[EM] Re: Approval Completed Condorcet

[Alex Small]

I just realized a situation where Approval Completed Condorcet could cause
a problem.  It's rare, but here it is:

Suppose that every voter is stubborn and only indicates approval for his #1
choice.  If there are 6 or more candidates it's entirely possible that the
Smith set could consist of 3 candidates who received NO first place
rankings.  Consider the following:

33%:  D>A>B>C>E>F
33%:  E>B>C>A>F>D
33%:  F>C>A>B>D>E

D, E, and F lose all pairwise contests against A, B, and C.  Meanwhile, A,
B, and C are cyclic.  Unfortunately, none of them received any approval.
How then to resolve it?

Granted, this is an incredibly unlikely situation.  But, if Florida ever
holds elections via this method we should be prepared for the possibility
that it will happen ;)

I'm in a hurry, but off the top of my head I can't imagine this occuring if
we implemented Approval Completed Condorcet via Cardinal Ratings.  If you
had, say, a scale of 0 to 5, everybody in the Smith set would have received
at least a little bit of approval (at least some ratings of 1), so the
situation above would seem to be impossible. (but I've learned that it's
best not to say that a complication is impossible when discussing election
methods, at least not without thinking for a while).

Alex Small