[EM] Re: CIBR examples, and its CC failure
Araucaria Araucana
araucaria.araucana at gmail.com
Fri May 27 12:17:57 PDT 2005
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
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