PAMSSEM II - Total ranking variant

Overview

Apply the F.steps in order; the final score determines the descending ranking.

Output

preference flow, higher is better

Data

Crisp, complete numeric matrix

Weights

Needs a weight source

Size

2+ alternatives, 3-12 criteria works best

Used for

Complex multi-stakeholder decisions

How it works

1. 1

   Local outranking index per criterion pair.

   $$S_j(A_i,A_l)\in [0,1]$$

   Martel-Aouni 1990, Sec.3 (PAMSSEM ancestor)

2. 2

   Concordance index C(A_i,A_l) = Σ_{j: A_i≽A_l} w_j / Σ w_j.

   $$C(A_i,A_l)=\frac{{\sum }_{j:A_i⪰A_l}{w}_j}{{\sum }_{j=1}^n{w}_j}$$

   PAMSSEM 1996, Eq.(1)

3. 3

   Local discordance index d_j(A_i,A_l) measuring how strongly A_l beats A_i on criterion j.

   $$d_j(A_i,A_l)=\frac{\max (0,C_j(A_l)-C_j(A_i))}{{\Delta }_j}$$

   PAMSSEM 1996, Eq.(2)

4. 4

   Comprehensive outranking degree S(A_i,A_l) combining concordance and discordance.

   $$S(A_i,A_l)=C(A_i,A_l)\prod _{\{j:d_j>C\}}\frac{1-d_j(A_i,A_l)}{1-C(A_i,A_l)}$$

   PAMSSEM 1996, Eq.(3)

5. 5

   Positive φ^+ and negative φ^- flows.

   $${\varphi }^{+}(A_i)=\sum _{l\ne i}S(A_i,A_l),{\varphi }^{-}(A_i)=\sum _{l\ne i}S(A_l,A_i)$$

   PAMSSEM 1996, Eqs.(4)-(5)

6. 6

   Net flow φ(A_i) = φ^+(A_i) − φ^-(A_i).

   $$\varphi (A_i)={\varphi }^{+}(A_i)-{\varphi }^{-}(A_i)$$

   PAMSSEM 1996, Eq.(6)

7. 7

   PAMSSEM I partial ranking from (φ^+, φ^-); PAMSSEM II full ranking from φ descending.

   $$\text{PAMSSEM I: }({\varphi }^{+},{\varphi }^{-})\text{ partial};\text{PAMSSEM II: rank by }\varphi \text{ descending}$$

   PAMSSEM 1996, Sec.4

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

• Applying PAMSSEM-II without verifying this assumption.

  Requirement: Decision-maker can specify preference (p), indifference (q), and veto (v) thresholds

• Applying PAMSSEM-II without verifying this assumption.

  Requirement: Non-compensatory preference structure

• Using PAMSSEM-II when: Small dataset (m<3) → outranking benefit minimal.

  An alternative method is recommended in this situation.

• Using PAMSSEM-II when: Compensatory preferences acceptable → simpler ranking method.

  An alternative method is recommended in this situation.

Works with

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