Why to mix methods...

[Gervase Lam]

Why not go a lot further with mixing Approval with Ranked Pairs and use 
Approval//Disapproval to sort the pairwise contests.  It's probably easier 
to explain by adapting an example from the list archives:

7:A>B>>C>D
5:B>>D>C>A
4:D>C>>A>B
4:C>D>>A>B
1:D>>B>C>A

(>> represents the Approval cut-off point).

The pairwise results are as follows:

A>B 15:6
C>A 14:7
D>A 14:7
B>C 13:8
B>D 12:9
C>D 11:10

Approval results are: A=7, B=12, C=8, D=9

The pairwise wins for each Candidate are sorted in Candidate Approval 
order.  The pairwise wins for each candidate is then sorted in Disapproval 
order.

The pairwise wins are sorted in Approval order of the pairwise winner.  
The pairwise wins for each candidate is then sorted in Disapproval order 
for each pairwise loser.

B: B>C
   B>D
D: D>A => B>D>A
C: C>A
   C>D => B>C>D>A
A: A>B (Ignore)

FINAL RESULT: B>C>D>A

Well, at least it makes the Margins v. Winning Votes debate pointless.  As 
no pairwise votes or margins are counted, I think it is reasonably 
truncation resistant.

I initially thought that this method may not select the Condorcet Winner.  
However, I think it will always select the Condorcet Winner as there is no 
pairwise result that can be added to the Beat Path that would make [This 
Ranked Pair Method Winner and Non-Condorcet Winner] > [Condorcet Winner].  
This is becuase, by definition, for each pairwise contest, [Condorcet 
Winner] > [Each of the other candidates].

I was just wondering if there is a reasonable Condorcet Method that does 
not always select the Condorcet winner.  To a certain extent, I think this 
woudl be a good thing as the method would more likely not fall into the 
Condorcet Criterion Incompatibility with the Participation, Consistency 
and Monotonicity Criteria.

CC incompatible with Participation & Consistency
<http://groups.yahoo.com/group/election-methods-list/message/8506>

CC incompatible with Monotonicity
<http://groups.yahoo.com/group/election-methods-list/message/8452>

Thanks,
Gervase.

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