[EM] Fixing IRV

[Richard Moore]

Markus Schulze wrote:
> Dear Richard,
> 
> you wrote (7 Aug 2001):
> 
>>Actually, IIRC, there is a proof somewhere in the literature
>>that elimination methods are not monotonic. Does anyone recall
>>the theorem I mentioned above about elimination and monotonicity?
>>
> 
> Some elimination methods are monotonic (e.g. Ranked Pairs).

Since when is RP considered an elimination method?

If we have

6 
ABC
5 
CAB
4 
BCA

then RP gives the following rankings for the pairwise contests:

11 
A>B
10 
B>C
9 
C>A

with A as the winner. If RP were done as an elimination 
method, then B would be eliminated following the highest 
pairwise defeat. We then wouldn't bother comparing B and C, 
and we would get

11 
A>B
9 
C>A

so the final ranking would be CAB.

>  Some
> methods are not monotonic although they don't use eliminations
> (e.g. Dodgson).

Granted, but disproving the converse doesn't disprove the 
original statement.

Richard