On the influence of altering the action set on PROMETHEE II’s relative ranks

Abstract

For some multi-criteria decision aid methods, the relative ranks of two actions may be inverted when the original set is altered. This phenomenon is known as rank reversal. In this contribution, we formalise rank reversal for the Promethee II method. The aim is not to debate about the legitimacy of such effect but rather to derive the exact conditions for its occurrence when one or more actions are added or removed from/to the original set. These conditions eventually lead us to: (1) assess whether rank reversal between a given pair of actions is, at all, possible, and (2) characterise the evaluations of the actions that have to be added or removed to induce rank reversal. We also propose two metrics that express the “strength” of and the “sensitivity” towards rank reversal. Finally, we show on a toy example how they could be used in a decision making process.