Quantum-like models cannot account for the conjunction fallacy

Human agents happen to judge that a conjunction of two terms is more probable than one of the terms, in contradiction with the rules of classical probabilities—this is the conjunction fallacy. One of the most discussed accounts of this fallacy is currently the quantum-like explanation, which relies on models exploiting the mathematics of quantum mechanics. The aim of this paper is to investigate the empirical adequacy of major quantum-like models which represent beliefs with quantum states. We first argue that they can be tested in three different ways, in a question order effect configuration which is different from the traditional conjunction fallacy experiment. We then carry out our proposed experiment, with varied methodologies from experimental economics. The experimental results we get are at odds with the predictions of the quantum-like models. This strongly suggests that this quantum-like account of the conjunction fallacy fails. Future possible research paths are discussed

A quantum theoretical explanation for probability judgment errors

A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning

Optical tests of Bell's inequalities not resting upon the absurd fair sampling assumption

A simple local hidden-variables model is exhibited which reproduces the results of all performed tests of Bell\'{}s inequalities involving optical photon pairs. For the old atomic-cascade experiments, like Aspect\'{}s, the model agrees with quantum mechanics even for ideal set-ups. For more recent experiments, using parametric down-converted photons, the agreement occurs only for actual experiments, involving low efficiency detectors. Arguments are given against the fair sampling assumption, currently combined with the results of the experiments in order to claim a contradiction with local realism. New tests are proposed which are able to discriminate between quantum mechanics and a restricted, but appealing, family of local hidden-variables models. Such tests require detectors with efficiencies just above 20%.Comment: 19 page

On the Foundations of the Brussels Operational-Realistic Approach to Cognition

The scientific community is becoming more and more interested in the research that applies the mathematical formalism of quantum theory to model human decision-making. In this paper, we provide the theoretical foundations of the quantum approach to cognition that we developed in Brussels. These foundations rest on the results of two decade studies on the axiomatic and operational-realistic approaches to the foundations of quantum physics. The deep analogies between the foundations of physics and cognition lead us to investigate the validity of quantum theory as a general and unitary framework for cognitive processes, and the empirical success of the Hilbert space models derived by such investigation provides a strong theoretical confirmation of this validity. However, two situations in the cognitive realm, 'question order effects' and 'response replicability', indicate that even the Hilbert space framework could be insufficient to reproduce the collected data. This does not mean that the mentioned operational-realistic approach would be incorrect, but simply that a larger class of measurements would be in force in human cognition, so that an extended quantum formalism may be needed to deal with all of them. As we will explain, the recently derived 'extended Bloch representation' of quantum theory (and the associated 'general tension-reduction' model) precisely provides such extended formalism, while remaining within the same unitary interpretative framework.Comment: 21 page

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