[EM] Smith,Minmax(margins) mono-add-top failure example

[Kevin Venzke]

Hi Kristofer,

--- En date de : Dim 27.6.10, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
> 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...

If necessary the program I made (last night) can be altered to test these
methods, but I'm not optimistic. I don't think looking at defeat strengths
is going to be the answer, if there is one. I think you need a rule that
non-Smith candidates are inherently bad at, and will still be worse at
than the previous winner, even when they do make it into the Smith set.
Margin would be perfect except that non-Smith candidates don't necessarily
have a bad worst margin.

> 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.

I didn't keep exact numbers but it seemed like mine needed 25k-100k trials
to find a scenario that fit. Specifically the Smith,MM and MM winners had
to be different, and the Smith,MM winner had to change. The quantity of
the new ballots would be 1+(MM winner's worst margin), to guarantee that
a contest would be reversed.

Kevin