[EM] About Condorcet//Approval

[Chris Benham]

Kevin,
I think the version of  DMC  that allows voters to rank among unapproved
candidates fails mono-raise, and both versions are vulnerable to Pushover
strategy. 

Would you say that that the plain "all ranked are approved" version
doesn't properly fail mono-raise but instead fails mono-raise-delete?

http://lists.electorama.com/pipermail/election-methods-electorama.com/2007-March/019824.html

I wrote in March 2007:
With the approval cutoffs, DMC  (and AWP) come close to failing mono-raise.

31: A>>B
04: A>>C
32: B>>C
33: C>>A

A>B>C>A   Approvals: A35,  B32,   C33. 
A eliminates (doubly defeats) B, and C wins. (AWP measures 
defeat-strengths by the number of ballots on the winning side that approve the 
winner and not the loser, and so says C's defeat is the weakest and so also
elects C.)

Now change the 4 A>>C ballots to C>>A

31: A>>B
32: B>>C
37: C>>A (4 were A>>C)

A>B>C>A   Approvals: C37,   B32,  A31
Now C doubly defeats A, and B wins. (AWP also elects B)

http://lists.electorama.com/pipermail/election-methods-electorama.com/2008-October/023017.html


Chris Benham




Kevin Venzke wrote (Mon.Oct.20):
Hi Kristofer,

--- En date de : Lun 20.10.08, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
>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.

This method has been invented from scratch a few times; most recently
it was called "Definite Majority Choice."

I don't think it can be described using double-slash or comma notation...

For instance Smith//FPP would mean that you eliminate all non-Smith
candidates and elect the FPP winner pretending that the eliminated
candidates never existed. Whereas Smith,FPP would mean that you elect
that Smith candidate who had the most first preferences to start with.

When "Condorcet" is the first or "Approval" is the second component, it's
not likely to make a difference which punctuation is used.

>Is Condorcet,Approval (Smith,Approval?) nonmonotonic? If
>not, and it is 
>Smith, then you have a simple Smith-compliant
>Condorcet/approval method.

It satisfies Smith and monotonicity.

Kevin Venzke


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