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Quantum stochastic walks on networks for decision-making.

Martínez-Martínez I, Sánchez-Burillo E - Sci Rep (2016)

Bottom Line: Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory.Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities.We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics.

View Article: PubMed Central - PubMed

Affiliation: Düsseldorf Institute for Competition Economics (DICE), Heinrich Heine Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.

ABSTRACT
Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

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Violation of the Sure Thing Principle.(a) Model fit for the experimental results in Busemeyer et al.51. See discussion in the main text. (b) Probability of defection for different values of λ independent of φ when the model is restricted to the classical part (α = 1).
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f5: Violation of the Sure Thing Principle.(a) Model fit for the experimental results in Busemeyer et al.51. See discussion in the main text. (b) Probability of defection for different values of λ independent of φ when the model is restricted to the classical part (α = 1).

Mentions: In order to make our case, we reproduce the experimental results in Busemeyer et al.51. The entries of the payoff matrix are a = 20, b = 5, c = 10, and d = 25. Their results show a defection rate of 91% when the subjects know their opponent will defect, and of 84% when they know the rival’s action is to cooperate. The Sure Thing Principle is violated in this experiment because the defection rate when the choice of the opponents is unknown drops to 66%. See model fit to this data in Fig. 5-Panel (a).


Quantum stochastic walks on networks for decision-making.

Martínez-Martínez I, Sánchez-Burillo E - Sci Rep (2016)

Violation of the Sure Thing Principle.(a) Model fit for the experimental results in Busemeyer et al.51. See discussion in the main text. (b) Probability of defection for different values of λ independent of φ when the model is restricted to the classical part (α = 1).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4815055&req=5

f5: Violation of the Sure Thing Principle.(a) Model fit for the experimental results in Busemeyer et al.51. See discussion in the main text. (b) Probability of defection for different values of λ independent of φ when the model is restricted to the classical part (α = 1).
Mentions: In order to make our case, we reproduce the experimental results in Busemeyer et al.51. The entries of the payoff matrix are a = 20, b = 5, c = 10, and d = 25. Their results show a defection rate of 91% when the subjects know their opponent will defect, and of 84% when they know the rival’s action is to cooperate. The Sure Thing Principle is violated in this experiment because the defection rate when the choice of the opponents is unknown drops to 66%. See model fit to this data in Fig. 5-Panel (a).

Bottom Line: Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory.Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities.We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics.

View Article: PubMed Central - PubMed

Affiliation: Düsseldorf Institute for Competition Economics (DICE), Heinrich Heine Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.

ABSTRACT
Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information. Evidence shows promise of a more general quantum theory providing a better explanation of the dynamics and structure of real decision-making processes than classical probability theory. Inspired by this, we show how the behavioral choice-probabilities can arise as the unique stationary distribution of quantum stochastic walkers on the classical network defined from Luce's response probabilities. This work is relevant because (i) we provide a very general framework integrating the positive characteristics of both quantum and classical approaches previously in confrontation, and (ii) we define a cognitive network which can be used to bring other connectivist approaches to decision-making into the quantum stochastic realm. We model the decision-maker as an open system in contact with her surrounding environment, and the time-length of the decision-making process reveals to be also a measure of the process' degree of interplay between the unitary and irreversible dynamics. Implementing quantum coherence on classical networks may be a door to better integrate human-like reasoning biases in stochastic models for decision-making.

No MeSH data available.


Related in: MedlinePlus