Dodgson Method — Condorcet completion by minimum pairwise swaps
DODGSON (Dodgson Method — Condorcet completion by minimum pairwise swaps) is a aggregationoperator multi-criteria decision-making (MCDM) method introduced by Dodgson, C. L. in 1900. It turns a decision matrix of alternatives scored on multiple criteria into a structured, reproducible result.
Key highlights
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
Intuition
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How it works
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When to use it
Dodgson selects the alternative that is 'closest' to being a Condorcet winner — measured in pairwise swap distance. Always returns a winner (no paradox), but winner determination is NP-hard for unrestricted preference profiles. For m ≤ 10, exhaustive search is practical; beyond that, use approximation algorithms. Orakçı 2024 (Bölüm 3) shows Dodgson fails to produce full rankings in 82-99% of random samples for m ≥ 3 — use Kemeny or RAT for guaranteed full rankings.
Strengths & limitations
- Follows a transparent, reproducible computational procedure that can be audited step by step.
- Handles multiple criteria of differing scales and units within a single decision matrix.
- Results depend on the chosen normalisation, weights, and parameter settings.
Common pitfalls
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Sources
- 1.Dodgson, C. L. (1900). A method of taking votes on more than two issues (1876). Pamphlet, Clarendon Press, Oxford (original 1876)
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ScholarGate. (2026, June 2). DODGSON. ScholarGate. https://scholargate.app/decision-making/dodgson