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.
Highlights
Recent experiments report violations of the classical law of total probability and incompatibility of certain mental representations when humans process and react to information
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
Summary
The cognitive state evolving as a quantum open system. We describe the cognitive state of the agent in a Hilbert space , and we denote a state by |ψ〉. The decision-maker faces simultaneously another cognitive activity: the formation of her beliefs about the state of the world (either a forecast on some external random event, or a prediction on the behavior of an interacting agent) We model this process through the definition of the matrix B such that its entries connect nodes of the form ai(Ωk) to those of the form ai(Ωl). The dynamical process of decision-making incorporates this effect as a consequence of higher values of λ generating lower weights in the connections of the cognitive network C(λ, φ) inherited from the matrix Π (λ) This effect is hardly obtainable with standard models based on decision-making trees, since their sequential structure does not allow for the interaction between nodes belonging to different states of the world. One can understand this by noticing that several type of transitions are not present in the dynamics when only the CRW applies (see Fig. 1-Panel (b) once again)
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