Ranking method · Roy, 1978

ELECTRE III

ELimination Et Choix Traduisant la REalité

Outranking with veto power and the honesty to declare two alternatives incomparable.

How it works

1. Define three thresholds per criterion: q (indifference), p (strict preference) and v (veto).
2. Build a concordance matrix how strongly the criteria coalition supports 'a outranks b'.
3. Build discordance indexes whether any single criterion opposes the claim strongly enough to veto it.
4. Combine both into a credibility matrix σ(a, b).
5. Exploit σ with descending and ascending distillations; their intersection yields a partial preorder where conflicting evidence produces incomparability instead of a forced order.

Use it when

• One disastrous criterion value should be able to veto an otherwise good alternative.
• You can state meaningful indifference/preference/veto thresholds.
• "The data cannot order these two" is an acceptable even desirable answer.

Watch out for

• The most parameter-heavy method here; results are sensitive to the thresholds.
• Partial preorders are harder to communicate than a scored list.

Parameters

q, p, v thresholds per criterion (auto-derived from data ranges when left blank) and the λ credibility cutoff.

Cite the method

Roy, B. (1978). ELECTRE III: un algorithme de classements fondé sur une représentation floue des préférences en présence de critères multiples. Cahiers du CERO, 20(1), 3-24.

@article{roy1978electre,
  author  = {Roy, Bernard},
  title   = {{ELECTRE III}: un algorithme de classements fond{\'e} sur une repr{\'e}sentation floue des pr{\'e}f{\'e}rences en pr{\'e}sence de crit{\`e}res multiples},
  journal = {Cahiers du CERO},
  volume  = {20},
  number  = {1},
  pages   = {324},
  year    = {1978}
}