In this article we show that quantitative methods for multi-criteria evaluation have three serious shortcomings. First, the addition of an alternative which has bad criterion scores may distort the comparison between other alternatives. Second, the addition of a criterion which does not differentiate between alternatives may distort the comparison between alternatives. Third, when a ranking of alternatives is derived from a multi-criteria evaluation, it suggests complete transitivity. It is shown that intransitivity may occur. Therefore a stepwise procedure is recommended. It involves the removal of all criteria which do not or hardly differentiate between the alternatives and a pairwise evaluation of alternatives.