Transitive indistinguishability and approximate measurement with standard finite ratio-scale representations
Abstract
Ordinary measurement using a standard scale, such as a ruler or a standard set of weights, has two fundamental properties. First, the
results are approximate, for example, within 0.1 g. Second, the resulting indistinguishability is transitive, rather than nontransitive, as in
the standard psychological comparative judgments without a scale. Qualitative axioms are given for structures having the two properties
mentioned. A representation theorem is then proved in terms of upper and lower measures.