Intermediate inequality and welfare

We introduce a new centrist or intermediate inequality concept, between the usual relative and absolute notions, which is shown to be a variant of the alpha-ray invariant inequality measures in Pfingsten and Seidl (1997). We say that distributions x and y have the same (x; pi)-inequality if the total income difference between them is allocated among the individuals as follows: 100 pi% preserving income shares in x, and 100(1 - pi)% in equal absolute amounts. This notion can be made as operational as current standard methods in Shorrocks (1983).