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Non-classical Measurement Theory: a Framework for Behavioral Sciences

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  • V. I. Danilov
  • A. Lambert-Mogiliansky

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.
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  • V. I. Danilov & A. Lambert-Mogiliansky, 2005. "Non-classical Measurement Theory: a Framework for Behavioral Sciences," Levine's Working Paper Archive 122247000000000899, David K. Levine.
    • Handle: RePEc:cla:levarc:122247000000000899
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    References listed on IDEAS

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    1. R. Luce, 2005. "Measurement analogies: comparisons of behavioral and physical measures," Psychometrika, Springer;The Psychometric Society, vol. 70(2), pages 227-251, June.
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    5. Ariane Lambert Mogiliansky & Shmuel Zamir & Herve Zwirn, 2003. "Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man," Discussion Paper Series dp343, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    6. Pierfrancesco La Mura, 2003. "Correlated Equilibria of Classical Strategic Games with Quantum Signals," Papers quant-ph/0309033, arXiv.org.
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    Cited by:

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    2. Houy Nicolas, 2008. "Choice Functions with States of Mind," Theory and Decision, Springer, vol. 65(1), pages 1-26, August.

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