LODECI (LOgarithmic DEcomposition of Criteria Importance)

LODECI, like Entropy and CRITIC, is not a ranking method; it does not rank alternatives, it produces criterion weights. Given a numerical decision table of alternatives and criteria, it asks no one which criterion is more important; it scans the table itself and derives a weight vector that sums to 1. These weights then feed into a ranking method such as TOPSIS, VIKOR or SAW.

Pala proposed the method in 2024, in a study comparing the social-progress levels of European Union countries. Its name summarises what it does: it takes each criterion's "decomposition value" and passes it through a logarithmic scale. What sets it apart from Entropy and CRITIC is that it looks not at the whole distribution but at the largest difference between alternatives.

Entropy and CRITIC share a common idea: the more the alternatives differ on a criterion, the more that criterion determines the decision. LODECI comes from the same family, but differs in how it measures that difference. Entropy looks at the evenness of the whole distribution, CRITIC at the standard deviation; LODECI instead asks, for every alternative, "what is the largest difference that separates me from the other alternatives", and sums this largest difference across all alternatives before taking its logarithm.

A consequence follows: in LODECI, a criterion's weight is determined not by the average behaviour on that criterion but by the sharpest contrast. If two alternatives sit far apart on a criterion, that criterion's weight rises, however close the remaining alternatives are to one another on it. This reflects the view that "what really separates the decision is the extreme difference." If this view, that the sharpest difference rather than the average spread should count, is acceptable, LODECI is the right tool; if the decision should be governed by the overall distribution rather than a few extreme alternatives, Entropy or CRITIC fits better.

The method proceeds through four steps.

First, scale equalisation. For a "higher is better" criterion, every value is divided by the column's largest value; for a "lower is better" criterion, the column's smallest value is divided by every value instead. Every column is thereby compressed to between 0 and 1, and the best alternative always takes the value 1 on that criterion.

Second, the decomposition value. For every alternative, the absolute difference between it and every other alternative, in the equalised column, is calculated, and the largest of these is taken. This shows how sharply that alternative stands apart from the others on this criterion.

Third, the logarithmic decomposition value. All the alternatives' decomposition values on a criterion are summed, averaged over the number of alternatives, and, after adding 1, the natural logarithm is taken. The logarithm softens the effect of a single extreme alternative dragging the weight on its own.

Fourth, the weight. Each criterion's logarithmic decomposition value is divided by the sum of these values across all criteria. The result is a weight vector summing to 1.

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

A LODECI weight measures not the criterion's importance in the decision-maker's eyes but the size of the sharpest difference observed between alternatives on that criterion. A weight of 0.42 does not mean "this criterion is 42 per cent of the decision"; it means "the largest alternative-versus-alternative contrast in this table is seen on this criterion." Even if most alternatives are close to one another on a criterion, if a single alternative stands sharply apart from the rest, that criterion receives a high weight.

LODECI weights should therefore not be read the same way as Entropy or CRITIC weights; the two answer different questions. The weights are tightly bound to the alternative set: the largest difference can change when an alternative is added or removed, and the weights are rebuilt. When there are few alternatives (three or four), a single extreme alternative drags the weight considerably; this is a fragility also seen in Entropy and CRITIC, but its effect is more direct in LODECI because it rests on the single largest difference.

Thus instead of writing:

"The LODECI analysis showed that cost is the most important criterion"

the report should read:

"In this alternative set, the sharpest contrast is seen on the cost criterion; the LODECI weight of 0.42 reflects this contrast, not the decision-maker's priority order"

Classical LODECI works with crisp data: a single number in every cell. Values must be positive, because in "lower is better" criteria the column's smallest value is divided into each value, and zero is undefined at this step. DecisionMind currently holds no extension of LODECI; it stands as its sole member.

You need alternatives in rows, criteria in columns, a positive number in every cell, with no empty cells. Direction information ("higher is better" or "lower is better") is needed for every criterion, because scale equalisation is carried out according to this direction. No weight is entered; the method produces the weight. A minimum of two alternatives and two criteria is required; three or four alternatives can be worked with, but because the method rests on the largest difference, the result becomes more reliable as the number of alternatives grows, since the effect of a single extreme pair is then absorbed into the average.

LODECI is a suitable weight source where expert opinion is unavailable or unwanted, and where it is believed that what truly determines the decision is the sharpest contrast on a criterion. It works meaningfully on tables built from broad, genuine measurements, such as country and region comparisons or rankings built from performance indicators.

The situations where it should not be used follow from its philosophy. If the number of alternatives is very small (two or three), the largest difference comes from an almost random pair and the weight becomes unreliable. If the decision should be governed by the overall distribution rather than a few extreme alternatives, and this is undesirable, Entropy or CRITIC is a more balanced choice. Where the decision-maker clearly regards one criterion as a priority, LODECI cannot see this, because it looks at nothing but the data.

No expert opinion, the contrast comes from extreme alternatives → LODECI

Let the overall distribution govern the decision, not the extremes → Entropy, CRITIC

The decision-maker's priority should show in the result → AHP, BWM, SWARA (subjective)

Both preference and data matter → a combination of subjective and objective weights

Few alternatives (two or three) → read LODECI weights with caution, or switch to a subjective method

LODECI's most important strength is its simplicity: the calculation involves only differencing, averaging and a logarithm, requiring no advanced statistics. It is objective; the same table gives everyone the same weight. It captures a sharp contrast on a criterion directly, a contrast that can be diluted in Entropy's or CRITIC's average-based measures. The logarithm stops a single extreme value from inflating the weight without limit.

Its limitations stem from the same structure. First, because the weight rests on the largest difference rather than the overall distribution, a single extreme alternative can raise a criterion's weight even while most alternatives sit close together, which can amount to mistaking noise for information. Second, the weights are tightly bound to the alternative set; when an alternative is added or removed, the largest difference changes and every weight is rebuilt. Third, because the method was proposed in 2024, an independent body of critique and comparison is still limited; Zavadskas and Podvezko's (2016) assessment of more established methods offers useful guidance here, on the general limitations of objective weighting methods such as dependence on the alternative set and instability in small samples. Fourth, it cannot work directly with zero or negative values.

The most common mistake is reporting a LODECI weight as "importance". The weight measures not the criterion's value in the decision-maker's eyes but the sharpest difference seen between alternatives.

A second mistake is marking criterion direction wrongly; if a "lower is better" criterion is marked "higher is better", scale equalisation runs in reverse and the largest difference shifts to the wrong end. A third is placing great confidence in a weight derived from a table of two or three alternatives; at this scale the largest difference may be a matter of chance. A fourth is using one study's LODECI weights on a different alternative set; the weight is specific to that table. A fifth is feeding a table containing zero or negative values directly into the calculation without first shifting it.

The governing principle is this:

A LODECI weight measures how sharp a contrast a criterion carries in the decision; if this contrast comes from a few alternatives, the report must say so plainly, not describe the criterion as "important".