On a Connection Between Factor Analysis and Multidimensional Unfolding
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TL;DR
The proposition that 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 is shown to be satisfied.
Abstract
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 of r 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 of r + 1 dimensions with the original r -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.