scholarly journals Quantum generalized observables framework for psychological data: a case of preference reversals in US elections

2017 ◽  
Vol 375 (2106) ◽  
pp. 20160391 ◽  
Author(s):  
Polina Khrennikova ◽  
Emmanuel Haven
Keyword(s):  
Statistical Data ◽  
Choice Theory ◽  
Transition Probability ◽  
Quantum Probability ◽  
Total Probability ◽  
Preference Reversals ◽  
Positive Operator Valued Measures ◽  
Link Type ◽  
Psychological Data ◽  
Stability Of Preferences

Politics is regarded as a vital area of public choice theory, and it is strongly relying on the assumptions of voters’ rationality and as such, stability of preferences. However, recent opinion polls and real election outcomes in the USA have shown that voters often engage in ‘ticket splitting’, by exhibiting contrasting party support in Congressional and Presidential elections (cf. Khrennikova 2014 Phys. Scripta T163 , 014010 ( doi:10.1088/0031-8949/2014/T163/014010 ); Khrennikova & Haven 2016 Phil. Trans. R. Soc. A 374 , 20150106 ( doi:10.1098/rsta.2015.0106 ); Smith et al. 1999 Am. J. Polit. Sci. 43 , 737–764 ( doi:10.2307/2991833 )). Such types of preference reversals cannot be mathematically captured via the formula of total probability, thus showing that voters’ decision making is at variance with the classical probabilistic information processing framework. In recent work, we have shown that quantum probability describes well the violation of Bayesian rationality in statistical data of voting in US elections, through the so-called interference effects of probability amplitudes. This paper is proposing a novel generalized observables framework of voting behaviour, by using the statistical data collected and analysed in previous studies by Khrennikova (Khrennikova 2015 Lect. Notes Comput. Sci. 8951 , 196–209) and Khrennikova & Haven (Khrennikova & Haven 2016 Phil. Trans. R. Soc. A 374 , 20150106 ( doi:10.1098/rsta.2015.0106 )). This framework aims to overcome the main problems associated with the quantum probabilistic representation of psychological data, namely the non-double stochasticity of transition probability matrices. We develop a simplified construction of generalized positive operator valued measures by formulating special non-orthonormal bases with respect to these operators. This article is part of the themed issue ‘Second quantum revolution: foundational questions’.

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.

scholarly journals Roots of quantum computing supremacy: superposition, entanglement, or complementarity?

2021 ◽  
Author(s):  
Andrei Khrennikov
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Probability Distributions ◽  
Statistical Tests ◽  
Joint Probability ◽  
Quantum Probability ◽  
Quantum Nonlocality ◽  
Total Probability ◽  
Probabilistic Algorithms ◽  
Quantum Phenomena

AbstractThe recent claim of Google to have brought forth a breakthrough in quantum computing represents a major impetus to further analyze the foundations for any claims of superiority regarding quantum algorithms. This note attempts to present a conceptual step in this direction. I start with a critical analysis of what is commonly referred to as entanglement and quantum nonlocality and whether or not these concepts may be the basis of quantum superiority. Bell-type experiments are then interpreted as statistical tests of Bohr’s principle of complementarity (PCOM), which is, thus, given a foothold within the area of quantum informatics and computation. PCOM implies (by its connection to probability) that probabilistic algorithms may proceed without the knowledge of joint probability distributions (jpds). The computation of jpds is exponentially time consuming. Consequently, classical probabilistic algorithms, involving the computation of jpds for n random variables, can be outperformed by quantum algorithms (for large values of n). Quantum probability theory (QPT) modifies the classical formula for the total probability (FTP). Inference based on the quantum version of FTP leads to a constructive interference that increases the probability of some events and reduces that of others. The physical realization of this probabilistic advantage is based on the discreteness of quantum phenomena (as opposed to the continuity of classical phenomena).

Rational Choice Theory, Heuristics, and Biases

2017 ◽  
Author(s):  
Megan Eileen Collins ◽  
Thomas A. Loughran
Keyword(s):  
Rational Choice ◽  
Rational Choice Theory ◽  
Choice Theory ◽  
Rational Behavior ◽  
Limited Time ◽  
Preference Reversals ◽  
Heuristics And Biases ◽  
Growing Body ◽  
The Face ◽  
Time Information

A growing body of research on offender decision making has focused on studying the use of heuristic biases, or cognitive shortcuts taken in certain situations, when offenders make decisions in the face of uncertainty. The idea is that when offenders (or any individuals) are contemplating uncertain decisions with limited time, information, or resources to make a rational choice calculus, heuristics enable a suitable decision to be reached quickly. However, often heuristics can lead to biases, errors, preference reversals, or suboptimal decisions. This chapter considers departures from rational behavior and heuristics and biases, specifically how the latter have been integrated into the study of offenders’ choice calculus. In particular, it reviews how biases and deviations from rationality have been routinely observed when studying offender decisions.

scholarly journals Instability of political preferences and the role of mass media: a dynamical representation in a quantum framework

2016 ◽  
Vol 374 (2058) ◽  
pp. 20150106 ◽  
Author(s):  
Polina Khrennikova ◽  
Emmanuel Haven
Keyword(s):  
Mass Media ◽  
Statistical Data ◽  
Political Information ◽  
The Political ◽  
Total Probability ◽  
Preference Reversal ◽  
Science Literature ◽  
The Us ◽  
The Mass Media ◽  
The Impact

We search to devise a new paradigm borrowed from concepts and mathematical tools of quantum physics, to model the decision-making process of the US electorate. The statistical data of the election outcomes in the period between 2008 and 2014 is analysed, in order to explore in more depth the emergence of the so-called divided government. There is an increasing urge in the political literature which indicates that preference reversal (strictly speaking the violation of the transitivity axiom) is a consequence of the so-called non-separability phenomenon (i.e. a strong interrelation of choices). In the political science literature, non-separable behaviour is characterized by a conditioning of decisions on the outcomes of some issues of interest. An additional source of preference reversal is ascribed to the time dynamics of the voters’ cognitive states, in the context of new upcoming political information. As we discuss in this paper, the primary source of political information can be attributed to the mass media. In order to shed more light on the phenomenon of preference reversal among the US electorate, we accommodate the obtained statistical data in a classical probabilistic (Kolmogorovian) scheme. Based on the obtained results, we attribute the strong ties between the voters non-separable decisions that cannot be explained by conditioning with the Bayes scheme, to the quantum phenomenon of entanglement . Second, we compute the degree of interference of voters’ belief states with the aid of the quantum analogue of the formula of total probability. Lastly, a model, based on the quantum master equation, to incorporate the impact of the mass media bath is proposed.

scholarly journals Probabilities and Epistemic Operations in the Logics of Quantum Computation

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 837 ◽  
Author(s):  
Maria Dalla Chiara ◽  
Hector Freytes ◽  
Roberto Giuntini ◽  
Roberto Leporini ◽  
Giuseppe Sergioli
Keyword(s):  
Quantum Information ◽  
Quantum Computation ◽  
Transition Probability ◽  
Quantum Probability ◽  
Quantum States ◽  
Quantum Version ◽  
Logical Connectives ◽  
Quantum Computational Logics ◽  
Absolute Concept ◽  
Relative Concept

Quantum computation theory has inspired new forms of quantum logic, called quantum computational logics, where formulas are supposed to denote pieces of quantum information, while logical connectives are interpreted as special examples of quantum logical gates. The most natural semantics for these logics is a form of holistic semantics, where meanings behave in a contextual way. In this framework, the concept of quantum probability can assume different forms. We distinguish an absolute concept of probability, based on the idea of quantum truth, from a relative concept of probability (a form of transition-probability, connected with the notion of fidelity between quantum states). Quantum information has brought about some intriguing epistemic situations. A typical example is represented by teleportation-experiments. In some previous works we have studied a quantum version of the epistemic operations “to know”, “to believe”, “to understand”. In this article, we investigate another epistemic operation (which is informally used in a number of interesting quantum situations): the operation “being probabilistically informed”.

SIG 15 Perspectives Vol. 20, No. 3, September 2015

2015 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Learning Center ◽  
Link Type

Abstract Download the CE Questions PDF from the toolbar, above. Use the questions to guide your Perspectives reading. When you're ready, purchase the activity from the ASHA Store and follow the instructions to take the exam in ASHA's Learning Center. Available until August 13, 2018.

SIG 11 Perspectives Vol. 22, No. 2, July 2012

2012 ◽  
Vol 22 (2) ◽  
Author(s):  
Kathryn Taylor ◽  
Emily White ◽  
Rachael Kaplan ◽  
Colleen M. O'Rourke
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 11 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 14 Perspectives Vol. 20, No. 3, December 2013

2013 ◽  
Vol 20 (3) ◽  
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 14 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

SIG 17 Perspectives Vol. 2, No. 1, May 2012

2012 ◽  
Vol 2 (1) ◽  
pp. 1-5
Author(s):  
Celeste Domsch
Keyword(s):  
Link Type

Sorry, this activity is no longer available for CEUs. Visit the SIG 17 page on the ASHA Store to see available CE activities. Use the CE questions PDF here as study questions to guide your Perspectives reading.

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