An axiomatic characterization of Promethee II's net flow scores based on a combination of direct comparisons and comparisons with third alternatives

Promethee ii is a multi‐criteria decision aid method working as follows: firstly, all alternatives are compared two by two to form a pairwise comparison matrix. Then the net flow score procedure is applied on this matrix to assign a score to each alternative according to which they are ranked. Methods of the Promethee family may suffer from rank reversal occurrences. The legitimacy of methods suffering from this phenomenon has been largely debated in the literature. The aim of this work is to provide a characterization of the Promethee ii net flow scores as a combination between two distinct methods based on different hypotheses. The first one is based on the direct pairwise comparison of the two considered alternatives while the second is based on the comparison with respect to all the other alternatives of the problem. This combination highlights the dependence on third alternatives as an inherent characteristic of the Promethee ii method.