[EM] IRNR question

[Kristofer Munsterhjelm]

Greg Nisbet wrote:
> Would Brian's IRNR benefit from an addditional level of recursion?
> 
> The current way to eject candidates is to compare range scores, what
> if you modify that slightly?
> 
> Instead of kicking out the person with the lowest range score you
> replace that with:
> 
> Kick out the person with the highest range score, shift the ratings
> and do the same thing again. You are left with one candidate.
> 
> Kick this candidate out from the main system and repeat the above step.
> 
> Just as a broader question, do methods such as IRV, Nanson, Baldwin,
> IRNR generally perform better or worse as additional levels of
> recursion are added?

This sounds similar, if not equal, to Rouse, which kicks out the Borda 
winner and repeats the count until there's only one. That person is then 
"genuinely" kicked out. Baldwin and Nanson are Condorcet, and Rouse 
seems to be so, too. The Yee diagrams for Rouse differs from Baldwin 
only in small details.

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.

I don't know the properties of n-elimination(X) for x > 1. Does it 
converge towards a certain candidate, or would it amplify the chaos of 
earlier rounds to produce sensitivity on initial conditions?