Rank reversal in the PROMETHEE II method: Some new results

The aim of this paper is to study properties of multicriteria decision-aid ranking methods based on pair-wise comparisons in regards to rank reversals. At first we introduce the notion of pair-wise rank reversal and we show that this notion is equivalent to rank reversal. Then we analyze more particularly the PROMETHEE II method and we clarify conditions under which the PROMETHEE II ranking might suffer from rank reversal problems. Finally, we prove that the PROMETHEE multicriteria net flow is the centered score that minimizes the sum of the squared deviations from the pair-wise comparisons of the alternatives.