In answer to the questions about voters regretting that they
turned out, my answer is: No, it isn't inevitable, because
there are a few methods that don't have that problem. And no,
it isn't patchable, where it occurs, because it's caused by
method attributes that seem essential to the properties of the
best methods. I don't offer a proof of that, but that's how it
seems to me.
The methods which I know of not having that problem are Plurality,
Approval, & Bucklin. Bucklin is the only rank-balloting methods which
I know to not have that problem. But Bucklin still has the problem
that, under some conditions, there could be incentive to insincerely
rank one's top choices equal. This can happen in Bucklin even
with a Condorcet winner & a 1-dimensional political spectrum, something
that isn't true of Condorcet(EM).
If we want the properties of the best methods, if we want methods
better than Approval & Bucklin (which aren't bad methods, and which
are valuable because of their count simplicity), then we have to
accept the regretted turnout problem.
***
There were some things that I accidentally omitted from my
posting yesterday. When I said, regarding the possibility of
the candidate whose greatest defeat is the least being also
the candidate whose greatest victory is the least, and said
"How likely is that?", I didn't mean it can't happen--only that
there's no particular reason to expect it to happen with Condorcet(EM).
For that reason it can't be called a property of that method.
Also, I meant to add one more thing about reversed rankings:
If candidates & voters are on a 1-dimensional political spectrum,
an assumption often made on this list, and which often is a good
approximation, then everyone's last choice will be one of the
two most extreme candidates, and one of them will be last choice
of a majority. And when the rankings are reversed, therefore,
one of the two most extreme candidates will always win with
a majority.
***
I must post this & continue with a new posting, to avoid losing
too much writing if the keyboard locks up. Posting again immediately.
***
Mike Ossipoff
