ELECTRE I (ELimination Et Choix Traduisant la REalité I)

ELECTRE I does not place alternatives into a single order when you hold a decision table. Instead, it is a choice method that sifts out the strongest alternatives into a set. Its output is not a ranking but a list called the "kernel", containing the alternatives that no other alternative outranks. Bernard Roy proposed the method in 1968. ELECTRE I is the founding member of the ELECTRE family and, more broadly, of outranking-based multi-criteria decision methods. Decision-makers favour ELECTRE I in complex, multi-stakeholder decisions, in fields such as public policy and infrastructure investment. The method produces no weights, taking them from outside.

The question behind ELECTRE I is not "which alternative gets the best score" but "which alternative is not clearly outranked by any other". To say that one alternative (a) outranks another (b), two conditions must hold together. The first condition is concordance: on a sufficiently large share of the criteria, a must be at least as good as b. The second condition is the absence of discordance: even a single criterion on which b is clearly, sharply superior to a can refute this claim. This second condition is the fundamental difference that sets ELECTRE I apart from TOPSIS and VIKOR. In TOPSIS and VIKOR, a weakness on one criterion can be offset by strength on others. In ELECTRE I, a very large weakness on a single criterion can invalidate a claim of outranking, regardless of concordance on every other criterion. This is a kind of veto mechanism.

Because of this philosophy, the method gives its result not as a number but as a network of relations. For every pair of alternatives, the question "does a outrank b" is answered. From these answers, an outranking graph is built. The alternatives that no arrow points to in the graph form the kernel; these alternatives are outranked by no other. If the set has a single member, there is a clear recommendation. If it has more than one member, the method has failed to distinguish between these alternatives. This is not a malfunction; it is an honest signal that the data does not support that distinction.

The method proceeds through six steps.

First, scale equalisation (normalisation). Criteria are in different units. As in TOPSIS, the method divides every column by its own magnitude (vector normalisation) to make it unit-free and comparable.

Second, weighting. The method multiplies each normalised column by the criterion's weight.

Third, the concordance index. For every pair of alternatives (a,b), the method sums the weights of the criteria on which a is at least as good as b. The larger this total, the more criteria support the view that "a outranks b on these criteria". The total can be at most 1 (every criterion).

Fourth, the discordance index. The method takes the ratio of the largest difference among the criteria on which a is worse than b, to the largest difference observable across the whole dataset. A very large weakness on a single criterion produces a high value here. The larger this value, the weaker the claim that a outranks b.

Fifth, thresholds. DecisionMind sets a "sufficiently concordant" threshold (c̄) and a "sufficiently undiscordant" threshold (d̄) by averaging the concordance and discordance indices across every pairwise comparison in the dataset. DecisionMind uses these averages by default. You may also set a fixed threshold if you wish.

Sixth, the outranking relation and the kernel. a outranks b (a S b) if and only if the concordance threshold is exceeded AND the discordance threshold is not exceeded. The method builds an outranking graph from all these relations. The alternatives outranked by no other in the graph form the kernel. ELECTRE I gives this set as its output, not an order.

DecisionMind gives the formulas for each step, the intermediate tables and the citation formats on the method page. This card carries no formulas.

ELECTRE I's output is a set, not an order. The alternatives within the kernel are those outranked by no other. The size of the set is itself information. If it has a single member, the data supports a clear distinction. If it has more than one, the method has failed to distinguish between these alternatives. This is not a failure; it is an honest result reading "with the chosen thresholds, these alternatives cannot be distinguished from one another". As the thresholds (concordance and discordance) are loosened or tightened, the set grows or shrinks. The kernel therefore does not on its own mean "the best ones"; it means "those that cannot be distinguished with these thresholds".

Thus instead of writing:

"ELECTRE I chose A2 as the best alternative"

it is correct to write:

"With the chosen concordance and discordance thresholds, the kernel is {A2}; A1 and A3 are outranked by A2 under these thresholds, but the set could change if the thresholds are changed"

and if the set contains more than one alternative, this should be read as "the data does not support this distinction", not "all are equally good".

ELECTRE I works with crisp data. Every cell can be a single number, a ratio, an interval, or on an ordinal scale. You need: alternatives in rows, criteria in columns, one number per cell, direction information for every criterion, and weights that sum to 1. You may optionally set a fixed concordance and discordance threshold. If you do not, DecisionMind uses the averages it calculates from the dataset as thresholds. ELECTRE I produces no weights, taking them from outside; these weights can come from methods such as AHP, BWM, Entropy or CRITIC. DecisionMind holds sixteen ELECTRE I members alongside the base method. A minimum of two alternatives is required. Below three, the benefit of outranking analysis remains limited. Three to fifteen alternatives and three to twelve criteria work comfortably.

ELECTRE I is a suitable choice if you want a very poor performance on one criterion never to be offset by good performance on others, and a "set of front-runners" suffices instead of a single ranking. Its typical territory is complex decisions where the interests of multiple stakeholders conflict.

ELECTRE I should not be used in two situations. If the number of alternatives is below three, the discrimination that outranking analysis provides remains limited. If a weakness on one criterion being offset by others is acceptable, a simpler ranking method suffices.

If you want to screen out an alternative that is very poor on one criterion from the start (veto-like logic) → ELECTRE I

If a "set of front-runners" suffices instead of a ranking → ELECTRE I

If a complete ranking (first, second, third...) is needed → PROMETHEE II, TOPSIS, VIKOR

If there are fewer than three alternatives → the benefit of outranking analysis is limited, a simple comparison may suffice

If a weakness on one criterion being closed by another is acceptable → TOPSIS, SAW

ELECTRE I's most distinctive strength is its veto-like discordance mechanism. A very large weakness on a single criterion can block outranking despite overall concordance on the other criteria. This offers a non-compensatory logic. Its second strength is that its output is honest: if the data cannot clearly distinguish the alternatives, the method does not conceal this, returning a wide kernel instead. Third, ELECTRE I is the founding member of the outranking family Roy defined in 1968. ELECTRE II, III, IS and many other outranking methods trace their origin to this family. Fourth, ELECTRE I is a suitable choice for complex, multi-stakeholder decisions where reducing everything to a single figure can be misleading.

Its limitations follow from the same structure. First, the choice of thresholds (concordance and discordance) directly determines the result. The literature, including Roy himself, largely regards ELECTRE I and its close variant ELECTRE Iv as historical or pedagogical. The literature recommends versions such as ELECTRE IS, which include thresholds/pseudo-criteria, for modern applications (Figueira, Mousseau and Roy, 2005). Second, because the output is a set rather than an order, it does not directly answer "which one is first". If the set has more than one member, an additional mechanism is needed; this could be ELECTRE II, ELECTRE III, or a second method. Third, the method assumes criteria sit on a common, comparable scale (Greco, Ehrgott and Figueira, 2016). If this does not hold, the result becomes meaningless. Fourth, rank reversal is a known problem in the general multi-criteria decision literature (Wang and Triantaphyllou, 2008). The kernel can change when the alternative set changes.

The most common mistake is accepting the concordance and discordance thresholds as fixed "standard" values without looking at the data, rather than as averages calculated from it. A second mistake is saying "the method did not work" when an empty kernel results, without reviewing the thresholds. An empty kernel is the case where no alternative outranks any other, and all remain in the set. This is generally a sign that the thresholds are too strict for the data. A third mistake is reading a full kernel as "all are equally good". This, too, is a sign that the thresholds are too loose, or that the dataset lacks discriminating power. A fourth mistake is presenting ELECTRE I's output as a ranking, saying "first, second, third". The method produces a set, not an order. A fifth mistake is comparing different units directly without checking that criteria sit on a common scale.

The governing principle is this:

The kernel is a consequence of the chosen concordance and discordance thresholds; if it is empty (a complete match) or the full set (no match at all), this is not an error but a sign that the thresholds need to be reviewed against the data.