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Dual Betweenness

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A key feature of the rank dependent model for decision making under risk is that the weighting of an outcome depends on its relative rank. This theory received numerous axiomatizations, however, all these sets of axioms need to make an explicit reference to the ranking of the outcomes. This situation is unsatisfactory, as it seems to be desirable to get the ranking property of this model as a consequence of the model, rather than as an assumption. Yaari offered a special version of this model (called dual theory), where the utility function is linear. This paper offers a set of axioms implying a generalization of Yaari's dual theory, without making any reference to the order of the outcomes. The main axiom is called dual betweenness, which, unlike the usual case, is made on random variables rather than distribution functions.

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  • Zvi Safra & Uzi Segal, 1998. "Dual Betweenness," UWO Department of Economics Working Papers 9814, University of Western Ontario, Department of Economics.
  • Handle: RePEc:uwo:uwowop:9814
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    1. Segal, Uzi, 1990. "Two-Stage Lotteries without the Reduction Axiom," Econometrica, Econometric Society, vol. 58(2), pages 349-377, March.
    2. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    3. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    4. Quiggin John & Wakker Peter, 1994. "The Axiomatic Basis of Anticipated Utility: A Clarification," Journal of Economic Theory, Elsevier, vol. 64(2), pages 486-499, December.
    5. Safra, Zvi & Segal, Uzi, 1998. "Constant Risk Aversion," Journal of Economic Theory, Elsevier, vol. 83(1), pages 19-42, November.
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