Non-Archimedean Representations

  • Ulrich Schmidt
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 461)


According to the aggregated empirical study of Harless and Camerer (1994), the certainty effect and boundary effects are the most prominent observed violations of the independence axiom. If preferences are representable by expected utility for lotteries with the same number of probable consequences, an explicit modelling of these effects requires a weakening of the continuity axiom. In order to analyze these effects, this second part is devoted to models which employ weakened forms of both the independence and the continuity axiom.


Utility Function Risk Aversion Stochastic Dominance Indifference Curve Expect Utility Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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    Recall that value functions represent preferences under certainty while utility functions are assessed under risk.Google Scholar
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    The interpretation of v as a measurable value function requires clearly the existence of a quaternary preference relation and some technical assumptions. However, these assumptions are also necessary in order to interpret the von Neumann-Morgenstern function as a measurable value function [cf. Sarin (1982, pp. 986-989)].Google Scholar
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    Gilboa (1988, pp. 409-410) notes that there is an intersection between the representation (2.20) and rank-dependent utility representations which would contradict the statements concerning the classification of non-expected utilty models in the preceeding section. But in the example of Gilboa, the distortion function is not continuous and, therefore, his example is not a special case of RDU as defined in section Scholar
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    Cf. Theorem 1.5.Google Scholar
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  56. 56.
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    To my knowledge the only empirical test of this operation, conducted by Seidl and Traub (1995), refers to choice problems under certainty only.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Ulrich Schmidt
    • 1
  1. 1.University of KielInstitut für Finanzwissenschaft und SozialpolitikKielGermany

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