Continuity in Transformation Invariant Social Orderings: Two Impossibilities

Abstract

We show that (1) a social ordering on R >= 0 that satisfies Strong Paretoness, Invariance with respect to a Positive Proportional Transformation and Lower Semi-Continuity does not exist and (2) that a social ordering on R > 0 that satisfies Weak Paretoness, Invariance with respect to an Affine Transformation and Lower Semi-Continuity is trivial.