best one) is replaced by an even worse candidate, say person D. That is, now we have B > D, and candidate B is replaced by D while candidates A and C remain in the pool of candidates with exactly the same characteristics as before. When the new set of alternatives (i.e., candidates A, D and C) are ranked together and by assuming that the criteria have exactly the same weights as before, then should not candidate A still be the best one? It turns out that under some decision making methods the best alternative may be different now. This is known as a rank reversal and it is one of the types of rank reversals. The first type of rank reversal in the above context was observed by Belton and Gear in 1983 as part of a study of the analytic hierarchy process (AHP). They first considered a simple decision problem comprised by 3 alternatives and 2 criteria. Next a copy of a non-optimal alternative was introduced. When the 4 alternatives (i.e., the previous 3 plus the copy) were evaluated, and under the assumption that the criteria weights are exactly the same as before, it was observed that now the indication of the best alternative can change. That is, a rank reversal may occur with the AHP. A few years later it was observed that the AHP, as well as a new variant to it that was introduced by Professor Thomas Saaty (the inventor of the AHP) in response to the previous observation by Belton and Gear, may exhibit rank reversals when a non-optimal alternative is replaced by a worse one (and not a copy of an alternative as in Belton and Gear's experiment). The issue of rank reversals has captured the interest of many researchers and practitioners in the field of decision-making. It is something that continues to be considered controversial by many and is frequently debated. Different types of rank reversals There are many different types of rank reversals, depending on how the alternatives in a problem are defined and evaluated. These types are described next as Type 1, Type 2, Type 3, Type 4, and Type 5. Rank reversals of Type 1 As stated earlier, one may introduce identical or near-identical copies of non-optimal alternatives and then check to see if the indication of the best alternative changes or not. Rank reversals of Type 2 Another