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Quantum models for psychological measurements: an unsolved problem.

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Summary
This summary is machine-generated.

Quantum theory (QT) faces challenges when applied to cognitive science, specifically with opinion polling. Current quantum formalisms struggle to simultaneously explain response replicability and question order effects in cognitive models.

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Area of Science:

  • Cognitive Science
  • Quantum Physics
  • Mathematical Psychology

Background:

  • Recent interest in applying quantum theory (QT) beyond physics, particularly in cognitive science.
  • Opinion polling exhibits two key properties: response replicability and question order effects.

Purpose of the Study:

  • Analyze the applicability of QT to opinion polling properties.
  • Identify limitations of current QT formalisms in explaining cognitive phenomena.

Main Methods:

  • Examined conventional QT with Hermitian operators.
  • Investigated the generalized QT framework of positive-operator-valued measures (POVMs).

Main Results:

  • Conventional QT can model response replicability but conflicts with question order effects.
  • POVMs require conventional operators to account for response replicability, posing issues.
  • The simultaneous occurrence of both properties presents a problem for existing QT.

Conclusions:

  • Current QT formalisms face unresolved problems in modeling cognitive phenomena like opinion polling.
  • New principles or more general quantum formalisms are needed to extend QT's applicability to cognition.