Rank Reversal as a Source of Uncertainty and Manipulation in the PROMETHEE II Ranking: A First Investigation
PROMETHEE II is an aggregating procedure based on pairwise comparisons for ranking alternatives evaluated on multiple criteria. As other outranking methods, PROMETHEE II does not satisfy the assumption of independence to third alternatives. In other words, the ranks of two given alternatives may be influenced by the presence of a third one. This phenomenon, also called rank reversal, can be viewed as a source of uncertainty on the final ranking. Additionally, it raises the natural question of possible rank manipulations by adding ”well-chosen” alternatives. This problem is studied in the context of a simplified version of the PROMETHEE II method also known as the Copland score. A linear program is proposed to test whether there is a way to rank a given alternative at the first position by adding artificial ones. Simulations are used to quantify the likelihood of this possibility and to test if it can be avoided.
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