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WIREs Cogn Sci
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Comparison of Markov versus quantum dynamical models of human decision making

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Abstract What kind of dynamic decision process do humans use to make decisions? In this article, two different types of processes are reviewed and compared: Markov and quantum. Markov processes are based on the idea that at any given point in time a decision maker has a definite and specific level of support for available choice alternatives, and the dynamic decision process is represented by a single trajectory that traces out a path across time. When a response is requested, a person's decision or judgment is generated from the current location along the trajectory. By contrast, quantum processes are founded on the idea that a person's state can be represented by a superposition over different degrees of support for available choice options, and that the dynamics of this state form a wave moving across levels of support over time. When a response is requested, a decision or judgment is constructed out of the superposition by “actualizing” a specific degree or range of degrees of support to create a definite state. The purpose of this article is to introduce these two contrasting theories, review empirical studies comparing the two theories, and identify conditions that determine when each theory is more accurate and useful than the other. This article is categorized under: Economics > Individual Decision‐Making Psychology > Reasoning and Decision Making Psychology > Theory and Methods
Expected time course of mean preference ratings generated from a typical Markov random walk model (left), a deterministic oscillating approach‐avoidance model (middle), and quantum walk model (right)
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Comparison of stopping times for Markov (left panel) and quantum (right panel) models. Horizontal axis is time (in the same arbitrary units for both models) and vertical axis is relative frequency of a stopping time. The parameters were set so that both models produce the same choice accuracy. Note that the horizontal and vertical scales are different because the quantum model is faster than the Markov model
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Illustrations of design for double confidence judgment experiment. Each condition had a different pair of time points (t1 and t2) for requests for ratings: the time intervals of the first two conditions are contained within condition 3. Conditions 1 and 2 were used to estimate model parameters and then these same model parameters were used to predict the ratings for condition 3. The time point t0 corresponds to stimulus onset
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Diagram of the choice‐confidence task. A fixation point indicated the choice/no‐choice condition, then the stimulus was shown for 0.5 s. A prompt (t1) then cued a decision on the direction of the dot motion (choice condition) or a motor response (no‐choice condition). The stimulus remained on the screen. A second prompt (t2) then cued a confidence rating on the direction of the dot motion. Finally, feedback was given on the accuracy of their responses
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Illustration of Markov (left) and quantum (right) evolution of probability distributions over time. The horizontal axis represents 101 belief states associated with subjective evidence scale values ranging from 0 to 100 in one‐unit steps. The vertical axis represents probability corresponding to each evidence level. The separate curves moving from left to right represent increasing processing time
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Diagram of a state representation of a Markov and a quantum random walk model. In the Markov model, evidence (shaded state) evolves over time by moving from state to state, occupying one definite evidence level at any given time. In the quantum model the decision‐maker is in an indefinite evidence state, with each evidence level having a probability amplitude (shadings) at each point in time
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Markov and quantum random walk models generate diverging predictions for how evidence evolves over time and how measurements like decisions interact with subsequent responses
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Pattern of mean preference strength elicited at different time points following a decision (choice) or irrelevant button press (no‐choice). Error bars indicate ±1 unit of standard error—differences between choice and no‐choice are substantive at 9‐ and 18‐s time points
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Psychology > Theory and Methods
Psychology > Reasoning and Decision Making
Economics > Individual Decision-Making

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