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.