ABSTRACT
This chapter shows that incomparability is compatible with measurement on a ratio scale. Measurability on such a scale implies additivity. There are several kinds of value, and the answers to questions about incomparability and measurement may differ for different kinds. The chapter focuses on the measurability of intrinsic or final value. To be able to measure value, we must first find a way to represent the value of an item, by means of some kind of mathematical entity. A representation is said to be unique to the extent that it implies a given type of scale. The chapter also shows that value incomparability does not preclude measurement on a ratio scale. It concludes by briefly considering the axioms. The purpose of the Archimedean axiom is to mirror the Archimedean property of the real numbers. The Monotonicity axiom is quite controversial, and some version of it seems indeed to be necessary for additive measurement.
