Additive differences and simple preference comparisons

Abstract

Two axiomatizations of the multiattribute additive difference representation of preferences are presented. One uses topological assumptions to obtain a continuous representation; the other uses a more general algebraic structure. Both use only simple preference comparisons and require three or more attributes. Proofs of the representation theorems are based on recent work in nontransitive additive conjoint measurement. Specializations of the additive difference model for homogeneous product sets are also axiomatized. Contexts for these specializations include time streams and finite-states decision under uncertainty.