Projective Expected Utility

Motivated by several classic decision-theoretic paradoxes, and by analogies with the paradoxes which in physics motivated the development of quantum mechanics, we introduce a projective generalization of expected utility along the lines of the quantum-mechanical generalization of probability theory. The resulting decision theory accommodates the dominant paradoxes, while retaining significant simplicity and tractability. In particular, every finite game within this larger class of preferences still has an equilibrium.Comment: 7 pages, to appear in the Proceedings of Quantum Interaction 200

Laboratory Games and Quantum Behaviour: The Normal Form with a Separable State Space

The subjective expected utility (SEU) criterion is formulated for a particular four-person “laboratory game” that a Bayesian rational decision maker plays with Nature, Chance, and an Experimenter who influences what quantum behaviour is observable by choosing an orthonormal basis in a separable complex Hilbert space of latent variables. Nature chooses a state in this basis, along with an observed data series governing Chance's random choice of consequence. When Gleason's theorem holds, imposing quantum equivalence implies that the expected likelihood of any data series w.r.t. prior beliefs equals the trace of the product of appropriate subjective density and likelihood operators.

Interference Effects in Quantum Belief Networks

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 decisions could not follow the rules of classical probability theory, because humans cannot process large amounts of data in order to make judgements. Consequently, the inferences performed are based on limited data coupled with several heuristics, leading to violations of the law of total probability. This means that probabilistic graphical models based on classical probability theory are too limited to fully simulate and explain various aspects of human decision making. Quantum probability theory was developed in order to accommodate the paradoxical findings that the classical theory could not explain. Recent findings in cognitive psychology revealed that quantum probability can fully describe human decisions in an elegant framework. Their findings suggest that, before taking a decision, human thoughts are seen as superposed waves that can interfere with each other, influencing the final decision. In this work, we propose a new Bayesian Network based on the psychological findings of cognitive scientists. We made experiments with two very well known Bayesian Networks from the literature. The results obtained revealed that the quantum like Bayesian Network can affect drastically the probabilistic inferences, specially when the levels of uncertainty of the network are very high (no pieces of evidence observed). When the levels of uncertainty are very low, then the proposed quantum like network collapses to its classical counterpart

Applying Quantum Principles to Psychology

This article starts out with a detailed example illustrating the utility of applying quantum probability to psychology. Then it describes several alternative mathematical methods for mapping fundamental quantum concepts (such as state preparation, measurement, state evolution) to fundamental psychological concepts (such as stimulus, response, information processing). For state preparation, we consider both pure states and densities with mixtures. For measurement, we consider projective measurements and positive operator valued measurements. The advantages and disadvantages of each method with respect to applications in psychology are discussed.Comment: one of the aims of this review paper is to attract attention of experts in quantum information and probability (as well as in quantum foundations) to a new rapidly growing field of applications of quantum theory. The paper establishes the correspondence between concepts of quantum theory and concepts of cognitive science and psychology. Submitted to Physica Script

Elementary Quantum Mechanical Principles and Social Science: Is There a Connection?

In this paper we provide first for a brief overview of some of the work which has been performed on the interface of quantum mechanics and macroscopic systems (such as economics). We then provide for an overview of how such quantum mechanical concepts can enter financial option pricing theory. We round off the paper with some suggestions on where this area of research can be heading in the near future.superposition; wave function; Black-Scholes option price; information function; probability amplitude; Schrödinger equation; Newton- Bohm trajectory; mean forward (backward) derivative

Introducing Quantum-Like Influence Diagrams for Violations of the Sure Thing Principle

It is the focus of this work to extend and study the previously proposed quantum-like Bayesian networks to deal with decision-making scenarios by incorporating the notion of maximum expected utility in influence diagrams. The general idea is to take advantage of the quantum interference terms produced in the quantum-like Bayesian Network to influence the probabilities used to compute the expected utility of some action. This way, we are not proposing a new type of expected utility hypothesis. On the contrary, we are keeping it under its classical definition. We are only incorporating it as an extension of a probabilistic graphical model in a compact graphical representation called an influence diagram in which the utility function depends on the probabilistic influences of the quantum-like Bayesian network. Our findings suggest that the proposed quantum-like influence digram can indeed take advantage of the quantum interference effects of quantum-like Bayesian Networks to maximise the utility of a cooperative behaviour in detriment of a fully rational defect behaviour under the prisoner's dilemma game