NANSON - Nanson - iterative Borda elimination

Borda-based iterative aggregation

Nanson, E. J.1882

Overview

Input: rank matrix (rows=alts, cols=rankings, cell=rank 1..m). Source: Orakçı 2024 §1.8.4.

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
Her turda hayatta kalan alternatifler üzerinde Borda skorlarını hesapla; mean Borda'nın altındaki TÜM alternatifleri ele; reduced set'te tekrarla; ≤1 alt kalana kadar veya hiçbir alt mean altında değilse dur.
$B_{i} = Σ_{j} (m_{r} - r an k_{j} (A_{i})); \overset{ˉ}{B} = m e an; e l imina t e A_{i} : B_{i} < \overset{ˉ}{B}; i t er a t e$
Orakçı 2024 §1.8.4 (Nanson 1882 mean-threshold; ≠ Baldwin 1926 single-min)

Fits when / Look elsewhere when

Fits when

•Native group-decision support (multi-DM aggregation built into the pipeline)

Look elsewhere when

•Cardinal preferences important. Use a MAUT method.

Assumptions to verify

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

Edge cases and pitfalls

Applying NANSON without verifying this assumption.
Requirement: Input is a rank matrix (1=best, m=worst per voter)
Applying NANSON without verifying this assumption.
Requirement: Each voter ranks all alternatives
Using NANSON when: Cardinal preferences important → use a MAUT method.
An alternative method is recommended in this situation.

How to cite

Nanson, E. J. (1882). Methods of election.

BibTeX RIS APA (.txt)

System ID, as it appears in reports and the API

NANSON

How it works

Her turda hayatta kalan alternatifler üzerinde Borda skorlarını hesapla; mean Borda'nın altındaki TÜM alternatifleri ele; reduced set'te tekrarla; ≤1 alt kalana kadar veya hiçbir alt mean altında değilse dur.

B_{i} = Σ_{j} (m_{r} - r an k_{j} (A_{i})); \overset{ˉ}{B} = m e an; e l imina t e A_{i} : B_{i} < \overset{ˉ}{B}; i t er a t e

Orakçı 2024 §1.8.4 (Nanson 1882 mean-threshold; ≠ Baldwin 1926 single-min)

Edge cases and pitfalls

Applying NANSON without verifying this assumption.

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

Applying NANSON without verifying this assumption.

Requirement: Each voter ranks all alternatives

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

An alternative method is recommended in this situation.