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Conclusion  The discussion about the appropriateness of the subtractive or the ratio model is highly reminiscent of the corresponding argumentation regarding the two equivalent representations of Thurstone’s Case V (Eisler, 1965a). Bock and Jones (1968, pp. 65–66, p. 273) provided evidence in favor of the ratio representation. For direct scaling, Eisler (1965b) argued, likewise, for the ratio representation. Further evidence in favor of the ratio representation can be found in Eisler (1975), where magnitude estimation of durations yields roughly the same power function exponent as the one obtained from duration reproduction. Also, the attempt to quantitatively relate different ratio-level estimates of the same stimuli proved successful (Eisler & Roskam, 1977a, 1977b), thereby supporting the ratio model.   From the above it may be tentatively concluded that there is an alternative to Birnbaum’s model, according to which combinations of “difference” and “ratio” instructions in psychophysical experiments can be represented by a single scale, the sensation scale, and a single operation, ratio formation. Whether this representation is preferable to Birnbaum’s (1978) or to one with two operations on two scales is a question that requires further investigation.

On the ability to estimate differences: A note on Birnbaum’s subtractive model