A fractional design in paired comparisons is developed based on the eigenvector of the comparison matrices. Mathematical proof of this fractional design is given in Theorems 1 and 2 of Chapter 2. A concrete example from the wealth of nations is chosen to compare the results of the fractional design with the results of the complete design.

Under the assumption of the lognormal distribution on error terms, the numerical distributions of the consistency index and goodness fit index are calculated and listed in the tables.

The optimal scale with respect to the consistency index has been proved not to exist. Finally, the multivariate one way analysis of variance has been used to deal with the variations between estimated weight vectors due to the differences among the judges and the sampling errors.