Consensus Reaching (Degree of Consensus)

Consensus Reaching originates as a model for bringing several human experts' preferences towards a common point; Herrera-Viedma, Herrera and Chiclana proposed it in 2002. DecisionMind runs the concept on a different input: instead of several experts' preference matrices, there is a single decision table, and every criterion in that table is treated as a judge. Each criterion ranks the alternatives from best to worst according to its own direction (more or less being preferred). The engine calculates how closely these criterion rankings agree with one another and how consistently each alternative holds its place across them. The output is not a classic "best alternative" score but a robustness, or consistency, score.

Most ranking methods answer the question "which alternative delivers the highest total benefit?" Consensus Reaching asks a different one: "how much do the criteria agree about this alternative's position?" An alternative that stays at roughly the same rank across every criterion holds an uncontested position. One that swings wildly from criterion to criterion, first on one and last on another, holds a position that depends on which criterion you consult, which makes it fragile.

This idea carries an important consequence: a high robustness score does not mean "good," it means "uncontested." An alternative held consistently in the middle by every criterion can score just as highly as one held consistently at the top. For that reason, Consensus Reaching is not used on its own to answer "which one should I choose," but alongside a primary ranking method (TOPSIS, COBRA and the like) to show how contested that ranking is across criteria.

DecisionMind's implementation of Consensus Reaching proceeds through five steps.

First, each criterion's own ranking. Every criterion ranks all alternatives from best to worst according to its own direction. This is the verdict that criterion delivers as a "judge."

Second, similarity between criteria. For every pair of criteria, the method calculates how much the two rankings overlap. If two criteria place the same alternatives in the same order, similarity is high; if they rank them in opposite order, it is low.

Third, the degree of consensus. The similarities of all criterion pairs are averaged into a single degree of consensus. A value close to 1 means the criteria rank the alternatives in largely the same way; a low value signals a marked disagreement among the criteria.

Fourth, flagging the criterion that deviates from the pattern. The engine measures how close each criterion sits to the average ranking of all criteria. Criteria that fall below a threshold are flagged; this is a diagnosis, and the criterion itself is not automatically changed.

Fifth, the robustness score. The spread among an alternative's ranks across the different criteria is calculated. A small spread, meaning the alternative holds a similar rank under every criterion, pushes the robustness score towards the high end; a large spread pushes it towards the low end. Alternatives are then ranked from the highest score to the lowest.

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

The robustness score shows how consistently different criteria hold an alternative at the same rank; it does not say whether that alternative is good or bad. An alternative with a high score might be one held in the middle by every criterion, or one held at the top by every criterion. The robustness score is therefore not on its own a reason to choose an alternative; the average rank of the criteria must be examined separately to see which alternative sits better on average.

A low degree of consensus (how much the criteria agree, and by how much) means the chosen criterion set is evaluating the alternatives from markedly different angles, and that there is no single "correct" ranking. For this reason, instead of writing:

"Consensus Reaching found the best alternative"

it is correct to write:

"The criteria agree on this alternative's position to this degree; a high robustness score shows that this position is uncontested, not that it is good"

Consensus Reaching works with crisp data: one number per cell. DecisionMind currently has no extension of this method for another data type.

You need alternatives in rows, criteria in columns, one number per cell, and no empty cells; and direction information for every criterion (whether more or less is preferred). Unlike most other ranking methods, Consensus Reaching does not ask for weights: every criterion is treated as an equal judge, because what is being measured is not the criteria's relative importance but the agreement among them. A minimum of two alternatives and two criteria is required; at least three criteria are recommended for a meaningful measure of consensus, because only a single similarity value can be calculated between two criteria.

Consensus Reaching is a suitable choice if you have several criteria and want to see how much they agree about the alternatives, or how uncontested a ranking is. It is generally used to test the robustness of a primary ranking method's result (TOPSIS, COBRA, VIKOR and the like), as part of a sensitivity analysis.

If your aim is a direct single answer to "which alternative should I take," Consensus Reaching is not sufficient on its own; a high robustness score does not guarantee a good alternative. If you already have a strong priority order among your criteria, with some clearly more important than others, a weighted method is more suitable, because Consensus Reaching treats every criterion as an equal judge.

Question is how much the criteria agree about the alternatives → Consensus Reaching

A direct answer to "which one should I choose" is needed → primary ranking methods such as TOPSIS, COBRA, Compromise Programming

There is a marked difference in importance among the criteria → a weighted ranking method

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

Consensus Reaching's greatest strength is that it surfaces information most ranking methods do not: how contested the result is. Because it asks for no weights, it offers a quick first diagnosis, and by flagging whichever criterion deviates from the general pattern it directs the decision-maker to examine that criterion more closely. The concept is simple and works on the same logic as the number of criteria grows.

Its limitations stem mainly from the risk of misinterpretation. The greatest risk is confusing a high robustness score with a "good alternative"; this confusion arises from the method's own nature and must be explicitly guarded against in the report. In the original Herrera-Viedma model, consensus is reached through experts updating their opinions over several rounds (Herrera, Herrera-Viedma and Verdegay, 1996; Herrera-Viedma, Alonso, Chiclana and Herrera, 2007). DecisionMind's criterion-based implementation has no such multi-round updating; the result is a diagnosis calculated in a single pass. Treating all criteria as equal judges is a limitation where some criteria are clearly more important than others.

The most common mistake is presenting a high robustness score directly as "the best alternative"; the score shows consistency only. A second is ignoring a low degree of consensus and reporting a single ranking as though it were certain; a low consensus signals that the criterion set itself needs to be discussed. A third is trying to measure consensus with two criteria; in that case only a single similarity value exists, and generalising from it is risky. A fourth is assuming a flagged criterion (one that falls below the threshold) is a data error and removing it automatically; the engine only flags it, it does not judge the criterion's validity.

The governing principle is this:

Consensus Reaching's robustness score shows how much the criteria agree about an alternative's position, not how good that alternative is; confusing the two leads to a wrong decision.