scholarly journals Perspectives on Correctness in Probabilistic Inference from Psychology

2019 ◽  
Vol 22 ◽  
Author(s):  
Emmanuel M. Pothos ◽  
Irina Basieva ◽  
Andrei Khrennikov ◽  
James M. Yearsley
Keyword(s):  
Decision Making ◽  
Information Theory ◽  
Probability Theory ◽  
Probabilistic Inference ◽  
Quantum Probability ◽  
Conjunction Fallacy ◽  
Selection Task ◽  
Classical Probability ◽  
Wason Selection Task ◽  
Classical Probability Theory

Abstract Research into decision making has enabled us to appreciate that the notion of correctness is multifaceted. Different normative framework for correctness can lead to different insights about correct behavior. We illustrate the shifts for correctness insights with two tasks, the Wason selection task and the conjunction fallacy task; these tasks have had key roles in the development of logical reasoning and decision making research respectively. The Wason selection task arguably has played an important part in the transition from understanding correctness using classical logic to classical probability theory (and information theory). The conjunction fallacy has enabled a similar shift from baseline classical probability theory to quantum probability. The focus of this overview is the latter, as it represents a novel way for understanding probabilistic inference in psychology. We conclude with some of the current challenges concerning the application of quantum probability theory in psychology in general and specifically for the problem of understanding correctness in decision making.

Uncertainty about the value of quantum probability for cognitive modeling

2013 ◽  
Vol 36 (3) ◽  
pp. 279-280 ◽  
Author(s):  
Christina Behme
Keyword(s):  
Probability Theory ◽  
Cognitive Modeling ◽  
Quantum Probability ◽  
Convincing Evidence ◽  
Logical Possibility ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Human Rationality

AbstractI argue that the overly simplistic scenarios discussed by Pothos & Busemeyer (P&B) establish at best that quantum probability theory (QPT) is a logical possibility allowing distinct predictions from classical probability theory (CPT). The article fails, however, to provide convincing evidence for the proposal that QPT offers unique insights regarding cognition and the nature of human rationality.

scholarly journals Quantum Bayesianism as the basis of general theory of decision-making

2016 ◽  
Vol 374 (2068) ◽  
pp. 20150245 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Decision Making ◽  
Probability Theory ◽  
Subjective Probability ◽  
Quantum Probability ◽  
Total Probability ◽  
Interpretation Of Quantum Mechanics ◽  
Classical Probability ◽  
Probability Interpretation ◽  
Formula Of Total Probability

We discuss the subjective probability interpretation of the quantum-like approach to decision making and more generally to cognition. Our aim is to adopt the subjective probability interpretation of quantum mechanics, quantum Bayesianism (QBism), to serve quantum-like modelling and applications of quantum probability outside of physics. We analyse the classical and quantum probabilistic schemes of probability update, learning and decision-making and emphasize the role of Jeffrey conditioning and its quantum generalizations. Classically, this type of conditioning and corresponding probability update is based on the formula of total probability—one the basic laws of classical probability theory.

Quantum Models of Cognition and Decision

2015 ◽  
Author(s):  
Jerome R. Busemeyer ◽  
Zheng Wang ◽  
Emmanuel Pothos
Keyword(s):  
Decision Making ◽  
Probability Theory ◽  
Dynamic Systems ◽  
Quantum Probability ◽  
Quantum Dynamic ◽  
Classical Probability ◽  
New Formalism ◽  
Probability Judgments ◽  
Advantages And Disadvantages ◽  
Quantum Approach

Quantum probability theory provides a new formalism for constructing probabilistic and dynamic systems of cognition and decision. The purpose of this chapter is to introduce psychologists to this fascinating theory. This chapter is organized into six sections. First, some of the basic psychological principles supporting a quantum approach to cognition and decision are summarized; second, some notations and definitions needed to understand quantum probability theory are presented; third, a comparison of quantum and classical probability theories is presented; fourth, quantum probability theory is used to account for some paradoxical findings in the field of human probability judgments; fifth, a comparison of quantum and Markov dynamic theories is presented; and finally, a quantum dynamic model is used to account for some puzzling findings of decision-making research. The chapter concludes with a summary of advantages and disadvantages of a quantum probability theoretical framework for modeling cognition and decision.

scholarly journals Probabilistic frames for non-Boolean phenomena

2016 ◽  
Vol 374 (2058) ◽  
pp. 20150102 ◽  
Author(s):  
Louis Narens
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Quantum Probability ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Foundations Of Probability ◽  
Quantifying Uncertainty ◽  
Behavioural Sciences ◽  
Generalized Probability ◽  
Provided Examples

Classical probability theory, as axiomatized in 1933 by Andrey Kolmogorov, has provided a useful and almost universally accepted theory for describing and quantifying uncertainty in scientific applications outside quantum mechanics. Recently, cognitive psychologists and mathematical economists have provided examples where classical probability theory appears inadequate but the probability theory underlying quantum mechanics appears effective. Formally, quantum probability theory is a generalization of classical probability. This article explores relationships between generalized probability theories, in particular quantum-like probability theories and those that do not have full complementation operators (e.g. event spaces based on intuitionistic logic), and discusses how these generalizations bear on important issues in the foundations of probability and the development of non-classical probability theories for the behavioural sciences.

An Overview of Uncertainty Concepts Related to Mechanical and Civil Engineering

2015 ◽  
Vol 1 (4) ◽  
Author(s):  
Ross B. Corotis
Keyword(s):  
Information Theory ◽  
Probability Theory ◽  
Structural Engineering ◽  
Partial Information ◽  
Economic Aspects ◽  
Partial Knowledge ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Generalized Information ◽  
Generalized Information Theory

Infrastructure decisions reflect multiple social, political, and economic aspects of society, leading to information/partial knowledge and uncertainty in many forms. Alternatives to classical probability theory may be better suited to situations involving partial information, especially when the sources and nature of the uncertainty are disparate. Methods under the umbrella of generalized information theory enhance the treatment of uncertainty by incorporating notions of belief, evidence, fuzziness, possibility, ignorance, interactivity, and linguistic information. This paper presents an overview of some of these theories and examines the use of alternate mathematical approaches in the treatment of uncertainty, with structural engineering examples.

scholarly journals Cold and hot cognition: Quantum probability theory and realistic psychological modeling

2013 ◽  
Vol 36 (3) ◽  
pp. 282-283
Author(s):  
Philip J. Corr
Keyword(s):  
Decision Making ◽  
Probability Theory ◽  
Nonlinear Dynamic ◽  
Psychological Theory ◽  
Quantum Probability ◽  
Formal Modeling ◽  
Information Uncertainty ◽  
Dynamic Effects ◽  
Classical Probability ◽  
Human Decision

AbstractTypically, human decision making is emotionally “hot” and does not conform to “cold” classical probability (CP) theory. As quantum probability (QP) theory emphasises order, context, superimposition states, and nonlinear dynamic effects, one of its major strengths may be its power to unify formal modeling and realistic psychological theory (e.g., information uncertainty, anxiety, and indecision, as seen in the Prisoner's Dilemma).

scholarly journals Quantum mechanics as a generalized probability theory

2020 ◽  
Author(s):  
William Icefield
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Quantum Probability ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Principle Of Maximum Entropy ◽  
Principle Of Indifference ◽  
Reconstruction Project ◽  
Principle Of Maximum ◽  
Generalized Probability

When quantum mechanics is understood as a new generalized theory of probability - to be called the quantum probability theory - mysteries and controversies regarding quantum mechanics are dissolved. In the classical probability theory, that a measurement of some system requires an additional measurement apparatus is of insignificant importance - in the quantum probability theory, this comes to change. For one central single reason around a particular classical probability equation, the generalized probability view has not gained much traction, despite the fact that this essentially echoes (and provides logical underpinnings of) the conventional wisdom that `quantum mechanics just works as it is.' A classical probability axiom is just an initial intuition - there is no reason why we have to dogmatically cling onto axioms that can clearly be generalized. Issues with the principle of indifference in the classical probability theory are emphasized, along with the quantum reconstruction project of deriving quantum mechanics from epistemic requirements and potential quantum gravity consequences from the principle of maximum entropy.

If quantum probability = classical probability + bounded cognition; is this good, bad, or unnecessary?

2013 ◽  
Vol 36 (3) ◽  
pp. 304-305
Author(s):  
Tim Rakow
Keyword(s):  
Probability Theory ◽  
Probabilistic Models ◽  
Current Knowledge ◽  
Quantum Probability ◽  
Model Specification ◽  
Probability Models ◽  
Classical Probability ◽  
Classical Probability Theory ◽  
Knowledge States

AbstractQuantum probability models may supersede existing probabilistic models because they account for behaviour inconsistent with classical probability theory that are attributable to normal limitations of cognition. This intriguing position, however, may overstate weaknesses in classical probability theory by underestimating the role of current knowledge states and may under-employ available knowledge about the limitations of cognitive processes. In addition, flexibility in model specification has risks for the use of quantum probability.

scholarly journals A search for a stochastic archetype of quantum probability

2021 ◽  
Author(s):  
Tim C Jenkins
Keyword(s):  
Probability Theory ◽  
Quantum Mechanics ◽  
Probability Density ◽  
Random Variables ◽  
Quantum Probability ◽  
Interference Term ◽  
Mathematical Foundation ◽  
Classical Probability ◽  
Quantum Process ◽  
Probability Densities

Abstract Superposed wavefunctions in quantum mechanics lead to a squared amplitude that introduces interference into a probability density, which has long been a puzzle because interference between probability densities exists nowhere else in probability theory. In recent years Man’ko and co-authors have successfully reconciled quantum and classical probability using a symplectic tomographic model. Nevertheless, there remains an unexplained coincidence in quantum mechanics, namely that mathematically the interference term in the squared amplitude of superposed wavefunctions has the form of a variance of a sum of correlated random variables and we examine whether there could be an archetypical variable behind quantum probability that provides a mathematical foundation that observes both quantum and classical probability directly. The properties that would need to be satisfied for this to be the case are identified, and a generic variable that satisfies them is found that would be present everywhere, transforming into a process-specific variable wherever a quantum process is active. This hidden generic variable appears to be such an archetype.

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