On the Influence of Altering the Action Set on PROMETHEE II's Relative Ranks

For some multi-criteria decision aiding 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 and derive the exact conditions for its occurrence when one ore more actions are added or removed from/to the original set. These conditions eventually lead us to: 1) assess whether or not 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; we show, on a toy example, how they could be used in a decision making process.