[EM] Cardinal Pairwise fails SFC.

James Green-Armytage jarmyta at antioch-college.edu
Tue May 3 01:01:39 PDT 2005

James replying to Mike...

>When you posted that Cardinal Pairwise meets SFC, I took your word for
>because I didn't know exactly the definition of Cardinal Pairwise. 

	Mike, your memory doesn't seem to be serving you very well. We discussed
cardinal pairwise's SFC failure months ago. If I ever posted that cardinal
pairwise meets SFC without the "majority beat provision", please provide a
link to that post.

Mike, 11/24/04: 
	"James: Doesn't your method gain stronger SDSC by losing SFC &  GSFC?"

James, 11/24/04:
	"It passes stronger SDSC and fails SFC and GSFC, yes. However, I've said
that SFC (and GSFC, I assume) can be achieved in the cardinal pairwise
method by the use of a provision that states that a defeat agreed-with by
a majority should always be counted as stronger than a defeat that is not
agreed-with by a majority."

	My 11/24/04 post also provides a link to this 10/17/04 post, where I
argue that cardinal pairwise's truncation resistance (similar criterion to
SFC) failure is not damaging.

	If you would like to discuss CWP's failure of SFC, I ask you to read my
10/17 and 11/24 posts with links provided above. Feel free to reply to
those directly if you like.

>Cardinal Pairwise:
>Same as wv, except that, if every candidate has a pairwise defeat, then,
>any particular voter and for any two particular candidates, that voter's 
>pairwise vote for one of those candidates over the other is weighted 
>according to the difference between that voter's points-assignments to
>two candidates.
>[end of guessed Cardinal-Pairwise definition]
	It's close, but I'm not sure if it's 100% correct. There's a clear
definition in part 3 of my paper at 
	The basic idea is that the direction of pairwise defeats is determined by
the ordinary pairwise count method, and the strength of pairwise defeats
is caused by the sum of winning rating differentials for that defeat. (For
an A>B defeat, only look at A-B rating differentials for A>B voters.)
There is no particular completion method specified for CWP, but I prefer
to limit the choices to Smith-efficient defeat-dropping methods such as
ranked pairs, beatpath, and river.


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