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

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.