way is to replace a non-optimal alternative with a worse one and then see if the indication of the best alternative changes or not. Rank reversals of Type 3 First consider a problem with all the alternatives together and get a ranking. Next, decompose the original problem into a set of smaller problems defined on two alternatives at a time and the same criteria (and their weights) as before. Get the rankings of these smaller problems and check to see if they are in conflict with the ranking of the alternatives of the original (larger) problem. Rank reversals of Type 4 Type 4 is like Type 3, but ignores the ranking of the original (larger) problem. Instead, check to see if the rankings of the smaller problems are in conflict with each other. For instance, suppose that the following 3 alternatives A, B, and C are considered. Next, suppose that some 2-alternative problems are solved and the rankings A > B, B > C, and C > A, are derived from these 2-alternative problems. Obviously, the above situation indicates a case of non-transitivity (or contradiction) as we get A > B > C > A. Rank reversals of Type 5 All previous types of rank reversals are known to occur with the analytic hierarchy process (AHP) and its additive variants, the TOPSIS and ELECTRE methods and their variants. The weighted product model (WPM) does not exhibit the previous types of rank reversals, due to the multiplication formula it uses. However, the WPM does cause rank reversals when it is compared with the weighted sum model (WSM) and under the condition that all the criteria of a given decision problem can be measured in exactly the same unit. The same is true with all the previous methods as well. This is the Type 5 ranking reversal. It is quite possible to define more types of rank reversals. One only needs to determine ways to alter a test problem and see how the ranking of the alternatives of the new problem differs from the original ranking of the alternatives of the original problem. Furthermore, the difference in rankings, somehow, should indicate the presence of undesirable effects. Are rank reversals always undesirable? Decision-making methods are used to make decisions in many aspects of human activity. This is especially true with decisions that involve large amounts of money or decisions that may have huge