Beat-Path GMC is better of course

[Mike Ositoff]

I don't use ordinary GMC to compete with or replace 
Beat-Path GMC. The latter has replaced the former, as the 
most useful version.

But I do use ordinary GMC because of its obviousness. What it
says not to do is very obviously something that is undesirable
to do. So, if it were necessary to show someone who isn't
willing to listen to anything that isn't immediately obvious,
then ordinary GMC would be somethign that would show him why
these Condorce versions are better than other methods, like
Instant Runoff (Hare, the Alternative Vote, etc.), and
Copeland, and the method that uses margins or overall margins.

Ordinary GMC is useful for that; it's quite sufficient for that.
And it's simpler to tell someone before they start walking away.

Of course Beat-Path GMC is more useful when fast explainability
isn't a consideration, because of the clone criterion and
because, in general, it doesn't disqualify a subcycle of
alternatives that all majority-beat eachother cyclically.

As for LIIAC, it's true that the version that Markus quoted
is incompatible with it. But I've re-worded it to say:

Never avoidably elect an alternative that has another alternative
ranked over it by a majority of all the voters.

If we've agreed that it's important to choose from the Smith
set, then, even if there's a non-majority-beaten alternative
outside the Smith set, but none in the Smith set, it's still
not possible to avoid picking a majority-beaten alternative.

But if there's no such prior requirement about the Smith set
then electing a majority-beaten alternative is unavoidable
only if everything is majority beaten.

So it's by "avoidably" that I avoid problems with LIIAC.

I realize that that results in a definition that lacks the
elegance of Beat-Path GMC's definition. I don't feel that the
above definition is imprecise, but it is inelegant. But
maybe someone else's opinion could be that it _is_ imprecise.

***

I use ordinary GMC to introduce GMC, then describe Beat-Path
GMC, saying why it's more useful.

Mike