title: Quantum stochastic walks on networks for decision-making.
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.
authors.affiliation: Düsseldorf Institute for Competition Economics (DICE), Heinrich Heine Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany.
authors.forename: Ismael
authors.initials: I
authors.lastname: Martínez-Martínez
authors.affiliation: Instituto de Ciencia de Materiales de Aragón (ICMA), CSIC-Universidad de Zaragoza and Departamento de Física de la Materia Condensada, Universidad de Zaragoza, E-50009 Zaragoza, Spain.
authors.forename: Eduardo
authors.initials: E
authors.lastname: Sánchez-Burillo
mesh_terms: D002755:Choice Behavior; D003071:Cognition; D003657:Decision Making; D006801:Humans; D015233:Models, Statistical; D000068956:Prisoner Dilemma; D011789:Quantum Theory; D013269:Stochastic Processes; D013997:Time Factors