On ratio scales

In the past, ratio scales have been a highly controversial issue between physicists and psychologists as regards the need for an empirical addition operation in order to attain them. This aspect is critical since such an operation is often unavailable in psychophysical experiments, as it is in physics, due to its intensive properties. We propose a reconsideration of ratio scales, showing how they can be obtained when ratio and difference empirical relations are available and when they satisfy proper compatibility conditions. We call such structures “intensive” and provide deterministic and probabilistic axiomatizations in the finite case. We also address the practical applications of these ideas to perceptual measurements.