Related papers: Decisions, Decisions, Decisions: Can Savage Salvag…
We provide here a general mathematical framework to model attitudes towards ambiguity which uses the formalism of quantum theory as a ``purely mathematical formalism, detached from any physical interpretation''. We show that the…
We explain the measure problem (cf. origin of the Born probability rule) in no-collapse quantum mechanics. Everett defined maverick branches of the state vector as those on which the usual Born probability rule fails to hold -- these…
Reasoning is key to many decision making processes. It requires consolidating a set of rule-like premises that are often associated with degrees of uncertainty and observations to draw conclusions. In this work, we address both the case…
Mainstream interpretations of quantum theory maintain that violations of the Bell inequalities deny at least either realism or Einstein locality. Here we investigate the premises of the Bell-type inequalities by returning to earlier…
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a…
An approach is presented treating decision theory as a probabilistic theory based on quantum techniques. Accurate definitions are given and thorough analysis is accomplished for the quantum probabilities describing the choice between…
In this PhD thesis the ancient question of determinism ('Does every event have a cause ?') will be re-examined. In the philosophy of science and physics communities the orthodox position states that the physical world is indeterministic:…
We recently considered the task of summoning an unknown quantum state and proved necessary and sufficient conditions for Alice to be able to guarantee to complete the task when there may be several possible calls, of which she need only…
{\it Ellsberg thought experiments} and empirical confirmation of Ellsberg preferences pose serious challenges to {\it subjective expected utility theory} (SEUT). We have recently elaborated a quantum-theoretic framework for human decisions…
Ambiguity and ambiguity aversion have been widely studied in decision theory and economics both at a theoretical and an experimental level. After Ellsberg's seminal studies challenging subjective expected utility theory (SEUT), several…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
Our representation of the Universe is built with sequences of symbols, numbers, operators, rules and undecidable propositions defining our mathematical truths, represented either by classical, quantum and probabilistic Turing Machines…
In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…
We compare and contrast two distinct approaches to understanding the Born rule in de Broglie-Bohm pilot-wave theory, one based on dynamical relaxation over time (advocated by this author and collaborators) and the other based on typicality…
Zurek's derivation of Born's rule using envariance (invariance due to entanglement) is considered to capture the probability in full generality, but only as applied to measurement of a quantum observable. Contrariwise, textbook formulations…
In the following we revisit the frequency interpretation of probability of Richard von Mises, in order to bring the essential implicit notions in focus. Following von Mises, we argue that probability can only be defined for events that can…
A semantics is given to possibilistic logic, a logic that handles weighted classical logic formulae, and where weights are interpreted as lower bounds on degrees of certainty or possibility, in the sense of Zadeh's possibility theory. The…
Objective probability in quantum mechanics is often thought to involve a stochastic process whereby an actual future is selected from a range of possibilities. Everett's seminal idea is that all possible definite futures on the pointer…
We provide foundations for decisions in face of unlikely events by extending the standard framework of Savage to include preferences indexed by a family of events. We derive a subjective lexicographic expected utility representation which…
Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are…