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
