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Draft:Comparison of voting methods

Single-winner voting methods are compared along many different criteria.

Comparison of single-winner voting systems
Criterion


Method
 Majority Majority loser Mutual majority Condorcet winner[Tn 1] Condorcet loser Smith[Tn 1] Smith-IIA[Tn 1] IIA/LIIA[Tn 1] Clone­proof Mono­tone Participation Later-no-harm[Tn 1] Later-no-help[Tn 1] No favorite betrayal[Tn 1] Ballot
type
Anti-plurality No Yes No No No No No No No Yes Yes No No Yes Single mark
Approval Yes No No No No No No Yes[Tn 2] Yes Yes Yes No Yes Yes Appr­ovals
Baldwin Yes Yes Yes Yes Yes Yes No No No No No No No No Ran­king
Black Yes Yes No Yes Yes No No No No Yes No No No No Ran­king
Borda No Yes No No Yes No No No No Yes Yes No Yes No Ran­king
Bucklin Yes Yes Yes No No No No No No Yes No No Yes No Ran­king
Coombs Yes Yes Yes No Yes No No No No No No No No Yes Ran­king
Copeland Yes Yes Yes Yes Yes Yes Yes No No Yes No No No No Ran­king
Dodgson Yes No No Yes No No No No No No No No No No Ran­king
Highest median Yes Yes[Tn 3] No[Tn 4] No No No No Yes[Tn 2] Yes Yes No[Tn 5] No Yes Yes Scores
Instant-runoff Yes Yes Yes No Yes No No No Yes No No Yes Yes No Ran­king
Kemeny–Young Yes Yes Yes Yes Yes Yes Yes LIIA Only No Yes No No No No Ran­king
Minimax Yes No No Yes[Tn 6] No No No No No Yes No No[Tn 6] No No Ran­king
Nanson Yes Yes Yes Yes Yes Yes No No No No No No No No Ran­king
Plurality Yes No No No No No No No No Yes Yes Yes Yes No Single mark
Random ballot[Tn 7] No No No No No No No Yes Yes Yes Yes Yes Yes Yes Single mark
Ranked pairs Yes Yes Yes Yes Yes Yes Yes LIIA Only Yes Yes No[Tn 5] No No No Ran­king
Runoff Yes Yes No No Yes No No No No No No Yes Yes No Single mark
Schulze Yes Yes Yes Yes Yes Yes Yes No Yes Yes No[Tn 5] No No No Ran­king
Score No No No No No No No Yes[Tn 2] Yes Yes Yes No Yes Yes Scores
Sortition[Tn 8] No No No No No No No Yes No Yes Yes Yes Yes Yes None
STAR No Yes No No Yes No No No No Yes No No No No Scores
Tideman alternative Yes Yes Yes Yes Yes Yes Yes No Yes No No No No No Ran­king
Table Notes
  1. ^ a b c d e f g Condorcet's criterion is incompatible with the consistency, participation, later-no-harm, later-no-help, and sincere favorite criteria.
  2. ^ a b c Approval voting, score voting, and majority judgment satisfy IIA if it is assumed that voters rate candidates independently using their own absolute scale. For this to hold, in some elections, some voters must use less than their full voting power despite having meaningful preferences among viable candidates.
  3. ^ Majority Judgment may elect a candidate uniquely least-preferred by over half of voters, but it never elects the candidate uniquely bottom-rated by over half of voters.
  4. ^ Majority Judgment fails the mutual majority criterion, but satisfies the criterion if the majority ranks the mutually favored set above a given absolute grade and all others below that grade.
  5. ^ a b c In Highest median, Ranked Pairs, and Schulze voting, there is always a regret-free, semi-honest ballot for any voter, holding all other ballots constant and assuming they know enough about how others will vote. Under such circumstances, there is always at least one way for a voter to participate without grading any less-preferred candidate above any more-preferred one.
  6. ^ a b A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
  7. ^ A randomly chosen ballot determines winner. This and closely related methods are of mathematical interest and included here to demonstrate that even unreasonable methods can pass voting method criteria.
  8. ^ Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.



References

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