Great Example! In Demorep's version every candidate with less than 50% approval is eliminated at the outset. If nobody is left, this is equivalent to NOTB being the Condorcet Winner.
Forest On Fri, 22 Feb 2002, [iso-8859-1] Alex Small wrote: > 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 > >
