ELECTRE IV - ELimination Et Choix Traduisant la REalité IV (no criterion weights)

Overview

ELECTRE IV is specifically designed for situations where criterion weights cannot be defined (equal importance assumed, but only ordinal thresholds). It uses four levels of outranking (from strict to lenient) to build a complete ranking. The absence of weights makes it more democratic but less flexible.

Output

net outranking count, higher is better

Data

Crisp, complete numeric matrix

Size

2+ alternatives, 3-12 criteria works best

Used for

Complex multi-stakeholder decisions

How it works

1. 1

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

   $$\{q_j,p_j,v_j\}\text{required, but no }{w}_j$$

   Roy-Hugonnard 1982, p.5 Sec.2

2. 2

   Categorise pairwise relations by counts of indifferent/preferred/very-preferred criteria.

   $$n_q(a,b)=\#\{j:q\text{-pref}\},n_p(a,b)=\#\{j:p\text{-pref}\},n_v(a,b)=\#\{j:v\text{-pref}\}$$

   Roy-Hugonnard 1982, p.7 Eq.(1)

3. 3

   Five embedded outranking relations S_q, S_c, S_p, S_s, S_v based on count thresholds.

   $$S_q\supseteq S_c\supseteq S_p\supseteq S_s\supseteq S_v$$

   Roy-Hugonnard 1982, p.7 Eq.(2)

4. 4

   Distillation on each relation; ascending and descending procedures.

   $$V_k^d\text{descending},V_k^a\text{ascending; same as ELECTRE-III}$$

   Roy-Hugonnard 1982, p.8

5. 5

   Final partial preorder = intersection of descending and ascending.

   $${⪰}^{\text{final}}={⪰}^d\cap {⪰}^a$$

   Roy-Hugonnard 1982, p.9

Look elsewhere when

Assumptions to verify

• Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds
• Non-compensatory preference structure

Edge cases and pitfalls

• Weight-free assumption: if criteria truly have different importance, use ELECTRE III or II instead.

Works with

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