ELECTRE Calculator

ELECTRE is a family of multi-criteria decision analysis. ELECTRE stands for ELimination Et Choice Translating REality.

There are two main parts to an ELECTRE application: first, the construction of one or several outranking relations, which aims at comparing in a comprehensive way each pair of actions; second, an exploitation procedure that elaborates on the recommendations obtained in the first phase.

Usually, the ELECTRE Method is used to discard some unacceptable alternatives to the problem. After that, we can use another MCDA to select the best one. The Advantage of using the Electre Method is that we can apply another MCDA with a restricted set of alternatives saving much time.

New here? Try it with example data

Fill every step with “Choosing a laptop” and see a result in one click.

Step 1: Alternatives

Enter at least three alternatives

Alternatives

Step 2: Criteria

Insert criteria

No.	Name	Type	Weight	Qualitative	Actions
1		Benefit
2		Benefit

Step 3: Performance Matrix

Complete previous steps

How ELECTRE works

ELECTRE (Elimination Et Choix Traduisant la REalite) is an outranking method. Instead of one score per alternative it compares every pair of alternatives and decides whether one outranks the other, which makes it well suited to discarding clearly weaker options.

Step by step

Rescale the criteria weights so they sum to 1, then normalize each criterion column (vector normalization) and multiply by the weights.
Concordance: for every ordered pair (A, B), add up the weights of the criteria on which A is strictly better than B (higher for benefit criteria, lower for cost criteria).
Discordance: for every ordered pair (A, B), take the largest weighted advantage B has over A on a criterion and divide it by the largest weighted difference between A and B on any criterion.
Compute the mean concordance and the mean discordance over all pairs. These means are the thresholds; the calculator does not ask for custom thresholds.
A outranks B when its concordance is above the mean concordance and its discordance is below the mean discordance.
The result lists every outranking pair as "A is better than B".

Formulas

Concordance of A over B (sum of weights where A beats B)

\[C(A,B) = \sum_{j:\, A \succ_j B} w_j\]

Discordance of A over B

\[D(A,B) = \frac{\max_{j:\, B \succ_j A} \lvert v_{Aj} - v_{Bj} \rvert}{\max_{j} \lvert v_{Aj} - v_{Bj} \rvert}\]

Outranking rule (bars are the means over all pairs)

\[A \text{ outranks } B \iff C(A,B) > \bar{C} \ \text{ and } \ D(A,B) < \bar{D}\]

Worked example

With the laptop data above, the calculator builds these concordance and discordance matrices (row = first alternative, column = second alternative).

Example data: choosing a laptop
Alternative	Price (EUR) (cost, weight 3)	Performance score (benefit, weight 3)	Battery (hours) (benefit, weight 2)	Weight (kg) (cost, weight 2)
Brisk 15	900	6	9	1.8
Cirrus Pro	1500	9	10	1.6
Aurora 14	1200	8	12	1.3
Delta Air	1050	7	15	1.2

Concordance matrix C(row, column), mean 0.50
	Brisk 15	Cirrus Pro	Aurora 14	Delta Air
Brisk 15	-	0.30	0.30	0.30
Cirrus Pro	0.70	-	0.30	0.30
Aurora 14	0.70	0.70	-	0.30
Delta Air	0.70	0.70	0.70	-

Discordance matrix D(row, column), mean 0.84
	Brisk 15	Cirrus Pro	Aurora 14	Delta Air
Brisk 15	-	0.78	1.00	1.00
Cirrus Pro	1.00	-	1.00	1.00
Aurora 14	0.96	0.52	-	1.00
Delta Air	0.37	0.69	0.77	-

Four pairs pass both thresholds: Delta Air is better than Brisk 15, Cirrus Pro and Aurora 14, and Aurora 14 is better than Cirrus Pro. Cirrus Pro beats Brisk 15 on weights worth 0.70, but Brisk 15 is so much cheaper that the discordance is 1.00 and the outranking is rejected.

Use the "Load example" button at the top of this page to fill in this data and run it yourself.

Frequently asked questions

What does "A is better than B" mean in the ELECTRE result?

It means A outranks B: A is at least as good on enough of the weighted criteria (concordance above the mean) and is not too much worse on any single criterion (discordance below the mean).

Why does ELECTRE not give one score or a single ranking?

ELECTRE compares pairs. Some pairs may not outrank each other in either direction, so the result is a list of outranking pairs rather than a score. It is often used to eliminate weak alternatives before applying another method such as TOPSIS.

Can I set my own concordance and discordance thresholds?

No. This calculator uses the mean concordance and mean discordance over all pairs as the thresholds, and the details panel under the result shows both means together with the matrices.

Why can a strong overall winner still fail to outrank an alternative?

Because of discordance. If another alternative is far better on even one criterion, the discordance can exceed the threshold and block the outranking, even when most of the weight agrees.

How many alternatives and criteria can I use?

You need 3 to 7 alternatives and 2 to 7 criteria, and every performance value must be greater than zero. Weights are relative importance: enter any positive numbers and the calculator rescales them so they sum to 1. Weights of 3, 3, 2 and 2 are the same as 30%, 30%, 20% and 20%.