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.
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