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In this paper the notion of the preference homogeneity is extended. We determine the value functions under the cumulative prospect theory such that the certainty equivalents related to them are invariant with respect to some classes of transformations. [ABSTRACT FROM AUTHOR]

In 1984 A. Reich proved that under Expected Utility Theory, a scale invariance of the Principle of Equivalent Utility just for two particular values of parameters implies its scale invariance. In this paper, we extend this result onto the Principle of Equivalent Utility under Cumulative Prospect Theory. [ABSTRACT FROM AUTHOR]