[EM] Re: Approval Completed Condorcet

[Forest Simmons]

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
> 
>