Goldfish--GMC & Smith? Clone Independence?

[Mike Ositoff]

That Tideman definition does sound like the same method that
failed the Tideman bad-example.

Though Goldfish has a similarity to Tideman, since eliminating
the most defeated alternative is much like locking-in its defeat,
it seems that it wouldn't have Tideman's problem, because it
doesn't skip & then ignore a defeat. Of course it doen't skip
a defeat at all, doesn't require that it not conflict with
bigger defeats. That would lock-in cycles, except that Goldfish
nibbles the cycles away.

I hesitate to make definite statements so soon, but I believe
that it can be shown that Goldfish meets GMC & Smith.

If something has a majority against it, then even if the alternative
that beats it with a majority gets eliminated, the alternataive
that eliminates it will then take over with that majority defeat.
So an alternative can't lose a majority defeat by Goldfish's
rules. It can't acquire one that it doesn't already have either.
And  majority-defeated alternatives naturally get eliminated
before non-majority-defeated ones.

It seems that however small the defeats of non-Smith-set
alternatives by Smith-set alternatives, those defeats will
still be there when eliminations have left only 1 remaining
member of the Smith set, and have similarly gotten rid of
cycles among non-Smith-set alternatives. So any remaining 
non-Smith-set alternatives would sooner or later be eliminated
by those defeats by Smith-set alternatives. That's if I've
understood Goldfish correctly.

***

That isn't rigorous, & may not even be correct, but I don't
even have that much of an idea about Goldfish's Clone Independence.
That would be the important thing, to set it apart from
Smith//Condorcet.

Also, as Markus pointed out, it would be desirable if a
Condorcet & GMC complying method, or a Smith & GMC complying
method, could also meet the new voter criteria, the ones that
say that a few new voters arriving at the election & voting
sincerely & identically shouldn't be able to cause the defeat
of their favorite or the victory of their last choice, when
that wouldn't have happened without their participation.
I suspect that compliance with all the criteria named in
this paragraph isn't possible, and that compliance with even
one of the new voter criteria is incompatible with Condorcet
& GMC. But that's just a suspicion.

Mike