On the monotonicity of the eigenvector method

Pairwise comparisons are used in a wide variety of decision situations where the importance alternatives should be measured on numerical scale. One popular method to derive priorities is based right eigenvector multiplicative pairwise comparison matrix. We consider two monotonicity axioms this setting. First, increasing an arbitrary entry matrix not allowed result counter-intuitive rank reversal, that is, favoured alternative corresponding row cannot ranked lower than any other if was case before change (rank monotonicity). Second, same modification decrease normalised weight (weight Both properties satisfied by geometric mean but violated method. The do uniquely determine mean. relationship between and Saaty inconsistency index investigated for via simulations. Even though their violation turns out usual problem even heavily inconsistent matrices, all decision-makers informed about possible occurrence such unexpected consequences entry.