RAT (Reference Alternative-based Aggregation Technique)

In a decision problem, several multi-criteria decision-making methods (TOPSIS, VIKOR, PROMETHEE, say) commonly rank the same alternatives by different logics, and these rankings turn out more or less different from one another. RAT was developed to collapse the rankings these different methods produce into a single common ranking. What sets it apart is that, instead of taking an average or a median, it declares one of the alternatives a fixed reference point and positions every other alternative relative to that reference. Its output is an aggregated value for every alternative; the higher this value, the more the alternative outperforms the reference. RAT is a technique introduced in Orakçı's (2024) Turkish-language book on aggregation techniques.

RAT's underlying idea is to perform relative positioning against a fixed point, rather than summing or averaging different methods' rankings directly. A reference alternative is chosen, and its aggregated value is taken as zero; every other alternative receives a value showing how far ahead of or behind this zero point it sits. This resembles reading a map in geography: declaring one city "kilometre zero" and describing every other city by its distance from it.

The philosophical consequence is that RAT measures the difference between alternatives through relative comparison rather than a search for an absolute "best." The further an alternative sits from the reference, the greater, in the eyes of the different methods, its gap from the reference is judged to be. The method accepts full compensation among criteria: a poor rank in one method dissolves, within the total difference computed against the reference, alongside good ranks in other methods.

The method proceeds through four steps.

First, building the rank matrix. A table is built with alternatives in rows and, in columns, the ranks produced by different decision-making techniques.

Second, choosing the reference alternative. One of the alternatives, usually the first alternative or one the decision-maker designates, is declared the reference; this alternative's aggregated value is zero by definition.

Third, computing the relative value. For every alternative, its rank under each technique is compared with the reference's rank. If the reference ranks better under that technique, the difference is marked negative; if the alternative ranks better, it is marked positive. The magnitude of these signed differences is combined across all techniques to give the alternative's total relative value.

Fourth, ranking. Alternatives are ranked by this relative value from highest to lowest; the alternative with the highest value comes first, and the reference itself stays wherever this ranking places it.

The formulas behind each step and the intermediate tables are given on the DecisionMind method page; this card carries no formulas.

The value RAT gives summarises an alternative's relative position, across different techniques, against the reference alternative; the reference itself is always zero. A positive value shows the alternative sits in a better position than the reference; a negative value shows a worse position. This value is not a percentage, and RAT values from two different analyses cannot be compared directly, because every analysis has its own reference and its own scale.

An important detail is that which alternative is chosen as the reference can affect the result. When the reference changes, the scale of every value changes; while the ranking itself mostly stays the same, the size of the numerical gap between alternatives changes depending on the reference. This is why, when interpreting RAT values, which alternative was taken as the reference must always be stated.

Thus instead of writing:

"RAT found the best alternative"

the report should read:

"With this alternative taken as the reference, the alternative in the most superior position according to the different techniques' rankings is this one; the numerical gaps can change if the reference is changed"

RAT works with a crisp rank matrix: alternatives in rows, and in columns the ranks produced by different decision-making techniques. The only parameter the user sets is the identity of the reference alternative; there is no mechanism requiring weights, and in the example all technique columns are treated as equal. DecisionMind currently holds no additional member alongside this base method; a minimum of two alternatives and two separate technique columns is required.

RAT is suitable when you hold different rankings produced by multiple decision-making techniques for the same problem and want to combine them relative to a particular reference alternative. If there is no natural alternative to serve as the reference, if every alternative is an equally plausible candidate "starting point," say, the choice of reference becomes arbitrary and this arbitrariness affects the result; in that case a method that requires no reference, such as median ranking or Schulze, may be more suitable. If the techniques' rankings differ sharply from one another, if one technique ranks an alternative first while another ranks the same alternative last, RAT dissolves this conflict into a single number; a decision-maker who wants to see the conflict itself should also carry out a technique-by-technique comparison.

Combine several techniques' rankings against a particular reference → RAT

Find an outlier-resistant middle position without needing a reference → Median Ranking

Find a pairwise-consistent winner without needing a reference → Schulze

Show the conflict among the techniques themselves, do not collapse it into one number → technique-by-technique comparative report

RAT's strength is that it combines the results of several techniques on a single relative scale, through a calculation that can be followed by hand. Taking the reference alternative as zero gives the decision-maker an intelligible starting point: it answers directly the question "how good or bad is this alternative relative to the reference I know." Its computational burden is small, and it continues to work on the same logic as the number of techniques grows.

Its limitations stem mainly from its dependence on the reference. First, the choice of reference alternative affects the result; with a different reference, the scale of the values changes, and this must be shown in the report. Second, because the method is relatively new, resting on a 2022 doctoral thesis, it does not yet carry as broad an independent body of scrutiny as TOPSIS or Borda; the information-loss problems general rank-aggregation methods carry (Dwork, Kumar, Naor and Sivakumar, 2001) may apply to RAT too, but no separate rank-reversal study specific to RAT could be found at the time this card was written. Third, it carries the assumption of full compensation; a very poor rank under one technique can be papered over, in the total, by good ranks under other techniques.

The most common mistake is choosing the reference alternative without justification and failing to state this choice in the report; because the numbers change with the reference, which alternative was taken as the reference, and why, must be explained. A second mistake is reading the RAT value as a percentage or a probability; the value is only a relative difference against the reference. A third is comparing RAT values from different analyses directly; every analysis has its own reference and its own scale. A fourth is trusting RAT's single number without noticing a large conflict among the techniques' rankings, one technique ranking an alternative first while another ranks it last, say; if such a conflict exists, its cause should be investigated first.

The governing principle is this:

A RAT result is a relative comparison against the chosen reference; the numbers change if the reference changes, so which alternative was taken as the reference, and why, must be reported.