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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