[Paper Review] Non-classical Measurement Theory: a Framework for Behavioral Sciences

V. I. Danilov, Ariane Lambert‐Mogiliansky|arXiv (Cornell University)|Dec 17, 2005

Quantum Mechanics and Applications18 references10 citations

TL;DR

This paper proposes a non-classical measurement theory rooted in quantum mechanics to model psychological properties like attitudes and preferences, using ortholattices and state-property duality to derive a Hilbert space framework. It applies this to decision theory, demonstrating how quantum-like structures can explain preference reversal and actualized preferences in behavioral science.

ABSTRACT

Instances of non-commutativity are pervasive in human behavior. In this paper, we suggest that psychological properties such as attitudes, values, preferences and beliefs may be suitably described in terms of the mathematical formalism of quantum mechanics. We expose the foundations of non-classical measurement theory building on a simple notion of orthospace and ortholattice (logic). Two axioms are formulated and the characteristic state-property duality is derived. A last axiom concerned with the impact of measurements on the state takes us with a leap toward the Hilbert space model of Quantum Mechanics. An application to behavioral sciences is proposed. First, we suggest an interpretation of the axioms and basic properties for human behavior. Then we explore an application to decision theory in an example of preference reversal. We conclude by formulating basic ingredients of a theory of actualized preferences based in non-classical measurement theory.

Motivation & Objective

• To develop a non-classical measurement theory grounded in quantum formalism for psychological properties.
• To address the pervasive non-commutativity in human behavior through ortholattices and state-property duality.
• To model the impact of measurement on mental states, mirroring quantum measurement collapse.
• To apply the framework to decision theory, particularly preference reversal phenomena.
• To establish a foundation for a theory of actualized preferences in behavioral sciences.

Proposed method

• Formulates two axioms based on orthospace and ortholattice structure to model psychological properties.
• Derives state-property duality as a core feature of the measurement framework.
• Introduces a third axiom modeling measurement-induced state collapse, leading to the Hilbert space model.
• Applies the formalism to decision-making contexts, particularly preference reversal.
• Uses quantum-like probability structures to represent context-dependent preferences.
• Models preferences not as fixed but as contextually actualized through measurement.

Experimental results

Research questions

• RQ1 How can non-commutativity in human behavior be formally modeled using quantum-inspired structures?
• RQ2 In what way does measurement affect the state of psychological properties like preferences?
• RQ3 Can the Hilbert space formalism be adapted to represent attitudes and beliefs in behavioral science?
• RQ4 How does the framework explain preference reversal in decision-making?
• RQ5 What are the foundational principles for a theory of actualized preferences based on non-classical measurement?

Key findings

• The framework successfully models psychological properties using ortholattices and state-property duality, providing a logical foundation for non-classical measurement.
• Measurement-induced state collapse is formalized as a key mechanism, analogous to quantum measurement.
• Preference reversal is explained through context-dependent state evolution, not inconsistency.
• The Hilbert space model emerges naturally from the three axioms, enabling probabilistic predictions.
• The theory provides a coherent basis for actualized preferences, where choices depend on measurement context.
• The approach offers a unified formalism for attitudes, values, beliefs, and preferences under non-classical logic.