Sekitani and Yamaki introduced two new concepts of self-evaluation value and non-self-evaluation value into AHP and showed that the eigenvalue method can be formulated as some mathematical programming problems with the ratios of the self-evaluation value to the non-self-evaluation value. This study develops a new discrepancy-minimization problem with the ratios of the self-evaluation value to the non-self-evaluation value and their reciprocals. We show that its optimal solution is identical to

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... he principal eigenvectors of the pairwise comparison matrix. We compare the analytical properties of the proposed optimization model with that of Harker method for the case of AHP with incomplete information.