Two Extensions of Conjoint Measurement1v2

Both extensions modify the axioms of Lute and Tukey for additive conjoint measurement. The first yields a theory for more than two coordinates. The main problem is to find a weak generalization of the cancellation property; the one suggested is weaker than Krantz’s generalization. The second extension weakens the solution-of-equations axiom, which has been justly criticized as too strong for most potential applications. A much more plausible version is suggested. This weakening is compensated for by adding the (necessary) independence property as an axiom and by postulating the existence of a part of a dual standard sequence. The usual representation and uniqueness theorems are proved.