[EM] ER-Bucklin fails monotonicity

[James Green-Armytage]

Kevin, you wrote:
>40 A>B>D
>35 D>B
>25 C>D
>B wins, with 75 votes in the second round.
>
>Now let's raise B on some ballots:
>40 A=B>D
>35 D>B
>25 C>D
>Now candidate D wins, with 100 votes in the second round.
>So, quite clearly, ER-Bucklin fails monotonicity.

Yes, this is interesting. However, I suggest that ER-Bucklin(whole) should
perhaps be tallied in a different way. In the second example, you assume
for tally purposes that D is in 2nd place on the A=B>D ballots. However, I
suggest that we should still consider D to be in 3rd place, because there
are still two candidates who are ranked strictly ahead of D. If we do
this, I think that B still wins. 

Here's another example: a ballot marked A>B=C=D>E>F=G=H=I>J. I think that
we should consider A to be in 1st place, B, C, and D to be in 2nd place, E
to be in 5th place, F, G, H, and I to be in 6th place, and J to be in 10th
place. Thus, the ballot would not count in favor of E until the 5th round,
and it would not count in favor of J until the 10th round.

If we use this method, does ER-Bucklin pass monotonicity again? If so, I
suggest that it is probably better than the version of ER-Bucklin(whole)
that you used in your example.

I've added a page for ER-Bucklin on the electowiki. Please feel free to
add to it, correct it, criticize it, etc.
http://wiki.electorama.com/wiki/ER-Bucklin

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