On deriving priority vectors from matrices of pairwise comparisons

Amongst the mathematical questions related to the AHP's theory the one of how to derive priority vectors from matrices of pairwise comparisons has found an especially large interest. Following a general discussion of scales for priorities and their evaluation by pairwise comparisons several concrete proposals are reviewed. An axiomatic approach is shown for deciding which method is the “best” one. Invariance principles are motivated and formulated as axioms. The only method which fulfills all these axioms uses the geometric row means. It is often called Logarithmic Least Squares Method (LLSM). However, only one axiom would have to be replaced in order to get the widely used Right Eigenvector Method.