On consistency of pairwise comparison matrices in the analytic hierarchy process

This paper discusses the inconsistency of the pairwise comparison in the AHP from several aspects. The pairwise comparison matrix is judged to be consistent if CI, the consistency index, or CR, the consistency ratio, does not exceed 0.10-0.15, where CR=CI/RI, and RI is the mean value of CI. But, it is unreasonable to judge of the consistency on CI or CR. The reasons are as follows: (1) the judgement depends on CI which increases generally in n, the number of alternatives; (2) the mean is not a good representative of the distribution, because each distribution has its own shape for n, which is shown from 10,000 random matrices; (3) the 10 or 15 percent point of the mean of a variable is meaningless; (4) there is a counter example in which even the pairwise comparison of four alternatives is consistent, those of any three alternatives out of them are inconsistent on CR. Some examples show that even if the matrix is consistent, it does not always give the good estimates of relative weights. [In Japanese.]