order to do so, it is necessary to let , which is in effect an arbitrary choice of the unit of measurement. Letting be the proportion of occasions on which i is judged greater than j, if, for example, and it is hypothesised that is normally distributed, then it would be inferred that . When a simple logistic function is employed instead of the normal density function, then the model has the structure of the Bradley-Terry-Luce model (BTL model) (Bradley & Terry, 1952; Luce, 1959). In turn, the Rasch model for dichotomous data (Rasch, 1960/1980) is identical to the BTL model after the person parameter of the Rasch model has been eliminated, as is achieved through statistical conditioning during the process of Conditional Maximum Likelihood estimation. With this in mind, the specification of uniform discriminal dispersions is equivalent to the requirement of parallel Item Characteristic Curves (ICCs) in the Rasch model. Accordingly, as shown by Andrich (1978), the Rasch model should, in principle, yield essentially the same results as those obtained from a Thurstone scale. Like the Rasch model, when applied in a given empirical context, Case 5 of the LCJ constitutes a mathematized hypothesis which embodies theoretical criteria for measurement. Applications One important application involving the law of comparative judgment is the widely used Analytic Hierarchy Process, a structured technique for helping people deal with complex decisions. It uses pairwise comparisons of tangible and intangible factors to construct ratio scales that are useful in making important decisions. References Andrich, D. (1978b). Relationships between the Thurstone and Rasch approaches to item scaling. Applied Psychological Measurement, 2, 449-460. Bradley, R.A. and Terry, M.E. (1952). Rank analysis of incomplete block designs, I. the method of paired comparisons. Biometrika, 39, 324-345. Krus, D.J., & Kennedy, P.H. (1977) Normal scaling of dominance matrices: The domain-referenced model. Educational and Psychological Measurement, 37, 189-193 (Request reprint). Luce, R.D. (1959). Individual Choice Behaviours: A Theoretical Analysis. New York: J. Wiley. Michell, J. (1997). Quantitative science and the definition of measurement in psychology. British Journal of Psychology, 88, 355-383. Rasch, G. (1960/1980). Probabilistic models for some intelligence and attainment tests. (Copenhagen, Danish Institute for Educational Research), expanded edition (1980) with foreword and afterword by B.D. Wright. Chicago: The University of Chicago Press. Thurstone, L.L. (1927). A law of comparative judgement. Psychological Review, 34, 273-286. Thurstone, L.L. (1929). The Measurement of Psychological Value. In T.V. Smith and W.K. Wright