A behavioral condition for Prelec's weighting function on the positive line without assuming W(1)=1

Abstract Prelec axiomatized a flexible 2-parameter weighting function W over probabilities in a utility context, and Luce reported a simpler axiomatic condition for the case W ( 1 ) = 1 . This article modifies the latter to yield also the generalized Prelec functions with W ( 1 ) ≠ 1 and deals also with the cases where the variables go through [ 1 , ∞ [ or through the whole positive line. This has arisen naturally in a psychophysical application.