International Journal of Theoretical Physics

, Volume 53, Issue 10, pp 3666–3682

Identifying Quantum Structures in the Ellsberg Paradox

Article

DOI: 10.1007/s10773-014-2086-9

Cite this article as:
Aerts, D., Sozzo, S. & Tapia, J. Int J Theor Phys (2014) 53: 3666. doi:10.1007/s10773-014-2086-9

Abstract

Empirical evidence has confirmed that quantum effects occur frequently also outside the microscopic domain, while quantum structures satisfactorily model various situations in several areas of science, including biological, cognitive and social processes. In this paper, we elaborate a quantum mechanical model which faithfully describes the Ellsberg paradox in economics, showing that the mathematical formalism of quantum mechanics is capable to represent the ambiguity present in this kind of situations, because of the presence of contextuality. Then, we analyze the data collected in a concrete experiment we performed on the Ellsberg paradox and work out a complete representation of them in complex Hilbert space. We prove that the presence of quantum structure is genuine, that is, interference and superposition in a complex Hilbert space are really necessary to describe the conceptual situation presented by Ellsberg. Moreover, our approach sheds light on ‘ambiguity laden’ decision processes in economics and decision theory, and allows to deal with different Ellsberg-type generalizations, e.g., the Machina paradox.

Keywords

Ellsberg paradox Ambiguity Quantum structures Complex Hilbert spaces 

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Center Leo Apostel for Interdisciplinary Studies (Clea)Vrije Universiteit Brussel (VUB)BrusselsBelgium
  2. 2.School of ManagementUniversity of LeicesterLeicesterUK
  3. 3.Pontificia Universidad Católica de ChileSantiagoChile