[EM] IRNR question

[Raph Frank]

On Tue, Oct 21, 2008 at 8:47 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> To be more general, let's call ordinary loser-elimination methods
> 0-elimination(X), where X is the base method. 1-elimination(X) successively
> eliminates the winners, according to X, then eliminates the last one
> eliminated. Presumably 2-elimination(X) would eliminate the losers,
> according to X, then the winners of that, then the losers of that; and so on
> for any n-elimination(X).
>
> It seems that no matter what X is (within reason), 1-elimination(X) is
> Condorcet. At least it is so for both X =  Borda and X = Plurality.

All 1-elimination(X) methods should be condorcet methods because the
only way to be eliminated is to lose pairwise against someone in the
last round.

In all ranked methods, the last round will just eliminate the pairwise
loser.  However, with range/score voting, the pairwise winner could be
eliminated, unless the ballots are rescaled.