On the normalisation of a priority vector associated with a reciprocal relation

In this paper we show that the widely used normalization constraint ∑ n i=1 wi = 1 does not apply to the priority vectors associated with reciprocal relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalization may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalization procedure which is compatible with additive transitivity and leads to better results.