Measurement, Theory of
R. Duncan Luce, Louis Narens · The New Palgrave Dictionary of Economics · 2008
Physical measurement, as embodied in dimensional analysis, consists of interlocked, qualitative, ordered structures. Analogous approaches to behavioural science are outlined for sensory scaling such as loudness, utility of uncertain alternatives, and qualitative foundations of probability. In many cases, they are an ordered structure with a binary operation for combining elements and a Cartesian product where each factor affects the ordering of the attribute. Axioms sufficient for measurement – for the existence of a homomorphism onto the positive real numbers – are mentioned, and their uniqueness (scale type – for example, ratio, interval, ordinal) is formulated qualitatively in terms of the structure’s symmetries (or automorphisms).