[EM] Non-pairwise clone characteristics

[Kristofer Munsterhjelm]

Let e be some election, and fpX(e) be X's first preference score in that
election (similarly lpX(e) last preferences).

Then if A1 and A2 are clones in e, and election f is that election
without the clones (i.e. A instead of A1 and A2), fpA1(e) + fpA2(e) =
fpA(f). It's also true that lpA1(e) + lpA2(e) = lpA(f).

So it's not that difficult to see that IRV is immune to exact
vote-splitting (i.e. clone-loser) because when one of the clones has
been eliminated, the other clone obtains as many points as the clone had
he not run.

For Coombs I *think* the same logic holds. Suppose A2 is the candidate
to be eliminated. Then after A2 is eliminated, we reduce to the case
where there's only one clone.

However, batch elimination methods like Carey can be susceptible to
vote-splitting because it's possible that every clone is eliminated in
one go.

Perhaps every one-at-a-time elimination method based on a weighted
positional system that's all ones and then all zeroes, is immune to
vote-splitting. I'm not sure.

One-at-a-time elimination methods in general don't need to be, I think,
because one could conceive of a method where the insertion of a clone
would alter the scores of other candidates so that in an A>B>C>A clone,
C is eliminated instead of B; then the later elimination that removes
either A1 or A2 won't be enough to save A from losing.

And this of course says nothing about teaming and crowding.

-km