Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences

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

Polina Khrennikova, Emmanuel E. Haven

Published Nov 30, 2015• 34 citations
Publisher

Abstract

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.

DOI
10.1098/rsta.2015.0106

Related papers

Voters’ Preferences in a Quantum Framework

Polina Khrennikova, Emmanuel E. Haven

Politics is regarded as a vital area of social science and strongly relies on the assumptions of voters’ rationality and as such the stability of preferences (at least in decisions that are made simultaneously). The phenomenon of divided government that has dominated the US political arena for many election periods over the last 40 years is not consistent with the notion of stable preferences of voters. The authors claim that there is no well defined ranking of their preferences on their utility function of “political preferences.” Recently, this problem has been handled by using the novel approach based on the formalism of quantum mechanics. The theory of quantum decision-making is applicable to the modeling of irrational and biased behavior of voters as well as to the nonseparability of their preferences. Irrationality, biases, and nonseparability lead to a deeper uncertainty than classical probabilistic uncertainty. In particular, quantum probability describes well the violation of Bayesian rationality. The authors model this nonclassical uncertainty in voters’ preferences by using elements of the fundamental quantum information structures such as superposition and entanglement. The chapter is an introduction to the quantum modeling of the behavior of an electorate with unstable preferences (contextual preferences) and the authors use one of the most potent theories of adaptive dynamics, namely, the theory of open quantum systems. In this model a voter’s decision is created in the process of interaction with an information bath in which the mass media play the key role. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Palgrave Macmillan UK eBooks•Jan 1, 2017•1 citation

Order effect in a study on US voters’ preferences: quantum framework representation of the observables

Polina Khrennikova

The US political system in the recent years has been mainly formed by a Divided Government, which is regarded as a consequence of 'non-separability' of voters' preferences. The non- separability phenomenon emerges as a result of strong correlations that the voters establish between their preferences for the Congress and the White House contests. We investigate with help of the empirical data from the Smith et al (1999 J. Polit. Sci. 43 737–764) study what implications the upcoming information (encoded in the observables- questions) has on the non- separability emergence. We show that the informational context of the questions alters the preference frequencies that cannot be captured in a classical probabilistic framework. We attribute the changes to the incompatibility of observables C and P, which correspond to questions being asked. We embed our data in a quantum framework and model the voters' mental state evolution as it is impacted by the operators, to show the non-commutativity of the transition probabilities as a result of the question order effect.

Physica Scripta•Dec 1, 2014•16 citations

The quantum-like description of the dynamics of party governance in the US political system

Polina Khrennikova, Andrei Yu. Khrennikov, Emmanuel E. Haven

This paper is devoted to the application of the mathematical formalism of quantum mechanics to social (political) science. By using the quantum dynamical equations we model the process of decision making in US elections. The crucial point we attempt to make is that the voter's mental state can be represented as a superposition of two possible choices for either republicans or democrats. However, reality dictates a more complicated situation: typically a voter participates in two elections, i.e. the congress and the presidential elections. In both elections he/she has to decide between two choices. This very feature of the US election system requires that the mental state is represented by a 2-qubit state corresponding to the superposition of 4 different choices (e.g. for republicans in the congress; for the president as a democrat). The main issue of this paper is to describe the dynamics of the voters' mental states taking in account the mental and socio- political environment. What is truly novel in this paper is that instead of using Schrödinger's equation to describe the dynamics in an absence of interactions, we here apply the quantum master equation. This equation describes quantum decoherence, i.e., resolution from superposition to a definite choice.

arXiv:1206.2888•Jun 11, 2012•3 citations

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

Polina Khrennikova, Emmanuel E. Haven

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 2014Phys. ScriptaT163, 014010 ( doi:10.1088/0031-8949/2014/T163/014010 ); Khrennikova & Haven 2016Phil. Trans. R. Soc. A374, 20150106 ( doi:10.1098/rsta.2015.0106 ); Smithet al.1999Am. 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-calledinterference effectsof 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 2015Lect. Notes Comput. Sci.8951, 196–209) and Khrennikova & Haven (Khrennikova & Haven 2016Phil. Trans. R. Soc. A374, 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 thenon-double stochasticityof 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’.

Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences•Oct 2, 2017•5 citations

Quantum Propensity Modeling of Economic Decision-Making: Capturing Preference Reversals and Contextual Interference

Ece Kozan

Classical economic decision-making models rely on assumptions of stable preferences, logical consistency, and additive probabilities. Yet decades of behavioral research consistently reveal systematic violations of these principles, including preference reversals, framing effects, and context-sensitive judgment patterns that challenge rational-choice theory. This study examines how quantum propensity modeling—grounded in mathematical structures derived from quantum theory—offers a compelling alternative for understanding these anomalies. Unlike classical models, quantum cognition treats decisions as evolving cognitive states represented in superposition, allowing individuals to hold simultaneous, uncertain predispositions before committing to a choice. Contextual interference, probability amplitude effects, and state-dependent transitions enable these models to accurately describe how information order, framing, and emotional cues distort decision trajectories. Through qualitative analysis of case studies from behavioral economics, cognitive psychology, and decision theory, this research highlights how quantum models capture the non-commutativity of choices, the instability of preferences under uncertainty, and the mechanisms behind cognitive interference patterns. The findings suggest that quantum propensity modeling not only explains well-documented behavioral anomalies more coherently than classical frameworks but also provides a theoretical foundation for applications in market forecasting, algorithmic pricing, consumer behavior analysis, and policy design. Ultimately, the study argues that quantum-inspired decision models represent a transformative step toward more realistic, context-aware interpretations of economic behavior.

Next generation.•Dec 10, 2025•0 citations

Evolution of quantum-like modeling in decision making processes

Polina Khrennikova

The application of the mathematical formalism of quantum mechanics to model behavioral patterns in social science and economics is a novel and constantly emerging field. The aim of the so called 'quantum like' models is to model the decision making processes in a macroscopic setting, capturing the particular 'context' in which the decisions are taken. Several subsequent empirical findings proved that when making a decision people tend to violate the axioms of expected utility theory and Savage's Sure Thing principle, thus violating the law of total probability. A quantum probability formula was devised to describe more accurately the decision making processes. A next step in the development of QL-modeling in decision making was the application of Schrödinger equation to describe the evolution of people's mental states. A shortcoming of Schrödinger equation is its inability to capture dynamics of an open system; the brain of the decision maker can be regarded as such, actively interacting with the external environment. Recently the master equation, by which quantum physics describes the process of decoherence as the result of interaction of the mental state with the environmental 'bath', was introduced for modeling the human decision making. The external environment and memory can be referred to as a complex 'context' influencing the final decision outcomes. The master equation can be considered as a pioneering and promising apparatus for modeling the dynamics of decision making in different contexts.

AIP conference proceedings•Jan 1, 2012•17 citations
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.
Politics is regarded as a vital area of social science and strongly relies on the assumptions of voters’ rationality and as such the stability of preferences (at least in decisions that are made simultaneously). The phenomenon of divided government that has dominated the US political arena for many election periods over the last 40 years is not consistent with the notion of stable preferences of voters. The authors claim that there is no well defined ranking of their preferences on their utility function of “political preferences.” Recently, this problem has been handled by using the novel approach based on the formalism of quantum mechanics. The theory of quantum decision-making is applicable to the modeling of irrational and biased behavior of voters as well as to the nonseparability of their preferences. Irrationality, biases, and nonseparability lead to a deeper uncertainty than classical probabilistic uncertainty. In particular, quantum probability describes well the violation of Bayesian rationality. The authors model this nonclassical uncertainty in voters’ preferences by using elements of the fundamental quantum information structures such as superposition and entanglement. The chapter is an introduction to the quantum modeling of the behavior of an electorate with unstable preferences (contextual preferences) and the authors use one of the most potent theories of adaptive dynamics, namely, the theory of open quantum systems. In this model a voter’s decision is created in the process of interaction with an information bath in which the mass media play the key role. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
The US political system in the recent years has been mainly formed by a Divided Government, which is regarded as a consequence of 'non-separability' of voters' preferences. The non- separability phenomenon emerges as a result of strong correlations that the voters establish between their preferences for the Congress and the White House contests. We investigate with help of the empirical data from the Smith et al (1999 J. Polit. Sci. 43 737–764) study what implications the upcoming information (encoded in the observables- questions) has on the non- separability emergence. We show that the informational context of the questions alters the preference frequencies that cannot be captured in a classical probabilistic framework. We attribute the changes to the incompatibility of observables C and P, which correspond to questions being asked. We embed our data in a quantum framework and model the voters' mental state evolution as it is impacted by the operators, to show the non-commutativity of the transition probabilities as a result of the question order effect.
This paper is devoted to the application of the mathematical formalism of quantum mechanics to social (political) science. By using the quantum dynamical equations we model the process of decision making in US elections. The crucial point we attempt to make is that the voter's mental state can be represented as a superposition of two possible choices for either republicans or democrats. However, reality dictates a more complicated situation: typically a voter participates in two elections, i.e. the congress and the presidential elections. In both elections he/she has to decide between two choices. This very feature of the US election system requires that the mental state is represented by a 2-qubit state corresponding to the superposition of 4 different choices (e.g. for republicans in the congress; for the president as a democrat). The main issue of this paper is to describe the dynamics of the voters' mental states taking in account the mental and socio- political environment. What is truly novel in this paper is that instead of using Schrödinger's equation to describe the dynamics in an absence of interactions, we here apply the quantum master equation. This equation describes quantum decoherence, i.e., resolution from superposition to a definite choice.
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 2014Phys. ScriptaT163, 014010 ( doi:10.1088/0031-8949/2014/T163/014010 ); Khrennikova & Haven 2016Phil. Trans. R. Soc. A374, 20150106 ( doi:10.1098/rsta.2015.0106 ); Smithet al.1999Am. 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-calledinterference effectsof 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 2015Lect. Notes Comput. Sci.8951, 196–209) and Khrennikova & Haven (Khrennikova & Haven 2016Phil. Trans. R. Soc. A374, 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 thenon-double stochasticityof 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’.
Classical economic decision-making models rely on assumptions of stable preferences, logical consistency, and additive probabilities. Yet decades of behavioral research consistently reveal systematic violations of these principles, including preference reversals, framing effects, and context-sensitive judgment patterns that challenge rational-choice theory. This study examines how quantum propensity modeling—grounded in mathematical structures derived from quantum theory—offers a compelling alternative for understanding these anomalies. Unlike classical models, quantum cognition treats decisions as evolving cognitive states represented in superposition, allowing individuals to hold simultaneous, uncertain predispositions before committing to a choice. Contextual interference, probability amplitude effects, and state-dependent transitions enable these models to accurately describe how information order, framing, and emotional cues distort decision trajectories. Through qualitative analysis of case studies from behavioral economics, cognitive psychology, and decision theory, this research highlights how quantum models capture the non-commutativity of choices, the instability of preferences under uncertainty, and the mechanisms behind cognitive interference patterns. The findings suggest that quantum propensity modeling not only explains well-documented behavioral anomalies more coherently than classical frameworks but also provides a theoretical foundation for applications in market forecasting, algorithmic pricing, consumer behavior analysis, and policy design. Ultimately, the study argues that quantum-inspired decision models represent a transformative step toward more realistic, context-aware interpretations of economic behavior.
The application of the mathematical formalism of quantum mechanics to model behavioral patterns in social science and economics is a novel and constantly emerging field. The aim of the so called 'quantum like' models is to model the decision making processes in a macroscopic setting, capturing the particular 'context' in which the decisions are taken. Several subsequent empirical findings proved that when making a decision people tend to violate the axioms of expected utility theory and Savage's Sure Thing principle, thus violating the law of total probability. A quantum probability formula was devised to describe more accurately the decision making processes. A next step in the development of QL-modeling in decision making was the application of Schrödinger equation to describe the evolution of people's mental states. A shortcoming of Schrödinger equation is its inability to capture dynamics of an open system; the brain of the decision maker can be regarded as such, actively interacting with the external environment. Recently the master equation, by which quantum physics describes the process of decoherence as the result of interaction of the mental state with the environmental 'bath', was introduced for modeling the human decision making. The external environment and memory can be referred to as a complex 'context' influencing the final decision outcomes. The master equation can be considered as a pioneering and promising apparatus for modeling the dynamics of decision making in different contexts.