Quantum models for psychological measurements: an unsolved problem.
There has been a strong recent interest in applying quantum theory (QT) outside physics, including in cognitive science. We analyze the applicability of QT to two basic properties in opinion polling. The first property (response replicability) is that, for a large class of questions, a response to a...
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doaj-32e9a769a696448fb32abfbe0d7e71492020-11-24T21:52:15ZengPublic Library of Science (PLoS)PLoS ONE1932-62032014-01-01910e11090910.1371/journal.pone.0110909Quantum models for psychological measurements: an unsolved problem.Andrei KhrennikovIrina BasievaEhtibar N DzhafarovJerome R BusemeyerThere has been a strong recent interest in applying quantum theory (QT) outside physics, including in cognitive science. We analyze the applicability of QT to two basic properties in opinion polling. The first property (response replicability) is that, for a large class of questions, a response to a given question is expected to be repeated if the question is posed again, irrespective of whether another question is asked and answered in between. The second property (question order effect) is that the response probabilities frequently depend on the order in which the questions are asked. Whenever these two properties occur together, it poses a problem for QT. The conventional QT with Hermitian operators can handle response replicability, but only in the way incompatible with the question order effect. In the generalization of QT known as theory of positive-operator-valued measures (POVMs), in order to account for response replicability, the POVMs involved must be conventional operators. Although these problems are not unique to QT and also challenge conventional cognitive theories, they stand out as important unresolved problems for the application of QT to cognition. Either some new principles are needed to determine the bounds of applicability of QT to cognition, or quantum formalisms more general than POVMs are needed.http://europepmc.org/articles/PMC4208824?pdf=render |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Andrei Khrennikov Irina Basieva Ehtibar N Dzhafarov Jerome R Busemeyer |
spellingShingle |
Andrei Khrennikov Irina Basieva Ehtibar N Dzhafarov Jerome R Busemeyer Quantum models for psychological measurements: an unsolved problem. PLoS ONE |
author_facet |
Andrei Khrennikov Irina Basieva Ehtibar N Dzhafarov Jerome R Busemeyer |
author_sort |
Andrei Khrennikov |
title |
Quantum models for psychological measurements: an unsolved problem. |
title_short |
Quantum models for psychological measurements: an unsolved problem. |
title_full |
Quantum models for psychological measurements: an unsolved problem. |
title_fullStr |
Quantum models for psychological measurements: an unsolved problem. |
title_full_unstemmed |
Quantum models for psychological measurements: an unsolved problem. |
title_sort |
quantum models for psychological measurements: an unsolved problem. |
publisher |
Public Library of Science (PLoS) |
series |
PLoS ONE |
issn |
1932-6203 |
publishDate |
2014-01-01 |
description |
There has been a strong recent interest in applying quantum theory (QT) outside physics, including in cognitive science. We analyze the applicability of QT to two basic properties in opinion polling. The first property (response replicability) is that, for a large class of questions, a response to a given question is expected to be repeated if the question is posed again, irrespective of whether another question is asked and answered in between. The second property (question order effect) is that the response probabilities frequently depend on the order in which the questions are asked. Whenever these two properties occur together, it poses a problem for QT. The conventional QT with Hermitian operators can handle response replicability, but only in the way incompatible with the question order effect. In the generalization of QT known as theory of positive-operator-valued measures (POVMs), in order to account for response replicability, the POVMs involved must be conventional operators. Although these problems are not unique to QT and also challenge conventional cognitive theories, they stand out as important unresolved problems for the application of QT to cognition. Either some new principles are needed to determine the bounds of applicability of QT to cognition, or quantum formalisms more general than POVMs are needed. |
url |
http://europepmc.org/articles/PMC4208824?pdf=render |
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