[EM] MinMax (pairwise opposition) and Approval

[Forest Simmons]

On Sun, 9 Mar 2003, [iso-8859-1] Kevin Venzke wrote:

> Looking at Schulze's example of:
>   20 ABCD
>   20 BCAD
>   20 CABD
>   13 DABC
>   13 DBCA
>   13 DCAB
>
> The scores are 66 for ABC and 60 for D, so D winning
> is of course not best.  But I think the problem is
> that an ordering low in the list is weighed as heavily
> as a first- and second-place ranking.  It's not
> intuitive, for instance, that the DABC voters should
> be able to create B opposition against C.

I look at this example differently.  The main reason the result looks bad
is that A, B, and C are ballot clones, and the clone supporters outnumber
the D supporters.

However, the clone supporters have an easy defense: equal ranking at the
top:

In other words, if the clone supporters realize that D is a serious
contender, then at least some of them should rank some of the clones
equally, depending on how strongly they prefer the clones to D.

If the first three factions ranked all clones equal, then we would have

60 A=B=C>D
13 D>A>B>C
13 D>B>C>A
13 D>C>A>B

The max opposition would still be 60 for D, but A,B, and C's max
opposition would be only 39, leaving plenty of room for expressing some
preference among the clones.

Forest