A Method of Successive Cumulations for the Scaling of Pair-Comparison Preference Judgments

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Abstract
The present model treats the scaling of pair-comparison preference judgments among a unidimensional set of stimuli across a population of individuals. Given a set S of n stimuli, S = {S1, S2, …, Sn}, the model yields a partially ordered metric on the interstimulus distances which may be used to construct an interval scale of values forS. Obtained also are a set of predictions P = {P1, P2, …, Pn} wherePi is the proportion of individuals in the population whose first choice among the elements of S is Si. A numerical illustration is offered and comparisons are drawn with Coombs' unfolding technique.