COOK-SEIFORD - Cook & Seiford (1978) - distance-based ranking aggregation

Overview

Input: rank matrix (rows=alts, cols=rankings, cell=rank 1..m). Source: Orakçı 2024 §1.8.7.

Output

rank position, lower 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

   Build m×m distance matrix where d_jk = sum over rankings of |rank(alt_j) − k|. Apply Hungarian algorithm to assign alternatives to target ranks minimizing total distance.

   $$d_{j,k}={\Sigma }_i|r_{i}j-k|;solveassignmentproblem(mintotaldistance)$$

   Orakçı 2024 §1.8.7

Fits when / 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 COOK-SEIFORD without verifying this assumption.

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

• Applying COOK-SEIFORD without verifying this assumption.

  Requirement: Each voter ranks all alternatives

• Using COOK-SEIFORD when: Cardinal preferences important → use a MAUT method.

  An alternative method is recommended in this situation.

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