INSIGHT IN RATIO SCALES
Ratio scales have been a highly controversial issue between physicists and psychologists in the past in regard of the necessity of an empirical addition operation for attaining them. This aspect is very critical, since such an operation is often unavailable in psychophysical experiments. Stevens indicated â€œequality of ratiosâ€ as a distinctive feature for ratio scales, but he did not provide any axiomatization, in support of this statement. In this paper we proposed a reconsideration of ratio scales, discussing which kinds of internal properties are really required for achieving them. In particular, we discuss ratio/difference representations, that have been studied to some extent, both theoretically and experimentally, but whose consequences have not been, as far as we know, fully exploited. We provide preliminary deterministic and probabilistic axiomatizations for finite structures and also mention some preliminary practical applications of these ideas.