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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.

No MeSH data available.


Related in: MedlinePlus

From the tree to the network.A first example step by step. We define an arbitrary toy-problem in which a decision-maker (the column-agent) chooses one option among S = {L, M, R}, with the payoff being a function of the state of the world Ω ∈ W = {U, D}. The numbers in panel (a) represent the profit for the column-agent given her choice of action and the state of the world that is realized, in the form of a payoff matrix. In panel (b) we show the normative representation of the sequential decision-making process as a tree. In this setting, the column-agent first makes her own belief about the state of the world and then, she optimizes her action as a response to her belief. In panel (c) we model the same problem with a networked topology. The numbers in the links represent the entries {πij} of the matrix Π(λ). They are weighted according to Eq. (3), with λ = 1 and using the information in panel (a). These two connected components define the dynamical comparison between alternatives, for each possible state of the world. This process happens simultaneously with the formation of beliefs through the matrix B (green connections), as stated in Eq. (4). For basic illustrative purposes, we do not need to specify if the state of the world is a random variable, or the choice of a row-player whose payoff rule is unknown for the column-player. We elaborate further on this issue and its influence on the definition of the matrix B in the main text.
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f2: From the tree to the network.A first example step by step. We define an arbitrary toy-problem in which a decision-maker (the column-agent) chooses one option among S = {L, M, R}, with the payoff being a function of the state of the world Ω ∈ W = {U, D}. The numbers in panel (a) represent the profit for the column-agent given her choice of action and the state of the world that is realized, in the form of a payoff matrix. In panel (b) we show the normative representation of the sequential decision-making process as a tree. In this setting, the column-agent first makes her own belief about the state of the world and then, she optimizes her action as a response to her belief. In panel (c) we model the same problem with a networked topology. The numbers in the links represent the entries {πij} of the matrix Π(λ). They are weighted according to Eq. (3), with λ = 1 and using the information in panel (a). These two connected components define the dynamical comparison between alternatives, for each possible state of the world. This process happens simultaneously with the formation of beliefs through the matrix B (green connections), as stated in Eq. (4). For basic illustrative purposes, we do not need to specify if the state of the world is a random variable, or the choice of a row-player whose payoff rule is unknown for the column-player. We elaborate further on this issue and its influence on the definition of the matrix B in the main text.

Mentions: Note that every node ni(Ω) has KΩ outgoing edges eΩ(i, j), generally with KΩ different weights pΩ(j). See Fig. 2 for a graphical example deriving the matrix Π(λ) from the sequential tree.


Quantum stochastic walks on networks for decision-making.

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

From the tree to the network.A first example step by step. We define an arbitrary toy-problem in which a decision-maker (the column-agent) chooses one option among S = {L, M, R}, with the payoff being a function of the state of the world Ω ∈ W = {U, D}. The numbers in panel (a) represent the profit for the column-agent given her choice of action and the state of the world that is realized, in the form of a payoff matrix. In panel (b) we show the normative representation of the sequential decision-making process as a tree. In this setting, the column-agent first makes her own belief about the state of the world and then, she optimizes her action as a response to her belief. In panel (c) we model the same problem with a networked topology. The numbers in the links represent the entries {πij} of the matrix Π(λ). They are weighted according to Eq. (3), with λ = 1 and using the information in panel (a). These two connected components define the dynamical comparison between alternatives, for each possible state of the world. This process happens simultaneously with the formation of beliefs through the matrix B (green connections), as stated in Eq. (4). For basic illustrative purposes, we do not need to specify if the state of the world is a random variable, or the choice of a row-player whose payoff rule is unknown for the column-player. We elaborate further on this issue and its influence on the definition of the matrix B in the main text.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f2: From the tree to the network.A first example step by step. We define an arbitrary toy-problem in which a decision-maker (the column-agent) chooses one option among S = {L, M, R}, with the payoff being a function of the state of the world Ω ∈ W = {U, D}. The numbers in panel (a) represent the profit for the column-agent given her choice of action and the state of the world that is realized, in the form of a payoff matrix. In panel (b) we show the normative representation of the sequential decision-making process as a tree. In this setting, the column-agent first makes her own belief about the state of the world and then, she optimizes her action as a response to her belief. In panel (c) we model the same problem with a networked topology. The numbers in the links represent the entries {πij} of the matrix Π(λ). They are weighted according to Eq. (3), with λ = 1 and using the information in panel (a). These two connected components define the dynamical comparison between alternatives, for each possible state of the world. This process happens simultaneously with the formation of beliefs through the matrix B (green connections), as stated in Eq. (4). For basic illustrative purposes, we do not need to specify if the state of the world is a random variable, or the choice of a row-player whose payoff rule is unknown for the column-player. We elaborate further on this issue and its influence on the definition of the matrix B in the main text.
Mentions: Note that every node ni(Ω) has KΩ outgoing edges eΩ(i, j), generally with KΩ different weights pΩ(j). See Fig. 2 for a graphical example deriving the matrix Π(λ) from the sequential tree.

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