[EM] Mike: cardinal pairwise

[James Green-Armytage]

Hi Mike,
	I'm going to chop my reply up into three parts, so that we don't get any
unwieldy, super-frustratingly-long e-mails.
	Part I: cardinal pairwise

>But I re-emphasize that I have no quarrel with CP. Either CP or AERLO &
>ATLO
>would be a powerful strategy-need-reducing enhancement for wv, and I'd
>just
>about just as soon have one as the other.

>Just as with the RP vs SSD or BeatpathWinner/CSSD dispute, I claim that 
>there's
>no significant merit difference, and therefore no genuine dispute or
>disagreement.

	Good to know. But I should point out that CP isn't intended only as an
anti-strategy enhancement. I also think that it naturally helps to find
the most suitable resolution for sincere cycles, which is why I prefer it
to other anti-strategy measures. Here's an example from an older version
of my paper:

	Rankings and (ratings)
26: Bush>Dean>Kerry (100,10,0) 
22: Bush>Kerry>Dean (100,10,0)
26: Dean>Kerry>Bush (100,90,0)              
1: Dean>Bush>Kerry (100,50,0)
21: Kerry>Dean>Bush (100,90,0)              
4: Kerry>Bush>Dean (100,50,0)

            Direction of defeats (using ranking information):
Bush > Dean : 52-48               
Kerry > Bush: 51-49                 
Dean > Kerry : 53-47

            Weighted magnitude of defeats (using rating information):
Bush > Dean:	(26x(100-10)) + (22x(100-0)) + (4x(50-0)) = 4740
Dean > Kerry:	(26x(10-0)) + (26x(100-90)) + (1x(100-0)) = 620
Kerry > Bush:	(26x(90-0)) + (21x(100-0)) + (4x(100-50)) = 4640

	Bush wins using most ordinal methods (wv or margins), but Kerry wins
using cardinal pairwise. Assuming that these are sincere votes, I feel
very definitely that it makes the most sense to resolve the majority rule
cycle in favor of Kerry. Yes, 53% agrees with the D>K defeat whereas only
51% agrees with the K>B defeat, but of the 53%, only 1% place a high
priority on the D>K defeat, while on the other hand, 47% of the 51% place
a high priority on the K>B defeat (and the remaining 4% place a medium
priority on it). We have to overrule one of the three defeats. Does it
make sense to you that we should try to overrule the defeat that the
fewest voters assign the least priority to?
	The topic is briefly covered in my cardinal pairwise paper, section 6
("Preference priority and defeat strength").
http://fc.antioch.edu/~james_green-armytage/cwp13.htm

end of part I

my best,
James
http://fc.antioch.edu/~james_green-armytage/voting.htm
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