Analagous to the notion of greater risk aversion being that the resulting utility function v = φ(u) is a concave transformation φ of the original utility function u (i.e., φ′′ < 0); the apparent definition of v being more downside risk averse is that φ′ is convex (i.e., φ′′′ > 0). This definition, however, suffers from logical inconsistencies as an ordering. We propose, instead, the...</0);>