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Non-classsical measurement theory: A framework for behavioral sciences

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Vladimir I. Danilov
Ariane Lambert-Mogiliansky

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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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Paper provided by PSE (Ecole normale supérieure) in its series PSE Working Papers with number 2005-37.

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Date of creation: 2005
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Handle: RePEc:pse:psecon:2005-37

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  1. Pierfrancesco La Mura, 2003. "Correlated Equilibria of Classical Strategic Games with Quantum Signals," Game Theory and Information 0309001, EconWPA. [Downloadable!]
  2. Amartya Sen, 1997. "Maximization and the Act of Choice," Econometrica, Econometric Society, vol. 65(4), pages 745-780, July.
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  3. R. Luce, 2005. "Measurement analogies: comparisons of behavioral and physical measures," Psychometrika, Springer, vol. 70(2), pages 227-251, June. [Downloadable!] (restricted)
  4. Ariane Lambert Mogiliansky & Shmuel Zamir & Herve Zwirn, 2003. "Type Indeterminacy: A Model of the KT(Kahneman-Tversky)-man," Discussion Paper Series dp343, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem. [Downloadable!]
  5. Erev, Ido & Bornstein, Gary & Wallsten, Thomas S., 1993. "The Negative Effect of Probability Assessments on Decision Quality," Organizational Behavior and Human Decision Processes, Elsevier, vol. 55(1), pages 78-94, June. [Downloadable!] (restricted)
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