[EM] Investigating criterion compliance

[Kristofer Munsterhjelm]

On 2025-09-06 00:57, Kevin Venzke wrote:
> Hi Kristofer,
> 
> If it's in scope of what you're proposing, I think Mono-add-top + Smith is the biggest outstanding one.
> 
> I can't quite picture how your program would tackle this. My DNA
> framework also essentially gives "definitely not" or "don't know."
> Unfortunately these two criteria are in the latter category (i.e.
> they actually look compatible). But the framework offers rather
> limited maneuvering room to test Mono-add-top.
Mine will be similar to the DNA generator, except with thousands to 
millions of scenarios. When it finds something that passes, it should 
constructively give the mapping "if in this election, elect these 
candidates".

If we're lucky and it says "don't know" about Smith + MAT, then we'd be 
left with a lot of concrete outcomes across election space giving a 
method that passes both for a low number of voters and candidates. It's 
still very difficult to deduce a general method from it, though.

And if I'm ambitious enough, I know there's a way to turn "definitely 
not" into a Woodall/Moulin-type disproof, i.e. "definitely not, and this 
is why". A paper I read a while back showed how to do that with 
participation, but it's still quite a bit of work to get it done! So I 
think I'll leave that for later, if I see a particularly interesting 
combination that it says is incompatible and I don't understand why.

> Another apparent compatibility in my framework is Condorcet and
> Later-no-help. They're known to be incompatible, but I dumped a lot of
> time into trying to understand how such a method would work according to
> the framework. Then I discovered I already had a named method that
> supposedly meets both. I plan to make a post on this soon, kind of
> interesting.

That's indeed interesting. I thought Woodall had proven them to be 
incompatible - perhaps the density of failures is low enough that they 
fit all the scenarios in your DNA generator?

-km