Abstract
The Ellsberg and Machina paradoxes reveal that expected utility theory is problematical when real subjects take decisions under uncertainty. Suitable generalizations of expected utility exist which attempt to solve the Ellsberg paradox, but none of them provides a satisfactory solution of the Machina paradox. In this paper we elaborate a quantum model in Hilbert space describing the Ellsberg situation and also the Machina situation, and show that we can model the specific aspect of the Machina situation that is unable to be modeled within the existing generalizations of expected utility.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
von Neumann, J., Morgenstern, O.: Theory of Games and Economic Behavior. Princeton University Press, Princeton (1944)
Savage, L.J.: The Foundations of Statistics. Wiley, New York (1954)
Ellsberg, D.: Risk, Ambiguity, and the Savage Axioms. Quart. J. Econ. 75(4), 643–669 (1961)
Machina, M.J.: Risk, Ambiguity, and the Dark–dependence Axioms. Am. Econ. Rev. 99(1), 385–392 (2009)
Knight, F.H.: Risk, Uncertainty and Profit. Houghton Mifflin, Boston (1921)
Gilboa, I.: Expected Utility with Purely Subjective Non-additive Probabilities. J. Math. Econ. 16, 65–88 (1987)
Gilboa, I., Schmeidler, D.: Maxmin Expected Utility With Non–unique Prior. J. Math. Econ. 18, 141–153 (1989)
Maccheroni, F., Marinacci, M., Rustichini, A.: Dynamical Variational Preferences. The Carlo Alberto Notebooks 1, 37 (2006)
Klibanoff, P., Marinacci, M., Mukerji, S.: A smooth model of decision making under ambiguity. Econometrica 73(6), 1849–1892 (2005)
Epstein, L.G.: A Definition of Uncertainty Aversion. Rev. Econ. Stud. 66, 579–608 (1999)
Baillon, A., L’Haridon, O., Placido, L.: Ambiguity Models and the Machina Paradoxes. Am. Econ. rev. 101(4), 1547–1560 (2011)
Aerts, D., Broekaert, J., Czachor, M., D’Hooghe, B.: A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 192–198. Springer, Heidelberg (2011)
Aerts, D., D’Hooghe, B., Sozzo, S.: A Quantum Cognition Analysis of the Ellsberg Paradox. In: Song, D., Melucci, M., Frommholz, I., Zhang, P., Wang, L., Arafat, S. (eds.) QI 2011. LNCS, vol. 7052, pp. 95–104. Springer, Heidelberg (2011)
Aerts, D., Sozzo, S.: Quantum Structure in Economics: The Ellsberg Paradox. In: D’Ariano, M., et al. (eds.) Quantum Theory: Reconsideration of Foundations, vol. 6, pp. 487–494. AIP, Melville (2012)
Aerts, D., Sozzo, S.: Contextual Risk and Its Relevance in Economics; A Contextual Risk Model for the Ellsberg Paradox. J. Eng. Sci. Tech. Rev. 4, 241–245, 246–250 (2012)
Camerer, C.F.: Ambiguity Aversion and Non–additive Probability: Experimental Evidence, Models and Applications. In: Luini, L. (ed.) Uncertain Decisions: Bridging Theory and Experiments, pp. 53–80. Kluwer Acad. Pub., Dordrecht (1999)
Aerts, D.: Quantum Structure in Cognition. J. Math. Psych. 53, 314–348 (2009)
Busemeyer, J.R., Lambert-Mogiliansky, A.: An Exploration of Type Indeterminacy in Strategic Decision-Making. In: Bruza, P., Sofge, D., Lawless, W., van Rijsbergen, K., Klusch, M. (eds.) QI 2009. LNCS, vol. 5494, pp. 113–127. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Aerts, D., Sozzo, S., Tapia, J. (2012). A Quantum Model for the Ellsberg and Machina Paradoxes. In: Busemeyer, J.R., Dubois, F., Lambert-Mogiliansky, A., Melucci, M. (eds) Quantum Interaction. QI 2012. Lecture Notes in Computer Science, vol 7620. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35659-9_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-35659-9_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-35658-2
Online ISBN: 978-3-642-35659-9
eBook Packages: Computer ScienceComputer Science (R0)