Methods · Ranking
ELECTRE III (ELimination Et Choix Traduisant la REalité III)
Compares pairs of alternatives on a fuzzy scale of "how credibly does one outrank the other" and distils these credibility degrees in two directions to derive an order; some pairs may remain incomparable.
Base method's data type: Classical
What Is the Method?
ELECTRE III is an outranking method that, given a decision table, places alternatives in an order that is almost, but not strictly, complete. Bernard Roy proposed it in 1978 because he found the binary ("outranks / does not outrank") result produced by ELECTRE I too coarse. Unlike ELECTRE I, ELECTRE III does not sort alternatives into a core set; it builds a near-complete order among alternatives through a two-stage ranking procedure known as distillation.
The difference lies in the structure of the thresholds. In ELECTRE I, concordance and discordance are compared against a sharp threshold, "sufficient or not". ELECTRE III instead defines three separate thresholds for each criterion (indifference, preference, veto) and calculates the outranking degree as a fuzzy "credibility" value between 0 and 1. Its output is an order in which almost every pair has been compared; only the small number of pairs that cannot be clearly separated are marked "incomparable". It is preferred for complex, multi-stakeholder decisions where thresholds can be expressed linguistically, such as infrastructure, environment and public-policy decisions.
The Philosophy Behind It
The idea behind ELECTRE III is to answer the question "is a better than b" not with yes or no but with a degree of "how credibly better". In ELECTRE I, a pair of alternatives either establishes an outranking relation or it does not; in ELECTRE III this relation is a number between 0 (not credible at all) and 1 (fully credible). What makes this grading possible is that three thresholds are defined separately for each criterion: an indifference threshold (a difference this small is unimportant), a preference threshold (a difference this large constitutes a firm preference), and a veto threshold (a difference this large against the alternative, however much concordance exists on every other criterion, entirely invalidates the outranking). These three thresholds may be fixed numbers or may be defined proportionally to the criterion's own scale; DecisionMind supports both forms.
The consequence of this philosophy is that ELECTRE III combines both ELECTRE I's veto logic and a sensitivity that spreads this logic over a degree. In ELECTRE I's veto logic, a very large weakness on a single criterion blocks outranking. In the newly added sensitivity, small differences are disregarded (the indifference threshold), moderate differences create a partial reduction in credibility, and very large differences (veto) cancel the outranking entirely. The result is neither a number nor a set. It is an order, mostly complete but possibly incomparable for some pairs, obtained by distilling the credibility degrees between alternatives from two directions (starting from the best and starting from the worst).
How It Works
The method proceeds through seven steps.
First, three thresholds. Indifference, preference and veto thresholds are set for each criterion. These thresholds come from the decision-maker or a domain expert; they may be a fixed number or may vary with the criterion's own value.
Second, criterion-level concordance. For every pair of alternatives (a,b) and every criterion, how far a is "sufficiently good" relative to b is calculated as a graded transition, from full concordance to full discordance, between the indifference and preference thresholds. If the difference is below the indifference threshold, concordance is full; if it is above the preference threshold, there is no concordance; differences in between take a graded value.
Third, overall concordance. The criterion-level concordance values are weighted by the criterion weights and summed into a single overall concordance value; this value is the fuzzy counterpart of the concordance index in ELECTRE I.
Fourth, criterion-level discordance. For each criterion, how much worse b is than a is calculated graded between the preference and veto thresholds. If the difference exceeds the veto threshold, there is full discordance (that criterion alone blocks outranking); if it is below the preference threshold, there is no discordance.
Fifth, the credibility degree. The overall concordance value is pulled down in the presence of criteria showing high discordance. If a criterion's discordance exceeds the overall concordance, that criterion pulls the credibility below the overall concordance; if several criteria do so, their effects combine multiplicatively. The result is a single number between 0 and 1 showing how credible it is that a outranks b.
Sixth, two-directional distillation. Two separate rankings are built from the credibility matrix: a "descending" distillation that extracts alternatives in sequence starting from the most credible outranking, and an "ascending" distillation that extracts them starting from the weakest alternative. Each is internally a consistent complete pre-order (some alternatives may tie).
Seventh, the intersection of the two rankings. The descending and ascending distillations are compared: where both agree in the same direction, a firm preference or a tie is established; where they disagree, that pair is marked incomparable. The final result is a partial order made up of firm preferences, ties and incomparable pairs.
The formulas behind each step, the intermediate tables and the citation formats are given on the DecisionMind method page; this card carries no formulas.
How to Read the Output
ELECTRE III's output, unlike ELECTRE I's core set, is a near-complete order. But it also differs from the unbroken order produced by TOPSIS or VIKOR: some pairs of alternatives may remain "incomparable". A pair being incomparable does not mean "equally good"; it means the two distillation directions (descending and ascending) contradict each other for that pair, that is, the data and the chosen thresholds cannot credibly separate these two alternatives.
An alternative coming out "first" in the order does not mean it is best on every criterion. It means that, given the credibility degrees built with the chosen thresholds, it remains at the top at the end of the distillation. Changing the thresholds (especially the veto threshold) can change both the order and the number of incomparable pairs.
Thus instead of writing:
"ELECTRE III ranked A6 as the best alternative"
the report should read:
"According to the credibility degrees built with the chosen thresholds, A6 comes out on top in both the descending and ascending distillations; some pairs of alternatives, however, could not be reliably ranked with these thresholds and remain incomparable"
Data Type and Inputs
ELECTRE III works with crisp data; each cell must hold a single number. Unlike ELECTRE I, ELECTRE III neither produces weights nor computes thresholds by itself. You need alternatives in rows, criteria in columns, one number per cell; direction information for every criterion; weights summing to 1; and three separately determined thresholds for every criterion (indifference, preference, veto). Setting these thresholds is the method's most difficult and most critical step; it requires the participation of the decision-maker or a domain expert. DecisionMind holds three ELECTRE III family members alongside the base method (fuzzy and multi-stakeholder extensions). At least two alternatives are required; three to fifteen alternatives work comfortably (up to thirty is supported); three to twelve criteria are recommended.
When to Use It, When Not To
ELECTRE III 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. This requires wanting a near-complete order rather than the broad core set produced by ELECTRE I, and being able to set the thresholds (indifference, preference, veto) together with a domain expert. Its typical territory is complex, multi-stakeholder decisions in which non-compensatory logic matters.
There are situations in which it should not be used. If there is no expert opinion available to set the thresholds, and a threshold-free ranking based solely on weights is sufficient, TOPSIS or SAW is simpler. If a weakness on one criterion can acceptably be offset by others, a non-compensatory method is unnecessary. If only the set of front-runners is needed, that is, a full order is not required, the simpler ELECTRE I is enough.
Non-compensatory logic plus a near-complete order is wanted, thresholds can be set → ELECTRE III
Non-compensatory logic is enough, only a "set of front-runners" is wanted → ELECTRE I
A threshold-free, compensatory ranking is sufficient → TOPSIS, SAW, VIKOR
Weights, not a ranking, are needed, and dependency between criteria matters → weight with DEMATEL first, then a ranking method
No expert opinion is available to set the thresholds → objective weighting plus a compensatory ranking method
Strengths
ELECTRE III's most important strength is that it spreads ELECTRE I's coarse binary outranking logic over a fuzzy degree. This preserves the non-compensatory logic while producing a more discriminating order. The indifference threshold prevents differences as small as measurement error from needlessly affecting the ranking; the veto threshold ensures that unacceptable poor performance on a single criterion blocks outranking regardless of the concordance on every other criterion. The two-directional distillation openly displays uncertainties (incomparable pairs) that a one-directional ranking might conceal; this is an honest output. It is one of the most used and most mature members of the ELECTRE family (Figueira, Greco, Roy and Słowiński, 2013).
Weaknesses
Its limitations stem from the same structure. First, setting the three thresholds (indifference, preference, veto) separately for each criterion is a heavy information burden; if these thresholds are chosen arbitrarily, the result is arbitrary too (Figueira, Greco, Roy and Słowiński, 2013). Second, the two-directional distillation procedure is itself complex and can produce different results with different distillation parameters; this issue has also been discussed in the literature (Govindan and Jepsen, 2016).
Third, as the number of incomparable pairs grows, the method's practical usefulness falls. If every pair turns out incomparable, ELECTRE III becomes as undiscriminating as ELECTRE I. Fourth, reducing the results to a single final recommendation (a single "best" alternative) can require a separate procedure, such as a net-flow rule or an additional decision rule.
Common Mistakes
The most common mistake is setting the three thresholds (indifference, preference, veto) either too close together or too far apart, as "standard" values without regard to the data; this eliminates the benefit of the graded transition. A second mistake is using only one of the descending and ascending distillations and ignoring the other; the final result is their intersection, and a one-directional distillation does not give the full picture. A third mistake is interpreting an incomparable pair as "equally good"; incomparability is a sign that the data cannot separate the two, not a claim of equality.
A fourth mistake is presenting ELECTRE III's result as a "core set" in the manner of ELECTRE I; ELECTRE III produces a partial order, not a set. A fifth is setting the veto threshold so low that almost every difference becomes a veto; in that case nearly every pair turns out incomparable and the method loses its discriminating power.
The governing principle is this:
The order ELECTRE III produces is a consequence of the three chosen thresholds (indifference, preference, veto) and the distillation procedure; incomparable pairs are not an error but an honest sign that the data and the thresholds cannot reliably separate those two.
Cases
Each case opens with a decision table, describes in words what the method does to it, and shows how to read the result. The first case is drawn from the method's own reference application in the literature; the remaining cases are illustrative constructions.
1. Transport: Comparative evaluation of eight car models (Skalka, Bouyssou and Bernabéu, 1986)
In the reference application guide for the ELECTRE III and IV methods, eight car models (A1-A8) were compared on four criteria: fuel consumption and price ("lower is better"), top speed and interior volume ("higher is better"). The weights were set at 0.30 each for fuel consumption and price, and 0.20 each for speed and interior volume. Separate indifference, preference and veto thresholds were defined for each criterion; some thresholds are fixed numbers, others are defined proportionally (affine) to the criterion's own value.
| Model | Fuel consumption | Price | Top speed | Interior volume |
|---|---|---|---|---|
| A1 | 7.8 | 41,360 | 140 | 6.13 |
| A2 | 7.5 | 45,700 | 150 | 6.70 |
| A3 | 8.2 | 46,450 | 160 | 6.63 |
| A4 | 8.4 | 48,200 | 153 | 6.91 |
| A5 | 8.5 | 48,800 | 164 | 6.65 |
| A6 | 7.0 | 50,830 | 148 | 7.36 |
| A7 | 8.1 | 51,700 | 155 | 7.40 |
| A8 | 7.8 | 52,500 | 170 | 6.19 |
| Direction | lower is better | lower is better | higher is better | higher is better |
| Weight | 0.30 | 0.30 | 0.20 | 0.20 |
The method calculates a credibility degree for every pair of models with the defined thresholds, then distils these degrees in two directions (starting from the best and starting from the worst). The intersection of the two distillations gives the final partial order.
| Rank group | Models |
|---|---|
| 1 | A6 |
| 2 | A2, A3 |
| 3 | A1, A5, A7 (incomparable among themselves) |
| 4 | A8 |
| 5 | A4 |
The result reads as follows: A6 comes out clearly on top. Its low fuel consumption and reasonable price, together with middling speed and volume, mean both distillations leave it at the top. A2 and A3 tie in second place. In the third group, A1, A5 and A7 turn out incomparable with one another: each is strong on one criterion and weak on another relative to the other two, and the chosen thresholds could not establish a credible outranking among these three. A4 comes fourth; the most expensive and highest-consumption model, A4, is fifth and last.
The committee's hesitation: A1, A5 and A7 coming out incomparable is not a computational shortfall. It means that all three are superior on one criterion and inferior on another relative to one another, and that the defined thresholds, particularly the veto thresholds, do not count these differences as a "firm outranking". If the final choice must be made among these three, ELECTRE III itself does not give a single answer; an additional criterion, such as maintenance cost, or the decision-maker's direct preference, must come into play.
In the report: "With the criterion weights and thresholds set, A6 comes out clearly on top and A4 at the bottom; A1, A5 and A7 remain incomparable with one another, and the choice among them should be left to an additional criterion or a direct preference."
Source: Skalka, J.M., Bouyssou, D., & Bernabéu, Y.A. (1986). Electre III et IV: Aspects méthodologiques et guide d'utilisation. Document du LAMSADE No. 25 (3rd ed.), Université Paris-Dauphine, pp. 37–95 (credibility matrix p. 60, distillation rounds pp. 82–95, final partial order p. 95). (no DOI — an institutional working paper) The ranking results are the guide's own values; DecisionMind's ELECTRE III engine uses these results, transcribed from an independent source (the publication itself), as a validation example.
2. Public sector: A municipality's prioritisation of a public-transport route investment
A municipality, working with a limited budget, must decide which of three public-transport route investments to prioritise. Four criteria have been set: estimated passenger numbers and the share of low-income neighbourhoods along the route ("higher is better"), and construction cost and estimated construction time ("lower is better"). The municipal council debated and set the weights, and defined separate indifference, preference and veto thresholds for each criterion. A low veto threshold has been accepted specifically for the cost criterion, because a route that seriously exceeds the budget is meant to be eliminated regardless of its advantage on the other criteria.
The method compares the three routes. Suppose the route with the greatest passenger potential is also the most expensive, and this difference exceeds the veto threshold; in that case this route cannot outrank the others despite its advantage in passenger potential. The route with a high share of low-income neighbourhoods and a moderate cost then comes out ahead in both distillations.
The council's hesitation: had the cost veto threshold been slightly relaxed, the route with the highest passenger potential could have established outranking. This is a value choice the council is making between "budget discipline" and "passenger potential", and the report must state this plainly. In addition, since the low-income-neighbourhood-share criterion rests on a social-impact score, how that score is calculated must be made transparent.
In the report: "With the thresholds set, the route with the highest passenger potential could not establish outranking because it exceeds the cost veto threshold; the route with a high share of low-income neighbourhoods and a balanced cost comes out ahead in both distillations. The choice of the cost veto threshold reflects the council's preference for budget discipline."
3. Environment: A preliminary site-selection assessment for a waste-management facility
An environmental agency will carry out a preliminary assessment of three candidate plots of land for a solid-waste sorting facility. Four criteria apply: distance to residential areas and land cost (distance "higher is better", cost "lower is better"), transport distance ("lower is better"), and a soil/water pollution risk score ("lower is better"). The agency has set a high veto threshold on the pollution-risk criterion: if this risk exceeds a certain limit, the plot must be eliminated regardless of its suitability on every other criterion.
The method compares the three plots. Suppose the plot furthest from residential areas and lowest in cost is also the candidate with the highest pollution risk, and this risk exceeds the veto threshold; in that case this plot cannot establish outranking despite its advantage on the other criteria. The plot with a moderate transport distance and low pollution risk then comes out ahead in both distillations.
The agency's hesitation: the pollution-risk score is not a laboratory measurement but a model-based estimate from an environmental-impact report. A score close to the veto threshold could easily shift within the model's margin of uncertainty. Since ELECTRE III's veto mechanism plays a critical role here, the confidence interval of this score should be reported separately.
In the report: "The plot with the highest pollution risk could not establish outranking because it exceeds the veto threshold; the plot with a balanced transport distance and low pollution risk comes out ahead. The uncertainty margin of the pollution-risk score should be assessed separately, given how close it is to the veto threshold."
4. What Not to Do
Had the price criterion in the car case been mistakenly marked "higher is better", the most expensive model, A8, would also be counted as advantaged on this criterion, and the result would become meaningless because of the direction error. A second error is ignoring the fact that A1, A5 and A7 come out incomparable and reporting instead that "all three are equally good, whichever is chosen makes no difference". The correct statement is that the chosen thresholds could not separate these three and that an additional criterion is needed. A third error is confusing the partial order ELECTRE III produces with ELECTRE I's core set and presenting it as "the set of those not outranked"; ELECTRE III produces a partial order, not a set.
Extensions: for different data types
ELECTRE III has 2 extensions in the library. Same decision logic, different data type: if your data is not a classical number, read the relevant data type card, then open that member.
Sources
For the formulas behind each step, the intermediate tables and citation formats, see the DecisionMind method page: decisionmind.app/library/electre-iii
Roy, B. (1978). ELECTRE III: Un algorithme de classement fondé sur une représentation floue des préférences en présence de critères multiples. Cahiers du CERO, 20(1), 3–24. (no DOI — no verifiable DOI for this 1978 article could be found in Crossref; the DOI recorded in the manifest [10.1051/ro/1977110201451] matched a different article in Crossref, so it was not included in this card.)
Figueira, J., Greco, S., Roy, B., & Słowiński, R. (2013). An overview of ELECTRE methods and their recent extensions. Journal of Multi-Criteria Decision Analysis, 20(1–2), 61–85. DOI: 10.1002/mcda.1482
Govindan, K., & Jepsen, M. B. (2016). ELECTRE: A comprehensive literature review on methodologies and applications. European Journal of Operational Research, 250(1), 1–29. DOI: 10.1016/j.ejor.2015.07.019
Skalka, J.M., Bouyssou, D., & Bernabéu, Y.A. (1986). Electre III et IV: Aspects méthodologiques et guide d'utilisation. Document du LAMSADE No. 25 (3rd ed.), Université Paris-Dauphine. (no DOI)