[EM] About Condorcet//Approval

[Chris Benham]

Kristofer Munsterhjelm  wrote (Sat.Oct.18):
>Because Smith is more complex to explain, my current favorite election 
>method is Condorcet//Approval. We don't need complex algorithms to find >a winner.

You could also have the approval version of Smith,IRV. Call it 
Condorcet,Approval. I think it's Smith (so it would be Smith,Approval), 
but I'm not sure. The method is this: Drop candidates, starting with the 
Approval loser and moving upwards, until there's a CW. Then that one is 
the winner.

 
Kristofer,
The method you describe isn't Smith,Approval (which is the same thing as
Smith//Approval).  Smith,Approval elects the member of the Smith set
highest-ordered by Approval on the original ballots, Smith//Approval first
eliminates (drops from the ballots) all non-members of the Smith set and
applies Approval to the remaining candidates. 

Since approval is treated as 'absolute' it doesn't make a difference like it does 
between Smith,IRV and Smith//IRV.
 
The method you describe has IRV-like mono-raise failure and Pushover 
strategy vulnerability.
 
31: A>B
32: B>C
31: C>A
06: C
 
All ranked candidates are approved, and all candidates are in the Smith set.
A>B 62-32,   B>C 63-31,  C>A 69-31.   
Approval scores:  A62,  B63,  C69.

A is eliminated and B wins, but if  2 of  the 6 C votes change to A then C wins. 
 
31: A>B
32: B>C
31: C>A
04: C
02: A
 
The Approval winner C is the clearly strongest candidate (the most first preferences 
and the most second preferences) in both cases.
 
"These methods would obviously need approval cutoff ballots (unless you 
go with the MDDA assumption, that the approval cutoff is where the voter 
truncates, but I don't think that would be a good idea here)."

Here I agree with Kevin Venzke. Allowing voters to rank among candidates they
don't approve just makes the method more vulnerable to Burial strategy and makes
the proposal much more complex.
 
 
Chris Benham

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