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Template:Comparison of voting systems

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Comparison of single-winner voting systems
Criterion: Majority Majority loser criterion Mutual majority criterion Condorcet winner[Tn 1] Condorcet loser Smith[Tn 1] ISDA[Tn 1] LIIA IIA[Tn 1] Cloneproof Monotone Participation Later-no-harm[Tn 1] Later-no-help[Tn 1] No favorite betrayal[Tn 1]
Anti-plurality No Yes No No No No No No No No Yes Yes No No Yes
Approval Yes No No No[Tn 2] No Yes Yes Yes Yes[Tn 3] Yes Yes Yes No Yes Yes
Baldwin Yes Yes Yes Yes Yes Yes No No No No No No No No No
Black Yes Yes No Yes Yes No No No No No Yes No No No No
Borda count No Yes No No Yes No No No No No Yes Yes No Yes No
Bucklin Yes Yes Yes No No No No No No No Yes No No Yes No
Coombs Yes Yes Yes No Yes No No No No No No No No No Yes
Copeland Yes Yes Yes Yes Yes Yes Yes No No No Yes No No No No
Dodgson Yes No No Yes No No No No No No No No No No No
Highest median Yes Yes[Tn 4] No[Tn 5] No[Tn 2] No No No Yes Yes[Tn 3] Yes Yes No[Tn 6] No Yes Yes
Instant-runoff voting Yes Yes Yes No Yes No No No No Yes No No Yes Yes No
Kemeny–Young Yes Yes Yes Yes Yes Yes Yes Yes No No Yes No No No No
Minimax Yes No No Yes[Tn 7] No No No No No No Yes No No[Tn 7] No No
Nanson Yes Yes Yes Yes Yes Yes No No No No No No No No No
Plurality Yes No No No No No No No No No Yes Yes Yes Yes No
Random ballot[Tn 8] No No No No No No No Yes Yes Yes Yes Yes Yes Yes Yes
Ranked pairs Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes No[Tn 6] No No No
Runoff Yes Yes No No Yes No No No No No No No Yes Yes No
Schulze Yes Yes Yes Yes Yes Yes Yes No No Yes Yes No[Tn 6] No No No
Score No No No No[Tn 2] No No No Yes Yes[Tn 3] Yes Yes Yes No Yes Yes
Sortition[Tn 9] No No No No No No No Yes Yes No Yes Yes Yes Yes Yes
STAR No Yes No No[Tn 2] Yes No No No No No Yes No No No No
Tideman alternative Yes Yes Yes Yes Yes Yes Yes No No Yes No No No No No
Table Notes
  1. ^ a b c d e f g |Condorcet, Smith and Independence of Smith-dominated alternatives criteria are incompatible with Independence of irrelevant alternatives, Consistency, Participation, Later-no-harm, Later-no-help, and Favorite betrayal[clarification needed] criteria.
  2. ^ a b c d In Approval, Score, and Majority Judgment, if all voters have perfect information about each other's true preferences, any Majority Condorcet or Majority winner can be strategically forced. In particular if every voter knows that "A or B are the two most-likely to win" and differentiates between the two, then the Condorcet winner, if one exists and is in the set {A,B}, will always win. Laslier, J-F (2006), "Strategic approval voting in a large electorate" (PDF), IDEP Working Papers (405), Marseille, France
  3. ^ 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.
  4. ^ 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.
  5. ^ 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.
  6. ^ 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.
  7. ^ a b A variant of Minimax that counts only pairwise opposition, not opposition minus support, fails the Condorcet criterion and meets later-no-harm.
  8. ^ 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.
  9. ^ Where a winner is randomly chosen from the candidates, sortition is included to demonstrate that even non-voting methods can pass some criteria.


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