On decision theory models incorporating the Ellsberg paradox

Open Access
Author:
Lee, Dongkeun
Area of Honors:
Economics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Kalyan Chatterjee, Thesis Supervisor
  • David Shapiro, Honors Advisor
  • N Edward Coulson, Faculty Reader
Keywords:
  • Ellsberg paradox
  • Economics
  • Microeconomics
  • Decision Theory
  • Anticipated Utility
  • Choquet Integral
  • Expected Utility
Abstract:
The Ellsberg paradox is a paradox in decision theory under uncertainty in which decision makers, when faced with multiple lotteries shy away from lotteries in which probabilities are uncertain, contradicting the hypothesis of Von-Neumann and Morgenstern Expected Utility theorem (1963). The so called 'Ellsberg preferences' not only seem to suggest that Von-Neumann and Morgenstern theories do not accurately represent the preferences of decision makers in certain situations, but violate many other axioms of decision theory as well. In this paper, I show which axioms the Ellsberg paradox contradicts and then introduce a couple of models that have incorporated the Ellsberg paradox. I compare/contrast the models and create functions for decision makers in which the model would be consistent with the Ellsberg paradox. For example, in Segal's process of evaluating ambiguous lotteries, the function $f(p)=\frac{e^p-1}{e-1}$ incorporates both versions of the Ellsberg paradox.