On 27 May 2005 at 11:46 UTC-0700, Ken Kuhlman wrote: > > While your CC failure example is helpful, my favorite is Condorcet's original > critique of Borda: > > 30:A>B>C > 10:B>C>A > 10:C>A>B > 1:C>B>A > 29:B>A>C > 1:A>C>B > > Condorcet picks A & Borda & CIBR pick B. Here's the explanation (summarized > from Saari): If symmetrical ballots, (which represent ties & should > cancel), > are factored out, the election outcome should be unchanged. > > The symmetrical ballots in Condorcet's critique are: > 10:A>B>C > 10:B>C>A > 10:C>A>B > and > 1:C>B>A > 1:B>A>C > 1:A>C>B > > The reduced profile is then: > 20:A>B>C > 28:B>A>C
I've seen this Borda-advocate logic before. Eliminating 'symmetric' votes is just eliminating votes. Among others, you've effectively ignored the net 9 vote preference for A over B among all the C voters. So you've effectively told them, "Tough luck, your votes were considered invalid, so we're not going to consider your lower-ranked preferences. Even if your voting block thinks that A is the lesser of two evils (and would contribute to a majority expressing that one-to-one preference), we're going to pick B anyway." To me, symmetry refers to reversing the ballot orders on all the ballots. Let's say we do this. Then whichever method you pick, Condorcet or Borda, the "reverse-winner" is C. So you should be able to go back to the original election and see who would win with the loser, C, eliminated. If you eliminate C from the original election, the voters prefer A to B, Borda or Condorcet. But introducing C to the ballots doesn't change the Condorcet winner, just the Borda winner. Borda is far more prey to weird IIA-violation effects than Condorcet. I've also been following your CIBR arguments. It seems to me that you're setting up a straw man for Borda, since clone independence is not Borda's worst failing. Burying is much worse and you haven't addressed that at all. Q -- araucaria dot araucana at gmail dot com http://www.metafilter.com/user/23101 http://wiki.electorama.com/wiki/User:Araucaria Q = Qoph = "monkey/knot" -- see http://www.ship.edu/~cgboeree/alphabet.html ---- Election-methods mailing list - see http://electorama.com/em for list info
