[EM]Ranked-Pairs (wv) can lose a Cond. Winner

[matt at tidalwave.net]

On 24 Nov 2002 at 14:41, Elisabeth Varin/Stephane Rouillon wrote:

> 3: A
> 2: A > B > C
> 2: B > A > C
> 2: B > C > A
> 4: C
> Ranked pairs with winning votes produces:
> A (7) > C (6) , B (6) > C (4) and A (5) > B (4).
> A is the Condorcet winner and wins.
> Margins and relative margins produce of course the same result.
> If I am one of the two B > A > C voter, my 2nd (A)
> choice harms my favorite 1st choice (B).
> The proof is, if I and my co-thinker vote B only:
> 3: A
> 2: A > B > C
> 2: B   (truncated !)
> 2: B > C > A
> 4: C
> Ranked pairs with winning votes produces:
> B (6) > C (4), C (6) > A (5) and A (5) > B (4) can't lock.
> B wins now.

This appears to be an example that illustrates a more stable outcome is achievable 
by counting equal ranked options 1/2 vote each.  With an additional 1/2 vote for 
each non-voted pair the option pair tally matrix after > 2: B (truncated !) looks like:
#	A	B	C
	7.0	7.0	6.0
	6.0	6.0	7.5
	7.0	5.5	8.0
and A still wins (RP and SSD).  You guys are (mis?)computing the tally matrix like:
#	A	B	C
	7.0	5.0	5.0
	4.0	6.0	6.0
	6.0	4.0	8.0
(diagonal represents "approval count").

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