[EM] Oops! :-) Bias-Free's fallacy

[Michael Ossipoff]

I said that Webster is large-biased because, though its step function is 
over the 1-seat-per-quota line as much as it is below it, the states in the 
low section are more hurt by being lower, because their lower q means that a 
given drop in s results in a bigger drop in s/q. What I missed was the fact 
that what happens in a state has to be weighted according to its size, 
because, since it has fewer people, you're less likely to be in it.

With Webster's step function symmetrically above & below the 1 seat per 
quota line, the cycle has one seat per quota. Every cycle has the same 
number of seats per person. Your expectation of representation is the same 
no matter which cycle you're in.

What brought this to my attention was when I approached BF in a different 
way, summing separately the seats and quoas in a cycle, and setting them 
equal, and solving for R. R turned out to be (a+b)/2.

I propose Weighted-Webster (WW), in which the integrand is weighted with a 
function that approximates the probability density. Just like Weighted 
Bias-Free, except that it's Webster now.
I propose that the weighting function be Bexp(-Aq), with A & B positive 
constants. But if that results in an antiderivative without an exact 
solution, then I'll use B/(q+A).

Mike Ossipoff