Strangeness

[Mike Ositoff]

A while back, it was said that Smith//Condorcet had a problem
peculair to it, in which it would choose the same alternative when
people were voting for the worst that it chooses when people vote
for their best.

Before I talk about why I don't expect that to happen in typical
situations, I want to first add that it doesn't seem to me that it
would be a problem even if it did happen. We've talked about
various standards & principles that are important to us, & to
many others, like LO2E & majority rule (Sorry, Mike S.). And
the further-refined desire to avoid less gross violations like
clone-set subcycle fratricide. But is it really important what
happens if we were to reverse all the rankings?

Say there's a Smith set, & there are also alternatives that aren't
in the Smith set. When we reverse all the rankings, the former members
of the Smith set become the set of alternatives such that every
alternative in the set is beaten by every alternative outside the
set. Smith//Condorcet wouldn't choose its winner from tht set.

But say that there are no alternatives outside the Smith set
(is that likely in a public political election?). Or that we're
talking about plain Condorcet rather than Smith//Condorcet:

For Condorcet to pick the same alternative whether or not the
rankings are all reversed, that requires that the alternative
whose greatest pairwise defeat is the least is also the alternnative
whose greatest pairwise win is the least. How likely is that in a
real election? Is it something to justify saying that a method
has a problem?

I'm not saying it could never happen. A long time ago somoene
pointed out that plain Condorcet (but not Smith//Condorcet) fails
the Majority Loser Criterion. I pointed out at the time that
that only happens in a bizarre & hopeless bottom-end situation
where the candidate who has fewest people preferring anyone else
to him is also the candidate who is the last choice of a majority.
I agree that "strange" is indeed the word for a situation like that.
Again, not the kind of thing that, in my opinion, justifies saying
that a method has a problem. I'm interested more in what happens
at the top-end, when there's a Condorcet winner, when a good outcome
is possible, not in improbable, bizarre, hopeless bottom-end
situations.

Mike Ossipoff