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A Metric Structure Derived from Subjective Judgments: Scaling Under Perfect and Imperfect Discrimination

Robert Bartoszynski

Abstract

Assume that to each pair (x, y) of elements of the set A there corresponds probability p(x, y) that y will be chosen as having more of a certain attribute, if the pair (x, y) is presented to the subject. It is shown that if the p(x, y) satisfy a certain set of (logically independent) conditions, then there exists an (essentially unique) measure f of the attribute of elements of A, such that probabilities p(x, y) depend only on differences between f(x) and f(y).