WAM - Weighted Arithmetic Mean

Overview

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

Output

rank position, higher is better

Data

Crisp, complete rank

Size

2+ alternatives, 3-12 criteria works best

Used for

Rank aggregation, social choice, preference fusion

How it works

1. 1

   Validate weights satisfy Σw_j = 1 and w_j ≥ 0.

   $$\sum _{j=1}^n{w}_j=1,w_j\ge 0$$

   Yager 1988, p.184 Eq.(1)

2. 2

   Weighted arithmetic mean WAM(x_1,…,x_n) = Σ w_j x_j.

   $$\text{WAM}(x_1,\dots ,x_n)=\sum _{j=1}^n{w}_j{x}_j$$

   Yager 1988, p.184 Eq.(2)

3. 3

   Apply WAM per alternative; descending ranking.

   $$S_i=\sum _{j=1}^n{w}_j{x}_{ij},i=1,\dots ,m$$

   Yager 1988, p.185 Eq.(3)

Look elsewhere when

Assumptions to verify

• Input is a rank matrix (1=best, m=worst per voter)
• Each voter ranks all alternatives

Edge cases and pitfalls

• Applying WAM without verifying this assumption.

  Requirement: Input is a rank matrix (1=best, m=worst per voter)

• Applying WAM without verifying this assumption.

  Requirement: Each voter ranks all alternatives

• Using WAM when: Cardinal preferences important → use a MAUT method.

  An alternative method is recommended in this situation.

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