TODIM (TOmada de Decisão Interativa e Multicritério, Interactive and Multicriteria Decision Making)

TODIM is a ranking method that arranges alternatives into a single order once you already hold a decision table. Its output is a normalised global value between 0 and 1 for every alternative, together with the rank that value produces. Unlike TOPSIS and PROMETHEE, it does not generate weights; weights are supplied from outside. It was proposed by Gomes and Lima in 1992, through the problem of ranking projects with environmental impact; its name is the abbreviation of the Portuguese phrase for "Interactive and Multicriteria Decision Making." What sets TODIM apart from other ranking methods is that it is one of the few MCDM methods to draw its mathematical machinery directly from behavioural decision theory (prospect theory). It has been applied in fields such as supplier selection, rental property valuation and resource allocation.

The idea behind TODIM rejects something most classical decision methods silently assume: that people weigh gains and losses symmetrically. Kahneman and Tversky's prospect theory shows that the satisfaction people draw from a gain is smaller than the discomfort they feel from a loss of equal size. This is known as loss aversion. TODIM carries this idea into multi-criteria ranking: when two alternatives are compared, the amount by which one "gains" over the other on a criterion and the amount by which it "loses" are not summed on the same scale; losses are magnified by a loss-aversion coefficient (θ) before being taken into account. The larger θ is, the more heavily a weakness on any one criterion drags an alternative down.

This construction has a consequence: TODIM is compensatory, but it offers a behaviourally asymmetric compensation, unlike TOPSIS's arithmetic-mean logic. A strong gain on one criterion can offset a loss on another, but this offsetting is not "equally weighted." The loss side carries more weight as the coefficient θ grows. The philosophical consequence is this: where the decision-maker behaves cautiously in the face of risk and loss, holding the intuition "I would rather not gain a little and risk losing a lot," TODIM offers a more realistic model than classical fully compensatory methods.

The method proceeds through five steps.

First, scale equalisation. The method takes each criterion's column and divides it by the sum of the values in that column, giving each cell a share; this brings criteria measured in different units (TL, points, years) onto the same scale.

Second, the reference criterion and relative weights. The method chooses the criterion with the highest weight as the reference criterion (the user may fix a different criterion as the reference instead). Every other criterion's weight is divided by the reference criterion's weight to convert it into a relative weight; the reference criterion's relative weight is 1.

Third, the pairwise gain-loss degree. For every pair of alternatives and every criterion, the method treats the case where one alternative "wins" over the other (is better on that criterion) as a positive contribution measured by the square root of the relative weight; where it "loses," the same magnitude is treated as a negative contribution magnified by the loss-aversion coefficient θ. For cost-type criteria the method reverses the gain-loss direction.

Fourth, the total dominance degree. For every pair of alternatives, the method sums the gain-loss contributions across all criteria, giving a single "how much more dominant" figure for that pair.

Fifth, the global value and rank. The method sums each alternative's total dominance degree against every other alternative and scales these sums between 0 and 1 (so that the lowest sum becomes 0 and the highest becomes 1). It then ranks the alternatives from the highest of these values to the lowest.

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

The global value is a number normalised between 0 and 1; the alternative with the lowest total dominance always receives 0, and the one with the highest receives 1. A value of 0 does not therefore mean "poor" and 1 does not mean "perfect"; it only shows relative standing within this particular set of alternatives. The value depends directly on the choice of the coefficient θ: the same table can produce a result of a different magnitude, and sometimes a different order, under a different θ. The report should therefore show which value of θ was used and how sensitive the result is to it.

Thus instead of writing:

"TODIM shows A2 is the best alternative"

the report should read:

"With the chosen loss-aversion coefficient (θ=1) and these weights, A2 has the highest global value; the ranking holds for this data set even as θ varies, but A3's relative distance from A2 is sensitive to θ"

TODIM works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, one number per cell and no empty cells; directional information for every criterion; weights that sum to 1; and a loss-aversion coefficient θ (if unspecified, DecisionMind assumes θ=1, the classical "loss and gain equally weighted" case). It does not produce weights, it requires them; these can come from sources such as AHP, BWM, CRITIC or Entropy. DecisionMind holds eighteen TODIM family members alongside the base method, including extensions for various types of uncertainty. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

TODIM is a sound choice if you believe the decision-maker is more sensitive to losses than to gains, that is, if the intuition "a gain and a loss of equal size do not carry the same weight" fits your decision. Its typical territory includes supplier and alternative selection, rental or sale property valuation, and the ranking of projects with environmental impact.

There are cases where it should not be used: where the loss-aversion assumption does not suit the nature of the decision (for instance, where gains and losses are genuinely weighed symmetrically, a classical compensatory method is simpler and sufficient), where no expert opinion exists to set θ with justification (the default θ=1 can then remain arbitrary), and where no compromise can ever be made on one criterion (in which case elimination logic is required).

The loss-aversion intuition reflects the decision → TODIM

Gains and losses are weighed symmetrically, a plain compensatory method suffices → TOPSIS, SAW, WASPAS

No expert opinion exists to justify θ → start with the default θ=1 and report the sensitivity

No compromise on one criterion, sub-threshold alternatives must be screened out → screening first, then ranking

Not a ranking but weights are needed → AHP, BWM, SWARA (subjective); Entropy, CRITIC (objective)

TODIM's greatest strength is that it draws its mathematical machinery from an empirically tested behavioural decision theory (prospect theory), which brings the method closer than many other MCDM methods to the question of "how people actually decide" (Gomes and Lima, 1992). Second, the coefficient θ lets the degree of loss aversion be tuned: at θ=1 the method approaches classical symmetric behaviour, and at large θ it approaches strong loss aversion. Third, the reference-criterion mechanism explicitly builds the most important criterion's standing relative to the others into the model. Fourth, in real-world applications, such as rental property valuation, it has been shown to give results comparable to and consistent with classical methods (Gomes and Rangel, 2009).

Its limitations arise from the same structure. First, the choice of the coefficient θ directly, and sometimes strongly, affects the result; this value does not come from the data but is an assumption made by the analyst or decision-maker, and it remains arbitrary if unjustified (Llamazares, 2018). Second, because the choice of reference criterion (by default, the highest-weighted criterion) determines the other criteria's relative weights, a small change in the weights can change the reference criterion and affect the whole structure of the calculation from the start. Third, for cost-type criteria the gain-loss direction must be reversed correctly; skipping this step makes the result meaningless. Fourth, TODIM's original form is computationally heavier than TOPSIS or SAW, since it requires a pairwise comparison for every criterion.

The most common mistake is leaving θ at its default value (θ=1) without ever questioning it, and reporting the result as though it were certain; whether the ranking changes as θ changes should always be tested. A second mistake is forgetting to reverse the gain-loss direction for a cost criterion; a high value on a "lower is better" criterion then gets wrongly counted as a gain. A third mistake is never stating why the reference criterion is the reference criterion (because it carries the highest weight); the user could choose a different reference criterion, and that choice changes the result. A fourth mistake is comparing the global value, normalised to the 0-1 range, against another analysis's global value; the normalisation (scaling between the lowest and highest) is done in every analysis relative to that analysis's own set of alternatives.

The governing principle is this:

The global value is a product of the chosen loss-aversion coefficient, the reference criterion and the weights; the result can change when these choices change, and the report must state clearly which value of θ was used.