[EM] question about Schulze example (A,B,M1,M2)

[Kristofer Munsterhjelm]

capologist wrote:
> I'm no expert in this field, but it is one I find interesting and
> visit from time to time. My first encounter with it was when I
> stumbled on a website advocating what was then called the Tideman
> method, before it was called Ranked Pairs and before the Schulze
> method was discovered. I had an email conversation with the author of
> that website during which I proposed several modifications that
> seemed to me to make sense. In each case he responded with examples
> demonstrating how my proposal failed important criteria and
> convincing me that it made the method worse, not better.
> 
> From the experience I learned that these methods can have behaviors
> that are not obvious to me and that I should never use a method
> that hasn't been carefully vetted by people who understand the
> field much better than I do.
> 
> You appear to be such a person. Would you say you have carefully
> vetted the suggestion you just made, or was it merely a thought off
> the top of your head?

Something in between. I haven't verified that extending the minmax logic 
in the manner I mentioned wouldn't break, say clone-independence.

However, since Schulze said that you could use any nondeterministic 
tiebreaker you'd like as long as the tiebreaker itself doesn't fail the 
criteria you want to have, one could reason that having a deterministic 
tiebreaker that itself doesn't fail the criteria won't make the method 
mysteriously fail a criterion it otherwise would pass.

Criteria failures are absolute: even if you fail just one in a million 
elections, you fail the criterion; and in the context of this, a 
nondeterministic tiebreaker that happens to emulate a deterministic one 
with very low probability would fail the criterion if the deterministic 
one did. Since Schulze said you can pick any random tiebreaker as long 
as it passes the criteria, that would also include such tiebreakers that 
could emulate deterministic ones if you were very lucky. Therefore, the 
same logic should hold for deterministic tiebreaks: as long as they pass 
the criteria you want, you can pick any of them.

With all that being said, I could be wrong. If you want to play it safe, 
and you want M1 > M2, your best bet is to pick a method that is decisive 
in that case. So if you're not sure whether I'm right, and if you don't 
need to have Schulze for other reasons (e.g. that it's a popular method, 
or the poll is explicitly a Schulze poll), pick Ranked Pairs. Unlike the 
  other advanced methods discussed here, it's not too obscure, and it's 
cloneproof, monotone, and elects from the Smith set -- just like Schulze.