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The pairwise comparisons method is a convenient tool used when the relativeorder of preferences among different concepts (alternatives) needs to bedetermined. There are several popular implementations of this method, includingthe Eigenvector Method, the Least Squares Method, the Chi Squares Method andothers. Each of the above methods comes with one or more inconsistency indicesthat help to decide whether the consistency of input guarantees obtaining areliable output, thus taking the optimal decision. This article explores therelationship between inconsistency of input and discrepancy of output. A globalranking discrepancy describes to what extent the obtained results correspond tothe single expert's assessments. On the basis of the inconsistency anddiscrepancy indices, two properties of the weight deriving procedure areformulated. These properties are proven for Eigenvector Method and Koczkodaj'sInconsistency Index. Several estimates using Koczkodaj's Inconsistency Indexfor a principal eigenvalue, Saaty's inconsistency index and the Condition ofOrder Preservation are also provided.

On the Properties of the Priority Deriving Procedure in the Pairwise Comparisons Method