[EM] Saari's Basic Argument
fsimmons at pcc.edu
Thu Feb 27 16:25:23 PST 2003
On Thu, 27 Feb 2003, Steve Barney wrote:
> Apparently, as I thought, your method of decomposition is to simply to remove
> cycles first, and then reversals. My point remains, then, that your
> decomposition method does NOT NECESSARILY yield the same outcome as Saari's
> matrix decomposition method.
Actually, the order of removal isn't important as along as you recognize
that whenever you have two non-adjacent factions left, more symmetry
reduction is possible. In other words, you can reduce the total number of
ballots in the set by addition and subtraction of cycles and reverse
I don't know if Saari is aware of this or not.
> There is a lot of disagreemnt over the correct outcome, in this example. Even
> Kemeny's Rule (which is also Condorcet's method, according to Hannu Nurmi, as
> I quoted previously in message # 10496) disagrees with both your decomp and
> Saari's. According to my calculations, Kemeny's Rule goes like this:
If you buy into the reduction-by-symmetry idea (which I don't, but was
willing to entertain), then how can you say that a multi-faction ballot
set is simpler than a single faction ballot set with fewer total ballots,
when both sets can be obtained by symmetry reductions of the same type
(addition and subtraction of cyclic and reverse order symmetries)?
Kemeny (wisely) doesn't believe in cyclic symmetry removal, and maybe
Saari doesn't try to remove all of it. If not, then even he must have some
reservations about the symmetry idea.
As I said before, I wasn't trying to duplicate Saari, I was just
dissecting the symmetry idea by carrying it to its logical conclusion to
find out where it went wrong ... a form of mathematical autopsy.
It's easier to see the defect of an idea in its extreme manifestations
than in its half hearted applications.
That's why I would rather have Bush than Gore as president. People will
wake up to the evils of Corporate control of government policy in its
extreme, flagrant form sooner than they would in a more veiled, toned down
(but equally virulent) form.
[I voted for Nader who referred to Gore and Bush as twiddle dumb and
twiddle dumber of the republicrat corporate duopoly. The same
corporations funded both of their campaigns and made sure that police
would keep Nader off of the premises during the corporate sponsored
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