[EM] Aha, now I understand Ossipoff...
MIKE OSSIPOFF
nkklrp at hotmail.com
Wed Jan 17 08:12:51 PST 2007
Warren said:
Hmm, oddly enough, this formula actually works despite my "proof" last post
based on
number theory that it could not. How can that be? Because the two rational
functions
in the two integrands are not the same, that is why (my sanity check had
assumed
they were the same!).
I reply:
Howabout because you made a fool of yourself again by writing about what you
don't understand.
Warren continues:
OK, good - Ossipoff's method has at least now been promoted into the land of
understanding what it is. However, it remains questionable in the sense
that the uniform
distribution assumption is self-contradictory (as I pointed out last post re
1 and 1.4)
and unjustified (as discussed http://rangevoting.org/NewAppo.html).
If it really were uniform it'd cutoff at some point, and near that point
Ossipoff's
formula would no longer be correct. You could still make an apportionment
method out of Ossipoff's formula plus another formula for dealing with the
high
end of the uniform distribution (Ossipoff did not) but even then you'd still
have
a bogus method because what if a state population just happens to be fairly
far ABOVE
the high end of the uniform distribution? In that case the way of dealing
with such a state
would be unspecified.
So then we can (which is what Ossipoff presumably did) just ignore all of
that
and proclaim we are going to use the y = (B^B / A^A)/e formula come hell
or high water
(including in regimes where the mathematical justification above clearly is
invalid).
That is fine if all that is asked is to define a method, not to present a
justification
for how the method got there.
I reply:
This is the posting in which Warren admits and corrects his errors, but
confusion is still the main ingredient of his posting. In this instance,
confusion about the range in which a divisor method's rounding rule could
need a disstribution assumption. BF only needs its assumption within a
cycle, not over the infinite number-line.
Confusion and error are evidently Warren's consistent trademark.
Mike Ossipoff
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