On a connection between factor analysis and multidimensional unfolding

Given the preference ordering of each of a number of individuals over a set of stimuli, it is proposed that if the preference orderings are generated in a Euclidean space ofr dimensions which can be recovered by unfolding the preference orderings, then a factor analysis of the correlations between individual's preference orderings will yield a space ofr + 1 dimensions with the originalr-space embedded in it, and the additional dimension will be one of social utility. The proposition is clearly shown to be satisfied by means of the Monte Carlo technique for both random and lattice stimuli in three dimensions and for two other examples with random stimuli in one and two dimensions.The preparation of this paper was supported in part by a grant from the National Science Foundation and in part by Project MICHIGAN, a project of the University of Michigan in the field of Combat Surveillance sponsored by the Department of the Army. The contract (DA-36-039 ac 78801) is administered by the U. S. Army Signal Corps. The authors are indebted to L. A. Raphael, Caroline K. Tefft, and F. M. Goode for programming assistance, and to L. W. Staugas for providing other computer services during various stages of this study.