Contributions to the method of paired comparisons

Abstract

A least-squares solution for the method of paired comparisons is given. The approach provokes a theorem regarding the amount of data necessary and sufficient for a solution to be obtained. This theorem establishes that it is possible to find a solution when there is a great deal of missing data. A measure of the internal consistency of the least-squares fit is developed. It is indicated that the method of paired comparisons need not be applied only to data obtained experimentally from the law of comparative judgment; indeed, an example (rating university football teams) involving observational data is worked out.