ABSTRACT
Paired comparison data consist of an N × [n(n− 1)/2] (subjects-bypairs of stimuli, X(j,k)) table, of which the element in the i-th row and the (j,k)-th column is 1 if Subject i prefers Stimulus j to Stimulus k, 0 if Subject i makes an equality judgment, and 2 if Subject i prefers Stimulus k to Stimulus j. The following example shows 3 subjects who made paired comparison judgments of four fruits, apples (A), pears (P), grapes (G) and mangos (M). The columns correspond to the pairs (A, P), (A, G), (A, M), (P, G), (P, M), and (G, M). We should note that in paired comparisons it is possible for a
Subject AP AG AM PG PM GM 1 1 2 2 2 2 2 2 2 1 1 2 1 2 3 1 2 2 1 2 2
subject to produce intransitive relations such as the subject prefers A to B, B to C, and C to A, rather than A to C. Such intransitive judgments must arise, for example, from subject’s adopting different judgmental criteria for different pairs, such as sweetness, spiciness, flavor and nutritional value. In the unidimensional scaling (Bock and Jones, 1968), intransitive judgments create some problems since they are considered to be associated with errors. In multidimensional quantification, however, intransitive judgments present interesting and perhaps important pieces of information.
