Extension card · Classical

ELECTRE IV (Roy and Hugonnard, 1982)

This is the member of the ELECTRE family that assigns no weight to criteria at all. It works with three thresholds per criterion (indifference, preference, veto), and its output is not a complete ranking but a partial pre-order that emerges from a two-way distillation.

Base method

ELECTRE →

Philosophy, mechanics, strengths and weaknesses are on the base method card; this card describes only the difference.

Data type (family)

Classical →

What this data type is, when to use it, how to write it in a cell: the family's full account is here.

What Changes from the Base Method?

Three things change; the family's non-compensatory logic does not.

Weight disappears entirely. The family's other members (ELECTRE I, II, III) all ask the user for every criterion's weight and build the concordance index as the sum of these weights. ELECTRE IV asks for no weight at all. The criteria's relative importance is not even treated as equal; it does not exist at all. Every criterion is defined solely by its own three thresholds: the indifference threshold (q), the preference threshold (p) and the veto threshold (v). These thresholds come from outside and are not derived from the data.

Five nested classes instead of a concordance/discordance index. The family's weighted-sum logic is absent here. In every pairwise comparison, the band into which each criterion's difference falls is first counted: within the indifference band (below q), the preference band (between q and p), or the strong-preference band (between p and v, or above v). From these counts, five nested outranking classes are built: quasi, canonical, pseudo, sub- and veto classes, each accepting a looser condition than the one before it. A pair is classified according to the strongest of these five classes it satisfies and is assigned an ordinal credibility level (1; 0.8; 0.6; 0.4; 0.2). This level is not a probability or a percentage; it only carries the order of the five classes.

Result and defuzzification. A two-way distillation, as in ELECTRE II, is run over these credibility levels: once from the strongest option downward, once from the weakest upward. For this classical ELECTRE IV, DecisionMind also fixes the discrimination threshold; by Roy and Hugonnard's own decision this threshold is a fixed figure here, 0.1, and is not computed with a graduated formula as in ELECTRE III. The intersection of the two directions gives a partial pre-order (the final outranking relation); no number or percentage is produced.

How to Read the Output

What stays the same as the base method: the output is a position, not a score. Strict preference, indifference and incomparability are three separate relations.

The difference is here: what determines this position is not a weighted concordance percentage but which of five classes (quasi, canonical, pseudo, sub-, veto) one option falls into relative to another. A credibility level of 0.8 does not mean "80 per cent certain"; it only means that the pair falls into the second-strongest class (canonical).

Thus instead of writing:

"ELECTRE IV found Line 2 first with 80 per cent credibility"

the report should read:

"Line 2 outranks the other two lines with a canonical or stronger outranking class; this classification does not rest on the criteria's weight but on the chosen indifference, preference and veto thresholds"

When to Prefer This over the Base Method

Use it when the relative importance of the criteria cannot be determined reliably. If no source of weight (AHP, BWM, expert voting) exists, and treating the criteria as "equally weighted" would itself look like an artificial assumption, this member, which never uses weight at all, is appropriate.

The thresholds (q, p, v) are still required from the user here, not estimated from the data; this is a feature it shares with the family's ELECTRE III member. The exit condition of the family's ELECTRE I member (if a partial ranking, not a set of front-runners, is needed) applies here too. If the criteria are known to genuinely differ in importance, ELECTRE II or III should be preferred; the absence of weight is a design decision, not a deficiency, but it is not the right decision for every situation.

Mistakes Specific to This Extension

Interpreting the absence of weight without noticing it. Using this method on a problem where the criteria genuinely differ in importance puts an important criterion's voice on a par with a trivial one's. This is the manifest's own warning: if the criteria genuinely differ in importance, ELECTRE II or III should be preferred.

Skipping one threshold and assuming zero. All three thresholds (q, p, v) are mandatory. Entering only the preference and veto thresholds and leaving the indifference threshold at zero treats even the smallest measurement difference as a "preference" and silently changes the classification.

Breaking the threshold order (q < p < v). The engine checks this order; entering the veto threshold equal to or smaller than the preference threshold does not lead to a calculation error but to an outright input rejection.

Reading the credibility levels (1; 0.8; 0.6; 0.4; 0.2) as a percentage or a probability. These are labels showing the order of the five classes; the gaps between them are not an evenly spaced scale.

The governing principle is this:

ELECTRE IV is for situations where assigning weight to criteria cannot be done reliably. The criteria's importance is not treated as equal, it is not used at all; the only thing that determines the result is the three chosen thresholds.

Cases

The first case is illustrative: a validation example prepared for DecisionMind's unweighted ELECTRE IV engine, constructed with a scenario similar to Roy and Hugonnard's (1982) suburban-line problem but not using the paper's own figures. The second case is a construction.

1. Transport: A preliminary comparison of three suburban-line extension projects (illustrative validation example)

A local authority is comparing three suburban-line extension projects (Line 1, Line 2, Line 3). There are three criteria: an estimated ridership score and a route-efficiency score (higher is better), and a construction-cost index (lower is better). Instead of assigning weight to the criteria, the authority set the same three thresholds for all three criteria: an indifference threshold of 0.5, a preference threshold of 1.0, a veto threshold of 2.0.

Project	Ridership score	Route efficiency	Cost index
Line 1	3	5	4
Line 2	5	3	2
Line 3	4	4	3
Direction	higher is better	higher is better	lower is better

The method counts, for each pair, which threshold band the difference on each of the three criteria falls into, tries all five nested outranking classes from these counts, and selects the strongest. A two-way distillation is then run on the credibility matrix built from these classes.

Rank	Project
1	Line 2
2	Line 3
3	Line 1

The result reads as follows. Line 2 is stronger than the other two projects on both ridership and cost, and does not fall behind enough on any criterion to trigger the veto threshold; this is why it outranks both projects. Line 3 outranks Line 1 because it beats it on cost and route efficiency; Line 1's one strong criterion (route efficiency) is not enough to reverse this outranking.

The authority's hesitation is this: what would happen if Line 1's ridership score rose from 3 to 4 (an increase above the indifference threshold but below the preference threshold)? Rerunning the same calculation independently, the relationship between Line 1 and Line 3 reverses completely: Line 1 now overtakes Line 3 and rises to second place, and Line 3 drops to last. Line 2 keeps first place. This shows that a one-point increase on a single criterion alone, with the weight entirely unchanged, can swap the position of two projects.

In the report: "With the thresholds set (indifference 0.5, preference 1.0, veto 2.0), the ranking is Line 2, Line 3, Line 1; the relationship between Line 3 and Line 1 sits on a margin narrow enough to reverse with a small improvement in Line 1's ridership score."

Source: An illustrative validation example prepared for DecisionMind's unweighted ELECTRE IV engine (based on Roy and Hugonnard's 1982 suburban-line ranking problem; not the paper's own table or figures). The ranking and threshold sensitivity were computed by this card's author by independently running the DecisionMind engine; the baseline result matches the manifest's own validation record exactly.

2. Waste Management: A local authority's choice of site for three recycling facilities

A local authority will build a recycling facility on one of three candidate plots. Three criteria apply: a distance-from-residential-area score and a transport-accessibility score (higher is better), and an estimated environmental-impact index (lower is better). There is no consensus in the council over which criterion should be considered more important than the others; instead of assigning weight, separate indifference, preference and veto thresholds were set for each criterion.

The method compares the three candidate plots pairwise, selects the strongest of the five outranking classes for each pair, and builds a partial ranking through two-way distillation. Suppose the result shows that the plot with the lowest environmental impact outranks the other two, while the remaining two plots cannot outrank one another (they stay incomparable).

The council's hesitation is this: if the veto threshold on the environmental-impact index were set more strictly (that is, if the line for "an environmental harm too large for any criterion to compensate" were drawn lower), the lowest-impact plot's outranking would not change, because there was no difference close to the veto boundary in the first place. But if this threshold is tightened for the two plots that remain incomparable, one may come to outrank the other. This shows that incomparability here is not a lack of data but a borderline condition sensitive to the choice of threshold.

In the report: "The plot with the lowest environmental impact outranks both other plots under the chosen thresholds; the remaining two plots cannot outrank one another and stay incomparable. This incomparability may change if the veto threshold is tightened."

3. What Not to Do

Secretly assigning different weight to the three criteria in the suburban-line table (for example, treating ridership as more important than cost) is the first error; ELECTRE IV is defined by never using weight at all, not even equal weight is assigned. The second error is skipping the indifference threshold and giving only the preference and veto thresholds; this treats even the smallest measurement difference as a preference and silently changes the result. The third error is reporting Line 2's outranking level (canonical class, 0.8) as "80 per cent certainly better"; this level is not a probability, it is only its place in the order among five classes.

Formulae

The computation step by step, with the formula behind each step.

1. Thresholds q_j, p_j, v_j WITHOUT criterion weights (unique to ELECTRE-IV).
${q_{j}, p_{j}, v_{j}} required, but no w_{j}$
2. For every ordered pair count the criteria on which a is strictly preferred (m_p), weakly preferred (m_q), indifferent but better (m_i) or equal (m_0), and whether a's advantage reaches the veto threshold on some criterion.
$u_{j} (a, b) = g_{j} (a) - g_{j} (b) (sign flipped for cost); m_{p} (a, b) = # {j : u_{j} > p_{j}}, m_{q} (a, b) = # {j : q_{j} < u_{j} \leq p_{j}}, m_{i} (a, b) = # {j : 0 < u_{j} \leq q_{j}}, m_{0} = # {j : u_{j} = 0}, a P V_{j} b ⟺ u_{j} \geq v_{j}$
3. Test the four nested dominance relations S_q ⊆ S_c ⊆ S_p and S_v; the strongest verified relation sets the credibility d(a,b) = 1, 0.8, 0.6 or 0.35 (0 if none).
$a S_{q} b ⟺ m_{p} (b, a) = m_{q} (b, a) = 0 \land m_{i} (b, a) \leq 1 + m_{i} (a, b) + m_{q} (a, b) + m_{p} (a, b); a S_{c} b ⟺ m_{p} (b, a) = 0 \land m_{q} (b, a) \leq m_{p} (a, b) \land m_{q} (b, a) + m_{i} (b, a) \leq 1 + m_{i} (a, b) + m_{q} (a, b) + m_{p} (a, b); a S_{p} b ⟺ m_{p} (b, a) = 0 \land m_{q} (b, a) \leq m_{q} (a, b) + m_{p} (a, b); a S_{v} b ⟺ ∄ j : b P V_{j} a \land [m_{p} (b, a) = 0 \lor (m_{p} (b, a) = 1 \land m_{p} (a, b) \geq m /2)]; d (a, b) \in {1, 0.8, 0.6, 0.35, 0}$
4. Distil the ordinal relation-credibility matrix in descending and ascending directions, preserving tie classes.
$δ (λ) = 0.30 - 0.15 λ; V^{d}, V^{a} = distil (σ)$
5. Intersect descending and ascending preorders; return a partial preorder without a scalar proxy.
$⪰^{final} = ⪰^{d} \cap ⪰^{a}$

Sources

Roy, B., & Hugonnard, J. C. (1982). Ranking of suburban line extension projects on the Paris metro system by a multicriteria method. Transportation Research Part A: General, 16(4), 301–312. DOI: 10.1016/0191-2607(82)90057-7

Vallée, D., & Zielniewicz, P. (1994). ELECTRE III-IV, version 3.x, Aspects méthodologiques (Tome 1). Document du LAMSADE n° 85, Université Paris-Dauphine. (no DOI)

Roy, B. (1968). Classement et choix en présence de points de vue multiples (la méthode ELECTRE). Revue Française d'Informatique et de Recherche Opérationnelle, 2(8), 57–75. DOI: 10.1051/ro/196802v100571

Roy, B. (1991). The outranking approach and the foundations of ELECTRE methods. Theory and Decision, 31(1), 49–73. DOI: 10.1007/BF00134132

What Changes from the Base Method?

How to Read the Output

When to Prefer This over the Base Method

Mistakes Specific to This Extension

Cases

1. Transport: A preliminary comparison of three suburban-line extension projects (illustrative validation example)

2. Waste Management: A local authority's choice of site for three recycling facilities

3. What Not to Do

Formulae

1. Thresholds q_j, p_j, v_j WITHOUT criterion weights (unique to ELECTRE-IV).

2. For every ordered pair count the criteria on which a is strictly preferred (m_p), weakly preferred (m_q), indifferent but better (m_i) or equal (m_0), and whether a's advantage reaches the veto threshold on some criterion.

3. Test the four nested dominance relations S_q ⊆ S_c ⊆ S_p and S_v; the strongest verified relation sets the credibility d(a,b) = 1, 0.8, 0.6 or 0.35 (0 if none).

4. Distil the ordinal relation-credibility matrix in descending and ascending directions, preserving tie classes.

5. Intersect descending and ascending preorders; return a partial preorder without a scalar proxy.

Sources