# [EM] Fixing IRV

Richard Moore rmoore4 at home.com
Wed Aug 8 17:36:27 PDT 2001

```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

```