Independence properties Vis-A-Vis several utility representations

A detailed theoretical analysis is presented of what five utility representations - subjective expected utility (SEU), rank-dependent (cumulative or Choquet) utility (RDU), gains decomposition utility (GDU), rank weighted utility (RWU), and a configural-weight model (TAX) that we show to be equivalent to RWU - say about a series of independence properties, many of which were suggested by M. H. Birnbaum and his coauthors. The goal is to clarify what implications to draw about the descriptive aspects of the representations from data concerning these properties. The upshot is a sharp rejection of SEU and RDU and no clear choice between GDU and TAX, but a list of 8 properties is given that should receive more attention to discriminate between the latter two models.