Kevin Venzke wrote:
Hi Kristofer,
Here's an attempt at a more concrete example:
A 3
ABCD 13
ACBD 1
ACDB 5
ADBC 5
BACD 16
B 3
BCDA 5
CDAB 20
DBCA 24
total 95
(...)
A does have two tied margins; I'm unsure if they make a difference, or
if it can be easily fixed if they do. But it doesn't seem like they
should make a difference (i.e. for checking Ext-Minmax) because those
margins are relatively weak.
I just checked it with my Ext-Minmax implementation, and it still works
(that is, fails the criterion). The debug data I get from Ext-Minmax is:
For the first scenario:
After sorting: 0 6 6 1
After sorting: 1 16 0 0
After sorting: 3 31 0 0
After sorting: 2 40 0 0
For the second scenario:
After sorting: 0 8 0 0
After sorting: 1 9 0 0
After sorting: 3 31 1 0
After sorting: 2 47 1 0
Plain Minmax consistently elects A here, which is no problem for plain
Minmax (or Ext-Minmax for that matter), but the Smith restriction causes
trouble.
Back to the drawing board, I guess! Do you think the compliance could be
salvaged by using Smith,Minmax(PO) instead -- or, more strictly, by
disallowing trunaction? Either might lead closer to a method that passes
Smith and mono-add-top...
Worse is the fact that my program didn't find a compliance disproof even
though I now know there to be one. I'll have to find out why; one
possibility is that the failures are exceedingly uncommon and it simply
can't stumble upon one by brute force.
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