of probability in quantum mechanics, we derive Born's law from the remaining postulates in quantum mechanics using type method. We also give a way of determining the unknown parameter in a state vector based on an…
This paper shows how inference is treated within the context of Eigenlogic projection operators in linear algebra. In Eigenlogic operators represent logical connectives, their eigenvalues the truth-values and the associated eigenvectors the…
We consider the problem of rational uncertainty about unproven mathematical statements, remarked on by G\"odel and others. Using Bayesian-inspired arguments we build a normative model of fair bets under deductive uncertainty which draws…
Expected utility theory (EUT) is widely used in economic theory. However, its subjective probability formulation, first elaborated by Savage, is linked to Ellsberg-like paradoxes and ambiguity aversion. This has led various scholars to work…
In this paper, we propose an interpretation of the Hilbert space method used in quantum theory in the context of decision making under uncertainty. For a clear comparison we will stay as close as possible to the framework of SEU suggested…
Emergence of the classical world from the quantum substrate of our Universe is a long-standing conundrum. I describe three insights into the transition from quantum to classical that are based on the recognition of the role of the…
I defend an analog of probabilism that characterizes rationally coherent estimates for chances. Specifically, I demonstrate the following accuracy-dominance result for stochastic theories in the C*-algebraic framework: supposing an…