[EM] Weighted Webster, Warren, and I

[Michael Ossipoff]

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 I’d thought BF achieved it. That’s 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. I’d 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 BF’s 
fallacy. At the time when I proposed, Weighted Webster on EM, Warren wasn’t 
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 Webster’s justifying 
virtue, in Warren’s 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.

I’m not saying that  WW is the best method, in terms of equal representation 
expectation for everyone--only that it’s the best true divisor method, by 
that goal. And I claim that goal is the only one that is about genuine 
justice.

Mike Ossipoff