Using Stevens' invariance scheme, an 'absolute' scale could not be rescaled by any multipier. Both zero AND one are fixed. Probability is an absolute scale. Bayes' Law and other axioms depend on absolute scaling. Just as a difference of intervals is ratio, some divisions of ratios produce absolute measures.
Counts are discrete, since only integers can result.
There is a real zero, and 2x does mean twice the quantity. Some measures are cyclical, with a fixed range. Multidimensional measures Multidimensional scales have extra relationships. In Stevens' scheme, an unbounded linear axis could not be fit into a fixed interval without losing information. Hence, test for equivalence only.