Borda Count: Positional scoring rule for rank aggregation

Overview

Rank aggregation (positional voting). Output typically rank_position (lower value = preferred).

Strengths

• •Method-specific: Rank aggregation (positional voting)
• •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 BORDA-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

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

Worked example

1. 1.Adım 1 (F1): Step 1: Collect K expert rankings R_k over m alternatives. Formül: \mathcal{R} = \{R_{1}, R_{2}, \ldots, R_{K}\},\ R_{k}: \{A_{1},\ldots,A_{m}\}\to\{1,\ldots,m\} Anchor: de Borda 1781, Sec.1
2. 2.Adım 2 (F2): Step 2: Borda count B_i = Σ (m − R_k(A_i)). Formül: B_{i} = \sum_{k=1}^{K} \big(m - R_{k}(A_{i})\big) Anchor: de Borda 1781, Sec.2
3. 3.Adım 3 (F3): Step 3: Descending ranking by B_i. Formül: \text{rank}(A_{i}) \propto -B_{i} Anchor: de Borda 1781

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