Copeland Method: Pairwise majority voting with net win-loss score

Overview

Pairwise majority rule (Condorcet-based aggregation). Output typically rank_position (lower value = preferred).

Strengths

• •Method-specific: Pairwise majority rule (Condorcet-based 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 COPELAND-specific edge handling. recommendation_metadata.assumptions_to_verify also lists boundary conditions.

Common pitfalls

• •Hatalı: 'COPELAND bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Input is a rank matrix (1=best, m=worst per voter)
• •Hatalı: 'COPELAND bu varsayımı kontrol etmeden uygulamak'. Doğrusu: Each voter ranks all alternatives
• •Hatalı: COPELAND'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 to derive pairwise preferences. Formül: \mathcal{R} = \{R_{1}, \ldots, R_{K}\} Anchor: Copeland 1951, Sec.1
2. 2.Adım 2 (F2): Step 2: Pairwise majority p_ik = #{k: R_k(A_i) < R_k(A_l)}. Formül: p_{il} = \sum_{k=1}^{K} \mathbb{1}[R_{k}(A_{i}) < R_{k}(A_{l})] Anchor: Copeland 1951, Sec.2
3. 3.Adım 3 (F3): Step 3: Wins minus losses C_i = Σ_l 1[p_il > p_li] − Σ_l 1[p_il < p_li]. Formül: C_{i} = \sum_{l\neq i}\mathbb{1}[p_{il}>p_{li}] - \sum_{l\neq i}\mathbb{1}[p_{il}<p_{li}] Anchor: Copeland 1951, Sec.2
4. 4.Adım 4 (F4): Step 4: Descending ranking by C_i. Formül: \text{rank}(A_{i}) \propto -C_{i} Anchor: Copeland 1951

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