NANSON: Nanson: iterative Borda elimination

Overview

Borda-based iterative aggregation. Output typically rank_position (lower value = preferred).

Strengths

• •Method-specific: Borda-based iterative aggregation
• •Native group-decision support (multi-DM aggregation built into the pipeline)

Limitations

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

Assumptions to verify

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

When not to use

• •Cardinal preferences important → use a MAUT method

Edge cases

• •See F.steps and D.parameters for NANSON-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'NANSON bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Input is a rank matrix (1=best, m=worst per voter)
• •Hatalı: 'NANSON bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Each voter ranks all alternatives
• •Hatalı: NANSON'yi 'Cardinal preferences important → use a MAUT method' durumunda kullanmak: recommendation_metadata.not_recommended_when alternatif öneriyor.

Worked example

1. 1.Adım 1 (F1): 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. Formül: B_i = Σ_j (m_r − rank_j(A_i)); B̄ = mean; eliminate {A_i : B_i < B̄}; iterate Anchor: Orakçı 2024 §1.8.4 (Nanson 1882 mean-threshold; ≠ Baldwin 1926 single-min)

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