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In this paper, we show that the third inverse stochastic dominances introduced by Muliere and Scarsini (1989) is nicely connected with the Yaari's dual model. We show especially that the third inverse stochastic dominance is closely linked with the non-negativity of third derivative of the decision-maker's frequency transformation function f. We also give new simple proofs for the known characterizations of first and second (inverse) stochastic dominances through signs of first and second derivatives in the case of differentiable f.
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