Preference Paradox and Nonlinear Expected Utility Theory

Chapter 7 explained that expected utility theoryExpected utility theory included counterexamples called the Allais paradoxAllais paradox (Allais, 1953) and[aut]Allais, M. the Ellsberg[aut]Ellsberg, D. paradox (Ellsberg, 1961). The Allais and Ellsberg paradoxesEllsberg paradox are interpreted as deviations from the independence axiomIndependence axiom. This chapter first explains the relations between these paradoxes and the independence axiomIndependence axiom. In recent years, these paradoxes have become explainable using such theory systemsNonlinear utility theory called nonlinear utility theory[aut]Edwards, W. (Fishburn, 1988; Edwards, 1992), which[aut]Fishburn, P. C. does not assume this independence axiomAxiom, and generalized expected utility theoryGeneralized expected utility theory (Quiggin, 1993). Prospect[aut]Quiggin, J. theory as proposed by Kahneman[aut]Kahneman, D. and Tversky[aut]Tversky, A. (1979), Tversky and Kahneman[aut]Kahneman, D. (1992) is a theory that particularly integrates knowledge and past findings in behavioral decision-making theory and nonlinear utility theory (or generalized expected utility theoryGeneralized expected utility theory). This chapter explains the idea of non-additive probabilityNon-additive probability assumed in nonlinear utility theoryNonlinear utility theory and the expected utility based on such non-additive probabilityProbability. The chapter finally describes the basic assumptions in prospect theoryProspect theory.