A closer look at the Russian roulette problem: A re-examination of the nonlinearity of the prospect theory's decision weight π

  • Authors:

  • Li-Bo Li;Shu-Hong He;Shu Li;Jie-Hong Xu;Li-Lin Rao

  • Affiliations:

  • School of Mathematics, University of New South Wales, Australia;Department of Mathematics, Yunnan University, China;Institute of Psychology, Chinese Academy of Sciences, Centre for Social and Economic Behavior, 4A Datun Road, Chaoyang District, Beijing 100101, China;Institute of Psychology, Chinese Academy of Sciences, Centre for Social and Economic Behavior, 4A Datun Road, Chaoyang District, Beijing 100101, China;Institute of Psychology, Chinese Academy of Sciences, Centre for Social and Economic Behavior, 4A Datun Road, Chaoyang District, Beijing 100101, China

  • Venue:
  • International Journal of Approximate Reasoning
  • Year:
  • 2009

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Abstract

Utilizing the Russian roulette problem as an exemplar, Kahneman and Tversky (1979) developed a weighting function @p to explain that the Allais Paradox arises because people behave so as to maximize overall value rather than expected utility (EU). Following the way that ''overweighting of small probabilities'' originated from the Russian roulette problem, this research measured individuals' willingness to pay (WTP) as well as their happiness for a reduction of the probability of death, and examined whether the observed figures were compatible with the nonlinearity of the weighting function. Data analysis revealed that the nonlinear properties estimated by straight measures differed from those derived from preferential choices [D. Kahneman, A. Tversky, Prospect theory: an analysis of decision under risk, Econometrica 47 (1979) 263-291] and formulated by [A. Tversky, D. Kahneman, Advances in prospect theory: Cumulative representation of uncertainty, Journal of Risk and Uncertainty 5 (1992) 297-323]. The controversies and questions to the proposed properties of the decision weight were discussed. An attempt was made to draw the research attention from which function was being maximized to whether people behave as if they were trying to maximize some generalized expectation.