On 5/27/05, Araucaria Araucana <[EMAIL PROTECTED]> wrote:
Not surprising. As I stated, it's a summary of an explanation made by Saari.
No vote has been eliminated.. some have cancelled. To again summarize Saari,
this is equivelant to telling a husband and wife team with diametrically
opposed views that it's OK if they don't vote, because the election method in
use understands that their views cancel eachother out.
In Condorcet's classic example, this is true. But it's just as easy to
identify profiles where if a candidate drops, the Condorcet winner changes
but the Borda or winner don't.
By "IIA-violation effects" I assume you mean candidate dropping? If so,
please give me a reference where this is proven.
Either you're in the minority in considering burying to be Borda's worst failing,
I've seen this Borda-advocate logic before.
Not surprising. As I stated, it's a summary of an explanation made by Saari.
Eliminating 'symmetric' votes is just eliminating votes.
No vote has been eliminated.. some have cancelled. To again summarize Saari,
this is equivelant to telling a husband and wife team with diametrically
opposed views that it's OK if they don't vote, because the election method in
use understands that their views cancel eachother out.
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.
In Condorcet's classic example, this is true. But it's just as easy to
identify profiles where if a candidate drops, the Condorcet winner changes
but the Borda or winner don't.
Borda is far more prey to weird IIA-violation effects than Condorcet.
By "IIA-violation effects" I assume you mean candidate dropping? If so,
please give me a reference where this is proven.
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.
or the random sampling of Borda criticism I've read has been strangely skewed.
Regardless, burying was the first problem identified with Borda (Borda, "My system
is only for honest men,") and I do take it seriously. Fortunately, it's untrue
that I "haven't addressed it at all."
If supporters of a strong candidate strategically rank a weaker candidate higher than
a close competitor, they would have to give the weak candidate enough support to
make it a Borda winner over the competitor they're trying to "bury." Otherwise, the
weak candidate will be certain to be eliminated when paired with the close
competitor. Even if they're able to do so, the "weak" candidate would then become
a serious contender to the candidate that's being "aided" by the burying tactic, and
so the strategy is likely to backfire.
Further, the voter block that's attempting the burying strategy is likely to create a
clone in the process, which would cause the weak candidate to be eliminated
immediately, gaining the block nothing.
-Ken
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