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
