STATISTICAL-THEORY FOR THE RATIO MODEL OF PAIRED COMPARISONS

This paper investigates the ratio model for paired comparisons. This model arises in Saaty's (1977, Journal of Mathematical Psychology, 5, 234-281) scaling method for priorities in hierarchical structures and it also arises in the constant sum paired comparison models presented by Hauser and Shugan (1980, Operations Research, 28, 278-320). This paper characterizes some experimental designs that yield an estimable ratio scale and it develops a uniformly minimum variance, unbiased estimator of the scale parameters. An estimator is developed when only a subject of all p(p-1) 2 comparisons are made and when the comparisons are correlated. Moreover an intercept version of the standard model is investigated and tests of consistency and reliability are presented. © 1992.