TAXONOMY (Wrocław Taxonomic Measure of Development)

TAXONOMY answers the question "how do I combine a group of units (regions, institutions, countries) on several indicators into a single development ranking?" Its output is a development share for every alternative and the rank that share produces. The method was proposed in 1951 by Florek, Łukaszewicz, Perkal, Steinhaus and Zubrzycki of the Wrocław school, and developed further by Hellwig in 1968 in a study of country typology. It is used in fields such as regional development comparison, institutional performance indices and supplier evaluation; official statistical bodies still apply it in regional development indices today (Roszkowska, 2024).

TAXONOMY, much like TOPSIS, builds an ideal reference point and measures every alternative's distance to it. The difference lies in how it scales the data. Where TOPSIS scales the raw data by its magnitude, TAXONOMY subtracts each criterion's own mean from it and divides by its own standard deviation; this is called a standard score, or z-score. It answers the question "how many standard deviations is the alternative above or below the mean," looking at relative position rather than raw magnitude.

An analogy makes this clear. A student's exam performance can be measured not just by the raw score but by how many standard deviations it sits from the class average. A score of 80 might count as middling on an easy exam, yet the same score might count as outstanding on a difficult one. TAXONOMY converts every criterion to this relative scale, builds a single hypothetical "most developed" reference alternative, and turns every real alternative's distance to that reference, scaled against the typical spread of distances in the data, into a development share. Its philosophical consequence is that the method is compensatory: a weakness on one criterion can be balanced out by strength on another, and criteria are treated as independent of one another.

The method proceeds through four steps.

First step, standardisation. Every criterion has its own mean subtracted and is then divided by its own standard deviation; this carries all criteria onto a unit-free, comparable scale (the z-score). For cost criteria this standardised value's sign is reversed, so that a larger value always means "good" on every criterion.

Second step, building the reference point. The highest value of every criterion in the standardised table is taken to build a hypothetical "most developed" reference alternative.

Third step, measuring the distance. Every real alternative's straight-line (Euclidean) distance to this reference point is computed.

Fourth step, computing the development share. The distance is scaled against the typical distance measure in the data (the mean of the distances plus a safety margin added on top) and subtracted from one. The alternative closest to the reference takes a share nearest to 1; alternatives are ranked from largest to smallest on this share.

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 development share shows an alternative's relative position against the ideal reference. The closer the share is to 1, the more "developed" the alternative is considered, but this is not a percentage or a probability. The share rarely comes out exactly 0 or 1, because the reference scale is derived from the typical distance distribution in the data; a very extreme alternative could theoretically even take a negative share. The share is meaningful only for this particular group of alternatives; it cannot be directly compared with a share from a different group, because the mean and standard deviation are recalculated for every group.

For this reason:

"This region's development share is 0.44, that is, 44 per cent developed"

should be written instead as:

"This region's relative distance to the ideal reference corresponds to a development share of 0.44 against the typical distance scale within this group of regions; this share is meaningful only within this group"

TAXONOMY works with crisp data: one number per cell. DecisionMind holds TAXONOMY only in this base form; there is no separate data-type extension. You need alternatives in rows, criteria in columns, one number per cell, no empty cells; direction information (higher is better/lower is better) for every criterion. Because a standard score is computed, every criterion must have at least a few distinct values; a criterion taking the same value across every alternative sets its standard deviation to zero and drops that criterion from the calculation.

Note: DecisionMind's TAXONOMY engine currently treats all criteria with equal weight; even if a criterion weight is entered, it is not taken into account, and the DecisionMind team is reviewing this point. A minimum of two alternatives is required, and the comfortable range for the number of criteria is three to twelve.

If your aim is to combine a group of units (regions, institutions, branches) on several indicators into a single development ranking, and you accept compensation between the indicators, TAXONOMY is a suitable choice. If the number of units in your group is very small (two or three units), the standard deviation stops being a reliable estimate and the z-scores can become meaningless. If you need to give the criteria different, justified weights, another method that supports weighting (TOPSIS, WSM) should be preferred, since DecisionMind's current TAXONOMY engine does not apply it.

Within-group development comparison, relative position matters → TAXONOMY

Very few units (two or three) → standard deviation unreliable, consider another method

Different weights need to be given to the criteria → weighting methods such as TOPSIS, WSM

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

TAXONOMY's core advantage is that it makes indicators of different scale and unit directly comparable through the z-score; this combines a large-valued indicator such as income with a small-valued indicator such as a satisfaction score in the same table on a balanced footing. The method has a broad body of applied experience in official statistics and regional development literature going back to 1951 (Roszkowska, 2024). Its computational burden is small and the result compresses into a single, easily interpreted number.

Its limitations stem from the logic of the standard score. First, the result is group-dependent: were the same alternative assessed within a different group, its mean and standard deviation would change, and so would its share. Second, the standard deviation is less reliable in small samples; working with only a few alternatives can leave the result fragile (Bielak and Kowerski, 2019). Third, DecisionMind's current engine does not apply criterion weights; this is a limitation for decisions that call for differentiated, justified weighting. Fourth, the method treats criteria as independent; for indicators that influence one another, this assumption can lead to implicit double counting.

The most common mistake is marking criterion direction wrongly. If a "lower is better" indicator such as an unemployment rate is marked "higher is better," the ideal reference is built from the unit with the highest unemployment, and the result becomes meaningless. A second mistake is applying TAXONOMY with very few units (two or three) and assuming the standard deviation is reliable. A third mistake is reading the development share as a percentage or a probability; the share shows only relative position within this group. A fourth mistake is assuming and reporting that different weights were given to the criteria; the current engine treats all criteria equally.

The governing principle is this:

A TAXONOMY result depends on the mean and standard deviation of the group the alternatives belong to; if the group changes, the share changes too, and the report must state this group dependence explicitly.