Contributions to the Method of Paired Comparisons

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Abstract
A least-squares solution for the method of paired comparisons is given. The approach pro vokes a theorem regarding the amount of data necessary and sufficient for a solution to be ob tained. 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 exam ple (rating university football teams) involving ob servational data is worked out.