MAIRCA (Multi-Attributive Ideal-Real Comparative Analysis)

MAIRCA is a ranking method for when you already hold a numerical decision table and want the alternatives placed in a single order. Its output is a "total gap" value for every alternative and the rank produced by that value from smallest to largest; the smallest gap marks the best alternative. Pamučar, Vasin and Lukovac proposed it in 2014, to support a decision on investing in safety equipment at railway level crossings. It takes weights from outside, it does not generate them.

MAIRCA's starting point is a simple assumption: if the decision-maker had no information at all, each of the m alternatives would be chosen with equal probability (1/m). This gives every alternative the share it "theoretically deserves" on each criterion; the higher a criterion's weight, the larger the deserved share. The method then multiplies the alternative's actual, equalised performance on that criterion by this theoretical share to find its "actual" share. The gap between the theoretical share and the actual share shows how far behind the alternative falls on that criterion. Summing the gaps across all criteria yields the "total gap": the smaller this gap, the closer the alternative is to its "deserved" performance.

This idea carries a philosophical consequence: MAIRCA is compensatory, because gaps are summed across criteria, and a large gap on one criterion is softened on average by a small gap on another. At the same time, unlike TOPSIS, the point of comparison is not "the best alternative" but "the share deserved under equal probability with no information at all"; this brings MAIRCA closer to being read as a kind of fairness or expectation comparison.

The method proceeds through four steps.

First, the theoretical preference. The decision-maker is assumed to have no priority at all: each of the m alternatives is chosen with equal probability, that is, 1/m. This probability is multiplied by each criterion's weight to find the share the alternative "theoretically deserves" on that criterion. A criterion with a high weight also carries a high deserved share.

Second, scale equalisation. Criteria are equalised to between 0 and 1 by linear normalisation; direction is reversed for "lower is better" criteria.

Third, the actual preference. The theoretical share is multiplied by the equalised actual performance on that criterion. If an alternative is in the worst position on a criterion (equalised value 0), its actual share is also zero; if it is in the best position, its actual share equals its theoretical share.

Fourth, the gap and the ranking. The gap between the theoretical share and the actual share is computed for every criterion and summed across all criteria. If an alternative is in the best position on a criterion, its gap there is zero; if it is in the worst position, the gap equals the entire theoretical share for that criterion. The alternative with the smallest total gap takes first place.

The formulas behind these steps are given on the DecisionMind method page; this card carries no formulas.

The total gap shows the distance between "the share deserved with no information at all" and "the performance actually delivered" for an alternative; it is not a percentage or a probability. A gap close to zero means the alternative is in, or nearly in, the best position on almost every criterion; a large gap shows the alternative falls short on many criteria. The value cannot be compared with a gap value from a different analysis, because the theoretical share depends on the number of alternatives (1/m); when the number of alternatives changes, so does the point of comparison.

For this reason, instead of writing:

"MAIRCA found the best alternative"

the report should read:

"With these weights and this alternative set, the alternative closest to its deserved share is this one; if the gap between the top two is small, the ranking is sensitive to the weights"

MAIRCA works with crisp data: one number per cell. DecisionMind currently carries only this crisp version; it has no extension in another data type. You need alternatives in rows, criteria in columns, a fully populated table with no empty cells, direction information for every criterion, and weights summing to 1. MAIRCA does not produce weights, it asks for them. A minimum of two alternatives and two criteria is required; three to twelve criteria work comfortably.

Where every alternative carries the same value on a criterion, the normalisation denominator becomes zero; this criterion must either be removed before the analysis or handled separately.

MAIRCA is a suitable choice if your criteria are numerical, your table is fully populated, and you accept that a weakness on one criterion may be offset, to some extent, by strength on another. Its typical territory includes supplier and alternative selection, and prioritising equipment and safety investment.

MAIRCA is not suitable where a criterion can never be compromised; because the theoretical-share-versus-actual-share gap is additive, a serious weakness on one criterion can be masked by others. Where criteria are strongly linked, this link needs handling first, because the method treats criteria as independent.

A numerical table, compensation accepted, the goal is ranking → MAIRCA

The number of candidates may change after the analysis, ranking stability matters → methods more robust to rank reversal should be separately tested

No compromise allowed on one criterion → screen first, then rank

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

MAIRCA's principal strength is its conceptual simplicity: the idea of "the share deserved with no information at all" is easy to convey to a decision-maker, and every step can be followed on the table. The computational load is small; it consists only of summation and multiplication, with no square roots or logarithms needed. The effect of criterion weights is direct and proportional, which makes sensitivity analysis easier. The method lends itself directly to questions such as safety investment, where the issue is where resources should be prioritised.

Its limitations stem from the same structure. First, the assumption of full compensation: a serious weakness on one criterion can be papered over by others. Second, the normalisation denominator becomes zero when every alternative carries the same value on a criterion, and this criterion must be handled separately. Third, MAIRCA is a comparatively new method and does not yet have as broad an independent body of critique and rank-reversal literature as TOPSIS or VIKOR. The rapidly growing number of multi-criteria decision methods generally makes it harder to track how independently each one has been tested (Mardani et al., 2015). Fourth, it treats criteria as independent; where criteria influence one another, weight can be implicitly double-counted.

The most common mistake is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better," the theoretical-share-versus-actual-share gap is computed in the wrong direction and the ranking becomes meaningless.

A second mistake is reading the total gap as a percentage or a probability; the gap only ranks this alternative set relative to itself. A third mistake is including a criterion where every alternative carries the same value without noticing it; the normalisation then becomes undefined. A fourth mistake is assigning equal weights without justification and presenting this as "neutrality." A fifth mistake is choosing a compensatory method for a situation where one criterion can never be compromised.

The governing principle is this:

A MAIRCA result is a summary of the weights and criterion directions you chose; if the gap between the top two is small, the ranking is contested, and the report must show this.