[EM] Criterion compliance of loser elimination and weighted positional methods

[Raph Frank]

On Sat, Jan 31, 2009 at 4:17 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> Therefore, it's useful to know what election methods one can combine with
> loser elimination so that the result passes mutual majority. Now, it might
> be that my intuition is wrong here and you can get a good multiwinner method
> out of something that doesn't pass mutual majority, but I don't quite see
> how; it probably won't be much like STV.

Assuming you give the voter's vote to their first choice and
automatically elect any candidate once he meets the Droop quota, then
the elimination method doesn't matter.

No matter what order you eliminate the candidates in the faction,
eventually there will be only one of them left.

That candidate will thus receive the faction's entire vote and since
the faction is larger than a Droop quota (by definition), the
candidate will automatically be elected.

Reading the rest of your post, I think you have come to the same
conclusion, but for single seaters.