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 tota
l income difference between them is allocated among the individuals as foll
ows: 100 pi% preserving income shares in x, and 100(1 - pi)% in equal absol
ute amounts. This notion can be made as operational as current standard met
hods in Shorrocks (1983).