ELECTRE (ELimination Et Choix Traduisant la REalité)

ELECTRE is not the name of a single computational procedure. It is the name of a family that has grown up around an approach Bernard Roy proposed in 1968. The family's common question is this: does one alternative (a) really outrank another (b)? That is, can it be said with confidence that a is clearly better than b? In seeking an answer to this question, the family behaves unlike compensatory methods such as TOPSIS or SAW: it does not let a very poor performance on one criterion be papered over by good performance on the others.

The family's members attach this common question to different kinds of output. ELECTRE I extracts from this relation a "core set" choice of alternatives not outranked by any other; this step is described in detail on its own card (see the ELECTRE I card). ELECTRE II and III turn the same relation into a full or partial ranking. ELECTRE TRI, by contrast, compares alternatives not with one another but with predefined category-boundary profiles, and assigns each to a class (such as accept/conditional/reject). This card describes the family's common logic and the difference between its members; it does not repeat ELECTRE I's step-by-step computation.

The family's philosophy places at its centre not the question "who scored best" but "can it credibly be said who beats whom". Claiming that one alternative beats another requires two things together. The first is concordance: a sufficiently large share of the criteria must support this claim. The second is the absence of discordance: even a single criterion on which the other side is clearly superior can refute the claim. This second condition is a non-compensatory logic, and it works like a kind of veto.

Family members harden or soften this shared philosophy to different degrees. ELECTRE I splits the relation with a sharp pair of thresholds (a concordance threshold, a discordance threshold) into "outranks / does not outrank" and stops there. ELECTRE II defines two different outranking relations, one strict and one loose, and combines them to build a full order. ELECTRE III uses graded thresholds (preference, indifference and veto thresholds) instead of sharp ones. It thereby answers the binary question "does it outrank or not" with a credibility degree between 0 and 1, expressing "to what extent it outranks".

These degrees are converted into a full order by a ranking (exploitation) procedure. ELECTRE TRI, by contrast, makes the comparison not between alternatives but between an alternative and fixed category-boundary profiles; the result is not an order but a class assignment. One point is common across all of them: a serious weakness on one criterion is never automatically closed by strength on the others.

All members of the family begin with the same three common steps, then diverge according to purpose.

First, scale equalisation (normalisation). This step is common to every member of the family. Criteria are in different units; each column is divided by its own magnitude to become unit-free and comparable.

Second, weighting. This step is also common. Each equalised column is multiplied by the criterion's weight. Here, weights are not an "exchange rate" as in TOPSIS but a "voting weight" the criterion brings to the decision.

Third, concordance and discordance. This step, too, is common. For every pair of alternatives, the weights of the criteria on which one is at least as good as the other are summed (concordance), and the largest difference on the criterion where the other side is clearly superior is measured (discordance).

The fourth step is where the family diverges. ELECTRE I compares these two indices against a threshold each and establishes a sharp outranking relation. It gives the set of alternatives not outranked by any other, that is, the core set; the detail of this step is on the ELECTRE I card. ELECTRE II evaluates the same indices against two differently strict thresholds; it combines the strong and weak outranking relations and produces an order.

ELECTRE III assigns each pairwise comparison a graded credibility degree, using the decision-maker's chosen preference, indifference and veto thresholds, instead of a sharp 0/1. A ranking procedure is then run on these degrees. ELECTRE TRI compares alternatives, using the same concordance/discordance logic, not with one another but with fixed category-boundary profiles, and places each alternative into a category according to these profiles.

Fifth, reading the result. The type of output varies by member: a set (I), an order (II, III) or a category (TRI); but in none of them is a very poor performance on one criterion automatically erased.

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

What the output means depends on which family member you use. A set (ELECTRE I) means "those that cannot be separated with these thresholds", not "the best ones". An order (ELECTRE II, III) is not a distance score in the manner of TOPSIS.

It is an order built up from pairwise outranking relations; the "first, second" relation between two consecutive alternatives is not always equally credible. A category assignment (TRI) states not the alternative's absolute quality but where it falls relative to predefined boundary profiles. If the boundary profiles change, the assignment changes with them.

Thus instead of writing:

"ELECTRE found A2 to be the best alternative"

the report should read:

"With the chosen ELECTRE member and thresholds, A2 comes out ahead in this relation (set/order/category); this result is a function of the thresholds and the weights"

stating clearly which member produced which type of output.

The family works with crisp data: one number per cell. You need alternatives in rows, criteria in columns, direction information for every criterion, and weights summing to 1. An additional input specific to the family is thresholds. For ELECTRE I, a single concordance and discordance threshold is enough.

ELECTRE III and TRI require the decision-maker to set, separately for each criterion, preference, indifference and veto thresholds; these thresholds come from outside and are not estimated from the data. The family does not produce weights, it asks for them; they can be drawn from sources such as AHP, BWM, Entropy or CRITIC. DecisionMind holds sixteen ELECTRE-family members alongside the base method (ELECTRE I, II, III, TRI and their derivatives). At least two alternatives are required; three to fifteen alternatives and three to twelve criteria work comfortably.

The family is a suitable choice if you do not want a very poor performance on one criterion to be offset by good performance on the others. It also serves whenever this non-compensatory logic needs to become a choice, a ranking or a sorting. Which member you choose depends on the type of output you need. The situation in which it should not be used is one where a weakness on one criterion can acceptably be closed by another; a compensatory method is then simpler and requires fewer parameters.

A set of front-runners is enough, no need for a full order → ELECTRE I

A full order is needed, sharp thresholds can be set → ELECTRE II

A full order is needed, thresholds are graded/uncertain → ELECTRE III

Alternatives need to be sorted into fixed categories (accept/reject and so on) → ELECTRE TRI

A weakness on one criterion can acceptably be closed by another → TOPSIS, SAW, MOORA

The family's clearest strength is its flexibility. From the same concordance/discordance core you can reach a simple choice (I), a detailed ranking (III), or an assignment to fixed categories (TRI). Its non-compensatory logic offers a natural framework for decisions where no compromise on one criterion is acceptable, such as safety or environmental thresholds. Roy's 1968 foundation has been supported by more than fifty years of application and extension literature. In Mardani and colleagues' 2000–2014 review, the ELECTRE family stands out as the fourth most applied family among the methods examined (Mardani et al., 2015, Table 4).

Its limitations stem from the same flexibility. First, there is a parameter burden: ELECTRE III and TRI require the decision-maker to set preference/indifference/veto thresholds separately for every criterion. Obtaining these thresholds is more demanding than TOPSIS's single set of weights. Second, the choice of thresholds determines the result directly, and this sensitivity has been examined in detail in the literature (Govindan and Jepsen, 2016).

Third, choosing a method without first deciding which output type (set, order, category) is needed among the family's members can lead to the wrong member being used. Fourth, as Roy himself has noted (Roy, 1991), the approach in practice requires a set of thresholds and parameters too technical for most decision-makers to follow intuitively. This increases the burden of explaining the method's transparency to the decision-maker.

The most common mistake is choosing a member from within the family at random, without first determining the required output type (set, order or category). Gathering ELECTRE III's detailed thresholds when a set would suffice, or settling for ELECTRE I's set when a full order is required, leads to needless complexity or incomplete information. A second mistake is taking the thresholds, particularly the veto threshold, as a default value without regard to the data and the decision-maker's real tolerance. A third is treating ELECTRE TRI's category-boundary profiles as a technical default and forgetting that they are in fact a value judgement, namely what performance counts as "acceptable". A fourth is comparing the result of one member in the family directly with another's; different members produce different types of output under different assumptions.

The governing principle is this:

ELECTRE is not a single computation but a family of choices; which member to use is determined first by the question "what type of output do I need", and then by how the thresholds are to be obtained from the decision-maker.