Clone Compliance

[Mike Ositoff]

True, Schulze complies with Clone Independence.

To what Markus said, I'd add that if X, before its clones are
added, wins because it has Schulze wins against everything, then
when its clones are added, that will be true of them too, that
they have Schulze wins against everything outside the clone set.
So, whichever clone subcycle member wins in the subcycle, it
wins the election.

***

The method that I defined that says:

Drop every defeat that conflicts with a larger one.

That method, though also indecisive, is Clone Independent too:

If X, before the clones are added, wins because its defeat is the
only one that conflicts with larger defeats, then, after X's
clones are added, the members of that clone set will be the only
alternatives whose defeats (not counting defeats within the
clone set) conflict with larger defeats. So when, within the
clone set, we drop the defeat(s) that conflict with larger ones,
the winner must come from the clone set.

***

What has always made me a little skeptical about judging methods
based on Clone Independence is: What about Subcycle Independence?

Say a candidiate is in the race, and then several very much
like him decide to run. Maybe they aren't a clone-set, or even
a near clone-set, but, even so, isn't there a good chance that
they'll at least have the same beat-relation, the same
win/lose relation, to everything other than eachother?

Subcycle Independence is more difficult to achieve.

So, it's just a matter of degree. Clone independent methods
are somewhat more nearly subcycle independent as a result,
but it isn't absolute.

Complete Subcycle Independence might very likely be incompatible
with Pareto, and seems to require more complicated rules.

So I'm forgiving of SC's clone non-compliance, and SD's much
rarer clone noncompliance.

***

That method that says to drop every defeat that conflicts with
a larger one--I'd call that "Simultaneous Dropping", except that
then it would have the same initials as Sequential Dropping.
So how about "Non-sequential Dropping" (ND).

***

Mike