KEMIRA (KEmeny MedIan Indicator Ranks Accordance)

KEMIRA is a ranking method for when you hold a measured decision table and more than one expert opinion on the importance of that table's criteria. Its output is a single combined score for every alternative, together with the rank that score produces. It does not ask for direct numerical weights on the criteria; instead, it asks experts to order the criteria by importance, reduces those orders to a single consensus order, and then searches for weights consistent with that consensus itself. Krylovas, Zavadskas, Kosareva and Dadelo proposed it in 2014; the method is designed specifically for situations where the criteria split into two distinct families, for example engineering criteria and social criteria.

The idea behind KEMIRA is this. Asking an expert to assign a criterion exactly 0.27 of weight is difficult and often artificial. But asking the same expert to say that one criterion matters more than another is easy. KEMIRA takes this observation seriously: it asks experts only to order the criteria by importance. If more than one expert exists and their orders differ, the method reduces these orders to a single consensus order using what is called the Kemeny median. This means finding the single ordering that, in total, sits closest to all the experts' orders; it is the counterpart, in the world of rankings, of the statistical idea of a median.

The resulting consensus order is not enough on its own, because infinitely many weight sets are consistent with the same order, every set that obeys the rule that a more important criterion receives a larger weight. KEMIRA adds a second idea at this point: it scans the whole space of consistent weight sets, at a given resolution, and picks from among them the set under which the two criterion groups, engineering and social, say, rank the alternatives most consistently with each other. In this way the method stays faithful to expert opinion, the order, while not forcing numerical precision from outside but searching for it within itself.

The philosophical consequence of this approach is a search for compromise. KEMIRA is neither a purely subjective weighting method, unlike AHP it does not ask for a single weight set, nor a purely objective one, unlike Entropy it does not look only at the data; it searches somewhere between the two, bounded by the expert ranking. Within a group it is compensatory: a weakness on one criterion can be offset by another criterion in the same group, and because the final score is the sum of the two groups, a kind of balancing exists between the groups too.

The method proceeds through five steps.

First, scale equalisation. Each criterion group is normalised separately, within itself. Cost-direction criteria are inverted first, then every column is scaled between 0 and 1 relative to its own minimum and maximum value.

Second, reconciling the experts' priority orders. Every expert orders the criteria in their own group by importance. If more than one expert exists, the orders can differ. KEMIRA finds, via the Kemeny median, the single consensus order that in total sits closest to these orders. This step is carried out separately for each group.

Third, scanning the consistent weight sets. Every weight set that does not conflict with the consensus order, where a more important criterion genuinely receives a larger weight, is scanned at a given resolution, in steps of one tenth, for instance. The finer the scan, the more candidate sets there are.

Fourth, selecting the most consistent weight set. For every candidate weight set, the alternatives are ranked within that group. The method selects the weight set that maximises how many alternatives the two groups share at the top of their rankings, and, in the case of a tie, the one that minimises the difference between the two groups' rankings.

Fifth, combining. The engineering-group score and the social-group score, both calculated with the selected weights, are summed. The alternative with the highest total is placed first.

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 combined score shows an alternative's total standing across the two criterion groups; it is not a percentage or a probability. The size of the score is meaningful only for this alternative set, these experts' priority orders, and the chosen scan resolution. It cannot be compared with a score from a different analysis.

Two layers of uncertainty lie behind the score. First, the Kemeny median calculation that finds the consensus order can produce more than one ranking tied at the same lowest distance; in that case a rule is needed to decide which order is chosen, and the report should state that rule. Second, the fourth step, which selects among the consistent weight sets, is itself an optimisation; as the scanned resolution coarsens, as the step size grows, a different weight set can be selected and the result can change.

Thus instead of writing:

"KEMIRA found the best alternative"

the report should read:

"With these experts' priority orders and this scan resolution, the alternative with the highest combined score is this one; if the consensus order involved a tie, the report should state which rule resolved it"

KEMIRA works with crisp numerical data. You need a decision table whose criteria can be split into at least two meaningful groups, for example measurable engineering criteria and context-dependent social criteria, direction information for every criterion, and independent orders from more than one expert ranking the criteria within each group by importance. It neither asks for nor produces numerical weights; the only thing it produces is the alternatives' order. DecisionMind carries no extension of this method; it is offered only in its base form, working with crisp numbers.

The number of criterion groups can exceed two, but the method's definition is built on two groups. There must be at least two experts; with a single expert the idea of the Kemeny median loses its meaning, and that expert's own order simply becomes the consensus order. As the scan resolution, the step size, shrinks, the computational burden rises quickly, and this burden grows further as the number of criteria increases.

If you want to take only an order of importance from experts rather than exact numerical weights, if more than one expert cannot agree among themselves, and if your criteria naturally split into two distinct families, KEMIRA is a suitable choice. It has been used in problems where both measurable and context-dependent criteria appear together, such as site selection, supplier evaluation and personnel selection.

If your criteria all belong to a single family, all of the same kind, all financial, say, you cannot benefit from KEMIRA's two-group split; direct weighting methods such as AHP, BWM or SWARA are more suitable in that case. If the number of criteria is large or a fast result is needed, KEMIRA's weight scan can become heavy.

Expert opinion available only as an order, two criterion families exist → KEMIRA

Expert opinion can be taken directly as a numerical weight → AHP, BWM, SWARA

Criteria from a single family, weight to be derived from the data → Entropy, CRITIC

Classification rather than ranking is needed → elimination-based methods

KEMIRA's most important strength is that it asks experts for information that is easy to give, an order of importance, rather than placing the burden of assigning numerical weight on them. It does not ignore disagreement among more than one expert; it turns it into an explicit consensus mechanism via the Kemeny median. By splitting the criteria into two distinct families, it allows engineering and social criteria, which are hard to compare on a single common scale, to be handled together; this is close to how domain experts naturally think.

Its limitations stem largely from its computational structure. The step that scans the consistent weight sets grows combinatorially; as the number of criteria increases or the scan resolution becomes finer, the number of candidate sets multiplies quickly (Krylovas et al., 2014). The Kemeny median calculation can produce more than one ranking tied at the same lowest distance; in that case which order is chosen becomes a matter of preference, and if this is not reported the result looks arbitrary. Which group a criterion is assigned to, engineering or social, also lies outside the method, as the analyst's own decision; if that split changes, the result changes too. Because of the method's heavy computational burden, later work (Krylovas, Dadelo, Kosareva and Zavadskas, 2017) has proposed forms that combine the expert ranking with objective entropy weights; this is itself a sign that the base KEMIRA does not suffice on its own in every situation.

The most common mistake is reading the combined score as a percentage or a probability; the score reflects only this alternative set and this consensus. A second mistake is deciding which group a criterion belongs to without justification and failing to report that decision. A third mistake is not stating which rule resolved a tie in the Kemeny median calculation; the reader may then assume the result is the only possible one. A fourth mistake is changing the scan resolution, the step size, and expecting the same result; a coarser scan can select a different weight set and hence produce a different ranking. A fifth mistake is working with a single expert and presenting the method as an "expert consensus"; the idea of consensus becomes meaningful only with more than one, genuinely independent, expert ranking.

The governing principle is this:

A KEMIRA result is the product of reconciling the experts' priority orders and searching for weights consistent with that consensus; if the consensus involved a tie, or a choice was made in the scan resolution, the report must state this plainly.