[EM] example correction from weighted pairwise and compressing-ranks posting

[James Green-Armytage]

	Hi folks. Chris Benham pointed out to me that I goofed up when I was
transcribing my example into the computer. That is, the example in my
posting from last night, "weighted pairwise method and compressing ranks
method".
http://lists.electorama.com/pipermail/election-methods-electorama.com/2004-June/013287.html
	Chris, thank you very much for taking the time to read the example so
carefully. I'm sorry that I goofed it up. The corrections follow.
Hopefully I got it right this time!!

>>24: A 100 > B 1 > C 0    *Should this read A100>B99>C0 ?*
>>24: A 100 > C 1 > B 0
>>22: B 100 > C 99 > A 0
>>4: B 100 > C 1 > A 0
>>1: B 100 > A 1 > C 0
>>22: C 100 > B 1 > A 0
>>3: C 100 > A 1 > B 0

	No, I think that the problem was with "22: C 100 > B 1 > A 0". I meant
that to be 22: C 100 > B 99 > A 0
	Note that this doesn't change the result using my method, since there is
no C-->B pairwise beat, and there is no B-->A pairwise beat. The C>B>A
voters lend the "weight" of their ratings to the C-->A defeat, and in both
the originally stated and the corrected example they each lend the full
100 points to that defeat.
	So the corrected example is

24: A 100 > B 1 > C 0
24: A 100 > C 1 > B 0
22: B 100 > C 99 > A 0
4: B 100 > C 1 > A 0
1: B 100 > A 1 > C 0
22: C 100 > B 99 > A 0
3: C 100 > A 1 > B 0

>>24: AB  **This should read 24:A
>>24: A
>>22: BC
>>4: B
>>1: B
>>22: C
>>3: C

	Yes, you're right. "24: AB" is incorrect."22: C" is also incorrect, with
regard to my intention. I Think that the approval scores should read as
follows...
24: A
24: A
22: BC
4: B
1: B
22: CB
3: C

	And the approval scores should be:
A: 48
B: 49
C: 47

>>	And I think that the approval scores of the candidates are sufficient to
>>tell us the winner.
>>A: 48
>>B: 49 **This should be 27.
>>C: 47
>>	So, where my method chooses C, your method chooses B. ***This should be
>A.

	Yes, I think that the uncorrected example chooses A in compressing-ranks.
The corrected example chooses B in compressing-ranks. I think that both
examples choose C in weighted pairwise.

	Chris also rightly pointed out that in my last posting I used the term
"ranking" in one paragraph where I meant rating. Sorry! I checked back,
and it looks like in each case it should be pretty clear from the context
that the word was an error. What I wrote was "That is, there were two
B>C>A voters who didn't rank C above 50, but all of the C>B>A voters
ranked B above 50. If those two B>C>A voters had ranked C above 50, then C
would have won instead of B." Hope that didn't cause much confusion.

my best,
James