[EM] Fixing IRV

[LAYTON Craig]

>What we are looking for is a definition of "elimination" 
>that will allow us to cleanly split the set of all possible 
>methods into elimination methods and non-elimination 
>methods. I agree with Markus that this isn't an easy thing 
>to define, but should we conclude that no useful definition 
>exists? (By "useful" I mean that you could build theorems 
>around the definition.)

The most general definition would have something to do with the fact that
each elimination step effects subsequent elimination steps - also, I think
all elimination methods involve a theoretical alteration of ballot papers; a
ballot of A1 B2 C3 D4 becomes B1 C2 D3 once A is eliminated (say in IRV or
Nanson).  The alteration of ballots is even clearer in
cumulative-elimination.  In pairwise methods, B2 C3 D4 is equivalent to B1
C2 D3, so it seems to me that it would be impossible for any pairwise method
to be an "elimination method" in this sense.

Craig