impact on large numbers of people. Given the well-established fact that different methods may yield different answers when they are fed with exactly the same problem, the question is how to evaluate them. Rank reversals are at the very heart of assessing the merits of such methods. At the same time, they are at the center of many heated debates in this area. Many authors use them as means to criticize decision making methods or to better explain rational behavior. Consider a simple example of buying a car. Suppose that there are two cars available to the decision maker: Car A and Car B. Car A is much cheaper than Car B but its overall quality is much less when compared to that for Car B. On the other hand, Car B is more expensive than Car A but it is also of better quality. A decision maker who is concerned of the high price issue, may choose Car A over the better quality and more expensive Car B. Next suppose that the car dealer presents to the decision maker a third car, say Car C, which is way more expensive than Car B but now the overall quality of Car C is marginally higher than that of Car B. Under such a scenario, it is quite possible for a decision maker to alter his/her opinion and purchase Car B instead of Car A, even if he/she has not actually seen Car C. Such events may take place with many rational decision makers. In other words, rank reversals may actually be possible in rational decision making. The issue of having rank reversals by rational decision makers has been studied extensively by Amos Tversky. In other words, having rank reversals in certain occasions and of certain types may not be indicative to faulty decision making. However, the key question is how to be able to distinguish when rank reversals indicate that something is wrong or when they do not conflict rational decision making. This is a highly debated issue in the decision making community. Methods that have been verified to exhibit rank reversals The following is just a partial list of multi-criteria decision making methods which have been confirmed to exhibit various types of rank reversals: The analytic hierarchy process (AHP) and some of its variants. The ELECTRE (outranking) method and its variants. The TOPSIS method. The PROMETHEE (outranking) method. Multi-attribute