In deriving the first method at his website, Warren said that his goal was
to zero the expected change resulting from the rounding. With that goal he
derived Weighted Webster, given the assumption that the state-size
frequency-distribution is exponential.
But, after that in the website, Warren describes some other goals, and the
resulting methods. One of th methods listed in that section is the
exponentially-weighted Bias-Free (My Weighted Bias-Free used a rational
function for weighing, to get an ant derivative with an exact solution).
Warren said that exponentially-weighted Bias-Free is the most morally right
of the methods listed, because it minimizes unfairness per person.
I myself used to believe that a Weighted Bias-Free was the fairest true
divisor method. I believed that till I found the fallacy in Bias-Free, which
is also the fallacy in my mistaken claim that ordinary Webster is
large-biased with a uniform frequency-distribution.
It turns out that, with uniform frequency distribution, it is Webster that
gives everyone the same representation expectation, by making the overall
s/q = 1 in each cycle.
It had occurred to me to check out the approach of calculating, with uniform
distribution, the total number of seats of the states in a cycle, and the
total number of quotas of those states, set those totals equal to each
other, and solve for R, the rounding-point, to find the rounding point that
thereby gives the cycle an overall s/q = 1.
R turned out to be (a+b)/2, or a + .5 At first I was puzzled by finding
that Webster achieves that, because Id thought BF achieved it. Thats when
I examined my claim that Webster is large-biased with uniform distribution ,
and found the fallacy in that claim.
My stated goal from the start was to give all the U.S. population the same
representation expectation, as nearly as possible, by making s/q =1 in each
cycle. That goal led me to Webster.
Then, for the same goal, I did the same thing--calculated the total seats
and total quotas in a cycle. But this time with a no uniform distribution. I
used exp, because it occurs in statistics and in nature. Id rejected it for
Weighted BF only because of its resulting lack of an exact solution.
That was how I arrived at Weighted Webster.
Warren, at his website, said that exponentially-weighted BF is the fairest
method, the most morally right. I myself believed that till I found BFs
fallacy. At the time when I proposed, Weighted Webster on EM, Warren wasnt
aware of that fallacy, and still believed that exponentially-weighted BF was
the fairest method.
Though he mentioned Weighted Webster, he derived it from a goal that was
different from mine (equal representation expectation for everyone by making
the cycles have the same s/q, by giving each cycle an s/q of 1. Pursuing a
different goal, he said that exponentially-weighted BF is the fairest
method.
That would leave relative simplicity as Weighted Websters justifying
virtue, in Warrens paper. Warren acknowledged that, exponentially-weighted
BF would require numerical solution.
When I found that Weighed Webster (WW) is what satisfies my goal for a true
divisor method, being the true divisor method that gives all the U.S
population equal representation expectation, I immediately announced that
publicly on EM, and proposed WW there.
At that time I had identified WW as the fairest true divisor method, and
said so on EM and proposed WW there.
Im not saying that WW is the best method, in terms of equal representation
expectation for everyone--only that its the best true divisor method, by
that goal. And I claim that goal is the only one that is about genuine
justice.
Mike Ossipoff
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