Some Comments on Measuring World Influence

Influence is inherently difficult to measure. Saaty and Khouja present a method which utilizes expert judgment to derive a scale of world influence. Of theoretic interest is their attempt to decompose influence into its component parts and then to recompose it into a whole. However, they do not test whether different components or different weighting of the components would produce significantly different results. This would enhance the usefulness of their work. The primary focus of their work is methodological, the core of the paper being a series of measurement efforts. One set of measurements is obtained for each component of influence, with a final set used to determine the relative importance of the components. For investigators interested in pursuing this approach to assessing world influence, the reasonableness of the measurement procedure is of critical importance. In this essay I intend to confront some of the issues which underlie the SaatyAKhouja measurement method and explore some alternatives to it. The observations Saaty and Khouja collect are a rater’s responses to questions of which of two stimuli possesses more of a particular attribute than the other. The observations are made over all pairs of stimuli in which the investigators are interested. In order to simplify the ensuing discussion I will assume countries are the stimuli and wealth is the attribute to be scaled. This discussion should apply with equal force to the other attributes and stimuli. The mathematical model Saaty and Khouja propose to translate the responses of the rater to scale values for the stimuli is: