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Build an ELECTRE III ranking from pairwise credibility, not a hidden total score
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Full chapter index · Independent practice · Judgement subject guide
ELECTRE III is an outranking method for ranking alternatives when criteria conflict, measurements are imperfect and poor performance on one criterion may resist compensation by strengths elsewhere. It asks whether the evidence is credible enough to say that alternative a is at least as good as b, then exploits the pairwise relation through descending and ascending distillations.
This article follows one small fictional decision from pseudo-criteria to concordance, discordance, credibility and final preorders. The worked numbers teach the audit trail; they are not a recommendation for a real procurement, policy or clinical choice.
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Full chapter index
See the mechanism · Chapters 1–2
Build the worked model · Chapters 3–5
Test what changes · Chapters 6–8
Check evidence and limits · Chapters 9–10
Practise and continue · Chapters 11–12
CHAPTER 1 OF 12 · See the mechanism
1. State the decision problem and the meaning of outranking
List the alternatives, decision owner, criteria, direction of preference, evaluation date and feasible set. ELECTRE III compares a fixed set of actions under a declared model. Adding or removing an option can change the exploitation result.
The statement aSb means there are sufficient arguments to regard a as at least as good as b and no excessively strong argument against it. It is not the same as “a has a larger total score”. Both aSb and bSa can be credible, or neither may be credible.
That possibility preserves indifference and incomparability instead of forcing every pair into a strict order. The decision record should therefore retain the pairwise relation and both distillations, not only one polished rank list.
Evidence check: for State the decision problem and the meaning of outranking, preserve the observation before the interpretation. Record alternatives, criteria, directions and decision owner. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Use criteria that are operational, non-duplicative enough for the intended model and tied to evidence. Mark benefit criteria, where higher is better, and cost criteria, where lower is better. Preserve units and missing-data rules.
Weights in ELECTRE III express the relative contribution of criteria to concordance. They do not convert every evaluation into a common currency, and the method does not infer them automatically. Elicit and test them separately from performance measurements.
Before calculating, inspect dominance, correlations and uncertainty. Two near-duplicate criteria can double-count one concern. A highly uncertain estimate should not be made decisive merely by reporting extra decimal places.
Evidence check: for Build the performance table before thresholds, preserve the observation before the interpretation. Record outranking rather than a hidden total score. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 3 OF 12 · Build the worked model
3. Use indifference, preference and veto thresholds deliberately
For each pseudo-criterion, an indifference threshold q represents a difference small enough to treat as negligible. A preference threshold p marks a difference large enough for clear preference. Between q and p, partial concordance changes gradually.
A veto threshold v represents a disadvantage large enough to oppose an outranking claim even when many other criteria support it. Some implementations use criterion-specific functions or omit vetoes. Every threshold needs a substantive interpretation in the criterion’s units.
Thresholds may be constant or depend on performance. Estimate them from measurement error, stakeholder discrimination and consequences, not from a desire to produce a convenient ranking. Test plausible ranges.
Evidence check: for Use indifference, preference and veto thresholds deliberately, preserve the observation before the interpretation. Record q, p and v meanings in criterion units. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 4 OF 12 · Build the worked model
4. Work one pair from partial concordance to credibility
Consider alternatives A and B on reliability, access and cost, with weights 0.40, 0.35 and 0.25. Higher reliability and access are better; lower cost is better. A=(84,72,76) and B=(79,80,56). Thresholds are q/p/v of 2/6/15 for reliability, 3/8/18 for access and 4/10/25 for cost.
For A outranking B, reliability supports A fully. A is eight points worse on access, reaching the preference threshold, so access contributes no concordance. A is 20 cost units worse, so cost contributes no concordance. The global concordance is therefore C(A,B)=0.40.
Cost discordance lies between its preference and veto thresholds: d=(20−10)/(25−10)=0.667. Because d exceeds C, it attenuates credibility: S(A,B)=0.40×(1−0.667)/(1−0.40)≈0.222. The exact formula and endpoint conventions must match the implementation.
| Criterion | Weight | A | B | q / p / v |
|---|---|---|---|---|
| Reliability, higher better | 0.40 | 84 | 79 | 2 / 6 / 15 |
| Access, higher better | 0.35 | 72 | 80 | 3 / 8 / 18 |
| Cost, lower better | 0.25 | 76 | 56 | 4 / 10 / 25 |
Evidence check: for Work one pair from partial concordance to credibility, preserve the observation before the interpretation. Record every concordance and discordance value in A versus B. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 5 OF 12 · Build the worked model
5. Calculate the reverse direction instead of assuming symmetry
For B outranking A, B is five reliability points worse. With q=2 and p=6, reliability partial concordance is (6−5)/(6−2)=0.25. B is better on access and cost, so those criteria contribute fully.
The global concordance is C(B,A)=0.40×0.25+0.35+0.25=0.70. The reliability disadvantage has not passed its preference threshold, so it creates no veto-style discordance in this simplified calculation. Credibility remains 0.70.
The pair therefore gives much stronger support to BSA than ASB. That is a directional evidence statement, not yet the final rank. Repeat the calculation for every ordered pair and preserve the matrices.
Evidence check: for Calculate the reverse direction instead of assuming symmetry, preserve the observation before the interpretation. Record reverse B versus A calculation. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Partial concordance records how each criterion supports the claim aSb. Weighted aggregation then forms a global majority index between zero and one. This allows broad support while preserving criterion-level evidence.
Concordance is still partly compensatory: several supportive criteria can outweigh a weak objection. Discordance and veto logic limit that compensation when a disadvantage becomes too large. This separation is central to the method.
Audit weights and thresholds together. Increasing one criterion’s weight raises its influence on the majority, while lowering its veto threshold makes severe opposition easier. Treating only weights as value judgements understates the model.
Evidence check: for Build concordance without hiding compensation, preserve the observation before the interpretation. Record global concordance and weight audit. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 7 OF 12 · Test what changes
7. Apply discordance and credibility attenuation correctly
For each criterion, discordance rises when a’s disadvantage passes the preference threshold and approaches the veto threshold. When discordance exceeds global concordance, the credibility of aSb is reduced. Several discordant criteria can compound the reduction.
A veto need not mean the alternative is infeasible. It means the particular outranking assertion lacks credibility under the declared model. Feasibility constraints should already have been handled before ranking.
Check boundary cases, benefit/cost transformations and missing values with hand calculations. A sign error on one cost criterion can reverse many pairwise relations while still producing a plausible-looking final order.
Evidence check: for Apply discordance and credibility attenuation correctly, preserve the observation before the interpretation. Record credibility attenuation and boundary cases. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 8 OF 12 · Test what changes
8. Distil the credibility relation into two preorders
ELECTRE III commonly uses descending and ascending distillation. The descending procedure identifies stronger alternatives first; the ascending procedure works from weaker alternatives. Each uses credibility cut levels and qualification scores to form classes.
The procedures can disagree because the outranking relation may be incomplete or non-transitive. Their intersection yields the final partial preorder, retaining ties or incomparability where warranted. Software variants can differ in cut-level details and tie handling.
Archive the algorithm version, parameters, credibility matrix and intermediate classes. A final label such as “A ranks second” is not reproducible without the exploitation settings that generated it.
| From / to | A | B | C | D |
|---|---|---|---|---|
| A | — | 0.22 | 0.74 | 0.66 |
| B | 0.70 | — | 0.61 | 0.81 |
| C | 0.48 | 0.55 | — | 0.69 |
| D | 0.31 | 0.42 | 0.58 | — |
Evidence check: for Distil the credibility relation into two preorders, preserve the observation before the interpretation. Record ascending and descending distillation settings. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 9 OF 12 · Check evidence and limits
9. Interpret ties, incomparability and rank reversals
A tie can reflect mutual outranking or the distillation’s inability to separate alternatives. Incomparability means neither direction is sufficiently credible. Those outcomes can be useful: they reveal conflict that a forced score would conceal.
Rank reversal can occur when the option set, thresholds or exploitation rules change. Test removal of clearly dominated or uncertain options and explain any reversal rather than treating it as a software anomaly.
Use pairwise explanation panels for decision meetings: strongest concordant criteria, active discordance, threshold proximity and evidence quality. That makes disagreement inspectable without pretending the model contains the only legitimate values.
Evidence check: for Interpret ties, incomparability and rank reversals, preserve the observation before the interpretation. Record ties, incomparability and option-set effects. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 10 OF 12 · Check evidence and limits
10. Run sensitivity and legitimacy checks
Vary weights, q/p/v thresholds and uncertain performances across defensible ranges. Record stable outrankings, fragile pairs and which parameter crossing changes a distillation class. One-at-a-time changes are helpful, but joint scenarios reveal interactions.
Compare with a no-veto case and with an alternative elicitation. If the recommendation depends on one threshold set by one stakeholder, that dependency belongs in the decision headline.
Technical robustness does not create legitimacy. Criterion selection, stakeholder standing, distributional effects and appeal routes remain governance questions. ELECTRE III structures reasons; it does not decide who is entitled to define them.
Document abstentions, unresolved evidence disputes and whose perspectives were absent from elicitation. Re-running a model after affected stakeholders review the criteria can be more important than refining a threshold by another decimal place. A decision-aid process is accountable only when participants can inspect both the numerical consequences and the reasons used to construct them.
Evidence check: for Run sensitivity and legitimacy checks, preserve the observation before the interpretation. Record parameter, legitimacy and governance limits. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
CHAPTER 11 OF 12 · Practise and continue
11. Independent practice and changed-context transfer
Practice case: using the worked pair, reduce A’s cost from 76 to 66. Recalculate cost discordance and S(A,B), keeping all other values fixed. Explain why the credibility changes even though global concordance remains 0.40.
Changed context: add a fourth alternative that is similar to B but slightly better on access and worse on reliability. Predict which pairwise calculations remain unchanged and why the distillation can nevertheless change. Then remove the cost veto and identify the claims affected.
Finish with a compact record: the strongest outranking, the least stable pair, the active veto or discordance, and the parameter range over which the final preorder survives.
Evidence check: for Independent practice and changed-context transfer, preserve the observation before the interpretation. Record the changed cost that alters credibility. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.
Is ELECTRE III a weighted-sum method?
No. Weights contribute to concordance, but discordance, vetoes and pairwise exploitation prevent the method from being reduced to one compensatory total.
Does a veto eliminate an alternative?
Not necessarily. It weakens or blocks a particular outranking assertion. Feasibility is a separate decision stage.
Why are there two distillations?
Opposite directions expose asymmetry and incomparability in the valued outranking relation. Their intersection supports a more cautious final preorder.
Continue with outranking, concordance and veto thresholds, PROMETHEE flows and rank reversal, and stochastic multicriteria acceptability analysis.
Authoritative background includes Bernard Roy’s paper on the outranking approach and foundations of ELECTRE methods, the established ELECTRE methods survey chapter, and Roy’s original paper introducing the ELECTRE family. Sources and links were checked on 22 October 2026.
Evidence check: for FAQ, sources and connected reading, preserve the observation before the interpretation. Record the reproducible partial-preorder claim supported. Then state the inference, one credible alternative, and the additional observation that would distinguish them. This compact audit keeps a fluent explanation tied to evidence that another reader can inspect.
Changed-context transfer: repeat this chapter’s decision after changing one consequential condition while holding the others fixed. Calculate or predict what should change, name the threshold or mechanism, and compare with the original case. If the conclusion survives, state the range tested; if it reverses, explain why. Transfer is demonstrated by the changed case, not asserted from the first example.
Practical decision record: write one sentence for what is known, one for what remains uncertain, and one for the next safe action. Include the evidence owner, the latest useful decision time, and the condition that would stop or reverse the action. This turns a technical result into a reviewable choice without pretending uncertainty has disappeared.