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Criteria

A basis on which an election method can be judged. Criteria are phrased in such a way that all methods will either pass or fail the criterion, and it can be proved which. There will still be arguments about whether the criterion is useful.

I have stated which of the methods pass which criteria, where I know the answer. In some cases, I have given an area of application for a criterion. Methods that fall outside this area are not scored as passing or failing. This is so as not to mislead the reader by claiming that a method passes or fails a criterion that was not intended to apply.  See my note on criteria in the introduction.

Name: Condorcet Criterion
Application: Ranked Ballots
Definition:
If an alternative pairwise beats every other alternative, this alternative must win the election.
Pass: Black, Borda-Elimination, Dodgson, Kemeny-Young, Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats
Fail: Borda, Bucklin, Coombs, IRV

Name: Condorcet Loser Criterion
Application: Ranked Ballots
Definition:
If an alternative pairwise loses to every other alternative, this alternative must lose the election.
Pass: Borda, Black, Borda-Elimination , Coombs, IRV, Kemeny-Young, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax
Fail: Bucklin, Dodgson, Minmax, Sum of Defeats

Name: Consistency Criterion
Definition:
For any way the ballots are divided into two groups, if X is the winner for both groups independently, X must also be the winner if the ballots are not separated.
Pass: Approval, Average Rating, Borda
Fail: Black, Borda-Elimination, Bucklin, Coombs, Dodgson, IRV, Kemeny-Young, Median Rating , Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats

Name: Independence of Clones Criterion: ICC
Definition:
If there are alternatives X1, X2 ... Xn that are a clone set, and if one of these clones is eliminated from every ballot, then, if the winner for the old ballots was in the clone set, the winner for the new ballots must also be in the clone set. If an alternative outside the clone set won for the old ballots, the same alternative must win for the new ballots.
Pass: Approval, Average Rating, IRV, Median Rating, Pairwise-Elimination , Ranked Pairs, Schulze
Fail: Black, Borda-Elimination, Borda, Bucklin, Coombs, Dodgson, Kemeny-Young, Median Rating, Minmax, Nanson (original), Smith//Minmax , Sum of Defeats

Name : Local Independence from Irrelevant Alternatives Criterion (LIIAC)
Application: Ranked Ballots
Definition:
If an election produces winner X, and a new alternative is added (Y), and Y is not in the Smith set, the new election must also produce winner X.
Pass: Kemeny-Young, Pairwise-Elimination, Ranked Pairs , Schulze, Smith//Minmax
Fail: Black, Borda, Borda-Elimination , Bucklin, Coombs, Dodgson, IRV, Minmax, Nanson (original) , Sum of Defeats

Name: Majority Criterion
Application: Ranked Ballots
Definition:
If an alternative is ranked first on a majority of ballots, that alternative must win.
Pass: Black, Borda-Elimination, Bucklin, Coombs, Dodgson, IRV, Kemeny-Young, Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats
Fail: Borda

Name: Monotonicity Criterion
Definition:
If an alternative X loses, and the ballots are changed only by placing X in lower positions, without changing the relative position of other candidates, then X must still lose.
Pass: Approval, Average Rating, Black, Borda, Bucklin, Kemeny-Young , Median Rating, Minmax, Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats
Fail: Borda-Elimination , Coombs, Dodgson, IRV, Minmax, Nanson (original) , Pairwise-Elimination

Name: Mutual Majority Criterion
Application: Ranked Ballots
Definition:
If there is a majority of voters for which it is true that they all rank a set of candidates above all others, then one of these candidates must win.
Pass: Borda-Elimination , Bucklin, Coombs, IRV, Kemeny-Young, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax
Fail: Black, Borda, Dodgson, Minmax, Sum of Defeats

Name: Pareto
Definition:
If an alternative (X) is ranked or rated lower than another alternative (Y) on every ballot, X must lose.
Pass: Approval, Average Rating, Black, Borda-Elimination, Borda, Bucklin, Coombs, Dodgson, IRV, Kemeny-Young, Median Rating , Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats
Fail:

Name: Reversal Symmetry Criterion
Definition:
If alternative X wins (excluding ties), and all rankings on all ballots are reversed, then X must lose.
Pass: Approval, Average Rating, Black, Borda, Kemeny-Young, Median Rating, Nanson (original), Ranked Pairs, Schulze
Fail: Borda-Elimination , Bucklin, Coombs, Dodgson, IRV, Minmax, Pairwise-Elimination , Smith//Minmax, Sum of Defeats

Name: Secret Preferences Criterion: SPC
Application: Ranked ballots
Definition:
If alternative X wins, and some of the ballots are modified in their rankings below X, X must still win.
Pass: IRV
Fail: Black, Borda, Borda-Elimination , Bucklin, Coombs, Dodgson, Kemeny-Young, Median Rating, Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats

Name: Smith Criterion
Application: Ranked ballots
Definition:
The winner must be a member of the Smith set
Pass: Borda-Elimination , Kemeny-Young, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax
Fail: Black, Borda, Bucklin, Coombs, Dodgson, IRV, Minmax, Sum of Defeats

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