An Alternative “Fundamental” Axiomatization of Multiplicative Power Relations Among Three Variables
Anthony A. J. Marley · Philosophy of Science · 1968
Suppose that the axioms of conjoint measurement hold for quantities having two independent components and that the axioms of extensive measurement hold for each of these components separately. In a recent paper, Luce shows that if a certain axiom relates the two measurement systems, then the conjoint measure on each component is a power function of the extensive measure on that component. Luce supposes that each component set contains all “rational fractions” of each element in that set; in this note we present an alternative form of the axiom relating the measurement systems that enables us to prove Luce's result without requiring that such “rational fractions” exist.