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Condorcet.vote Alpha
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Tally methods

Method comparison

Each method guarantees some properties and gives up others. Our methods side by side, set against first-past-the-post and three benchmark methods.

Offered on Condorcet.Vote Benchmarks, not offered
Criterion Schulze Ranked Pairs Copeland Dodgson Quick First-past-the-post Instant-runoff voting (IRV) Borda Kemeny-Young
Majority An option ranked first by more than half of the voters wins. Yes Yes Yes Yes Note 1 Yes Yes No Yes
Majority loser An option ranked last by more than half of the voters never wins. Yes Yes Yes Not established No Yes Yes Yes
Mutual majority If a majority ranks a group of options ahead of all the others, the winner belongs to that group. Yes Yes Yes Not established No Yes No Yes
Condorcet winner The option that beats each of the others in a duel is always elected. Yes Yes Yes Yes Note 2 No No No Yes
Condorcet loser The option beaten by each of the others in a duel is never elected. Yes Yes Yes Not established No Yes Yes Yes
Smith criterion The winner belongs to the smallest group of options that beat every option outside it. Yes Yes Yes Not established No No No Yes
Independence of clones Adding an option very similar to another does not change the outcome among the others. Yes Yes Note 3 No Not established No Yes No No
Monotonicity Ranking the winner higher can never make them lose. Yes Yes Yes Not established Yes No Yes Yes
Local independence Removing the option that finished last (or first) in the result does not change the order of the others. No Yes No Not established No No No Yes
Reversal symmetry If every ballot is reversed, the former winner no longer wins. Yes Yes Yes Note 4 Not established No No Yes Yes
Participation Voting sincerely can never leave a voter worse off than abstaining. No No No No Note 5 Yes No Yes No
Consistency If an option wins in two separate groups, it wins when they are combined. No No No No Note 5 Yes No Yes No
Later-no-harm Ranking an additional choice can never hurt those already ranked ahead of it. No No No No Note 5 Yes Note 6 Yes No No
Resolvability A final tie becomes unlikely as the number of voters grows. Yes Yes No Not established Yes Yes Yes Yes
Fast computation The result is computed in polynomial time, even with many options. Yes Yes Yes Yes Yes Yes Yes No Note 7
  • ✓ always satisfied
  • ✕ can be violated in some votes
  • ? no published source establishes it
  1. 1 A direct consequence of the Condorcet criterion: an option ranked first by a majority beats every other option in a duel.
  2. 2 Guaranteed by construction: CondorcetPHP always places the Condorcet winner first.
  3. 3 When two duels have exactly the same strength, full independence of clones requires the Zavist and Tideman (1989) tie-breaking rule, which CondorcetPHP does not apply: it breaks ties by the weakest opposition, then processes together any duels that remain tied.
  4. 4 Blank cell in Wikipedia’s general table; “yes” in its table of Condorcet methods and in the legacy condorcet.vote table.
  5. 5 No method that satisfies the Condorcet criterion can satisfy this criterion: this is a general result.
  6. 6 Trivially: first-past-the-post never looks beyond the first choice.
  7. 7 The exact computation is NP-hard: it becomes impractical beyond about ten options.
Reading guide

How to read this table.

  • A “no” is a worst case. It means there is at least one vote, sometimes a highly contrived one, where the criterion is violated; not that the method violates it often.
  • Some “no”s are unavoidable. No method that elects the Condorcet winner can guarantee participation, consistency or later-no-harm: these are theorems.
  • The variants are equal here. Winning votes and margins share every cell of this table.
  • Dodgson Quick is an approximation. No published table covers it: only the established cells are filled in, and the others are marked as such.
Sources

Where this data comes from.

Wikipedia’s criteria table, supplemented by its table of Condorcet methods and, for the resolvability of the benchmark methods, by the legacy condorcet.vote table. Disagreements between sources are flagged in the notes.

Encyclopedia Comparison of electoral systems Wikipedia
Encyclopedia Condorcet method — Evaluation by criteria Wikipedia

The other methods

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