A method of successive cumulations for the scaling of pair-comparison preference judgments

The present model treats the scaling of pair-comparison preference judgments among a unidimensional set of stimuli across a population of individuals. Given a setS ofn stimuli,S = {S₁,S₂, ,S_n}, 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 predictionsP = {P₁,P₂, ,P_n} whereP_i is the proportion of individuals in the population whose first choice among the elements ofS isS_i. A numerical illustration is offered and comparisons are drawn with Coombs' unfolding technique.This work was supported in part by Grant GB 2345 from the National Science Foundation. An earlier version of this paper was prepared while the author was a consultant to Proctor & Gamble Co. during the summer of 1964.Now with Proctor & Gamble Co.