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Transitivity, contextuality and decision making.

William H Sulis1

  • 1CILab, Psychiatry and Behavioral Neurosciences, McMaster University, Hamilton, Ontario, Canada.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|November 27, 2025
PubMed
Summary
This summary is machine-generated.

True contextuality, essential for quantum mechanics, is explored in decision-making systems. Researchers identified conditions like option loss and intransitivity necessary for its presence in non-deterministic dynamics.

Keywords:
contextualitydecision makingprocess algebratransitivity

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Area of Science:

  • Decision Science
  • Quantum Mechanics
  • Dynamical Systems

Background:

  • True (Type II) contextuality, defined by context-independent marginals, is a key feature of quantum mechanics.
  • While essential for quantum mechanics, true contextuality has also been observed in human decision-making experiments.
  • Transitivity is traditionally linked to rational decision-making, yet intransitivity is common in nature.

Purpose of the Study:

  • To investigate the relationship between intransitivity and true contextuality in non-deterministic dynamical systems.
  • To identify necessary conditions for the presence of true contextuality.
  • To analyze the structural properties of preference graphs in these systems.

Main Methods:

  • Introduction of a preference graph analogue for non-deterministic dynamical systems.
  • Comparison of the system's preference graph with a reference graph derived from observable marginals.
  • Identification of necessary conditions for true contextuality based on graph properties.

Main Results:

  • Loss of options and intransitivity were identified as necessary conditions for true contextuality.
  • The study highlights specific structural requirements for contextuality in decision-making models.
  • The preference graph analysis reveals key differences between system dynamics and marginal distributions.

Conclusions:

  • Intransitivity and loss of options are crucial indicators for the presence of true contextuality.
  • The findings provide a framework for understanding contextuality in decision-making and non-deterministic systems.
  • This research bridges concepts from quantum mechanics, decision theory, and dynamical systems.