# [EM] Various Criteria and the 3 matrices

DEMOREP1 at aol.com DEMOREP1 at aol.com
Sun Jul 23 22:50:42 PDT 2000

```http://www.fortunecity.com/meltingpot/harrow/124/criteria.html

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.

D- Irrelevant.  There is ONE election using ALL of the ballots.
---
Name: General Independence from Twins Criterion: GITC
Definition: If there are alternatives X1, X2 ... Xn that are twins, and
if all of these twins except one are eliminated from every ballot, then,
if one of these twins won for the old ballots, the remaining twin must
win for the new. If a different alternative won before, it must still
win.

D- Based on a YES/NO vote all the twins would remain or be eliminated so this
criterion is irrelevant.
---
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.

D- Changing ballots is fraud. This criterion is irrelevant.
---
Name: Reversal Symmetry Criterion
Definition: If alternative X wins, and all rankings on all ballots are
reversed, then X must lose.

D-  If YES and NO majorities are reversed, then this criterion makes sense.
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Name: Secret Preferences Criterion: SPC
Definition: If alternative X wins, and some of the ballots are modified
in their rankings below X, X must still win.

D- Changing ballots is fraud. This criterion is irrelevant.
---
Name: Smith Criterion
Application: Ranked ballots
Definition: The winner must be a member of the Smith set.

D- This is connected to majority rule.
---
Name: Condorcet Criterion
Application: Ranked ballots
Definition: If an alternative pair-wise beats every other alternative,
this alternative must win the election.

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Name: Condorcet Loser Criterion
Application: Ranked ballots
Definition: If an alternative pair-wise loses to every other
alternative, this alternative must lose the election.

---
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.

---
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.

D- Another variation of majority rule.
---
Name: Pareto
Definition: If an alternative (X) is ranked or rated lower than another
alternative (Y) on every ballot, X must lose.

D- Another variation of majority rule (and from a head to head matrix).
---
Name: Majority Criterion
Application: Ranked ballots
Definition: If an alternative is ranked first on a majority of ballots,
that alternative must win.

D- Majority rule using place votes.
---
Summary- the various criteria appear to use bits and parts of a YES/NO