[EM] Various Criteria and the 3 matrices

[DEMOREP1 at aol.com]

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

has various criteria.  My comments about each.

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.
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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.
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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.
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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.
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Name: Smith Criterion 
Application: Ranked ballots 
Definition: The winner must be a member of the Smith set. 

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

D- This comes from a head to head matrix.
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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. 

D- This also comes from a head to head matrix.
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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. 

D- This also is derived from a head to head matrix.
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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.
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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).
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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.
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Summary- the various criteria appear to use bits and parts of a YES/NO 
matrix, a head to head matrix and a place votes matrix.

If there are other criteria, they should be added to the criteria.html.