[EM] Minmax under-representaton causes small-bias

[Michael Ossipoff]

Brian--

The small states are the ones whose s/q is most greatly affected by rounding 
up, or by not rounding up. So it would usually be a small state that has the 
lowest s/q due to not rounding up. So if we minimize the greatrest 
under-representation,  as good as that goal sounds, the result is that we 
preferentially round-up the smaller states. We make systematic small-bias.

Webster puts each state as close as possible to a seat per quota. WW, CW & 
AR put each cycle as close as possible to 1 seat per quota overall. All this 
is with the goal of equal representation (or representation expectation) for 
everyone, as nearly as possible.

So I’m sticking with CW, AR, WW and W. They meet one of your standards, 
don’t they?

By the way, when Webster puts each state as close as possible to 1 seat per 
quota, it also automatically ensures that no pair of states could be any 
closer in s/q than it already is.

Webster  has no intrinsic bias. And it will test unbiased,  by empirical 
tests, if the frequency distribution is flat.  Webster can be improved on by 
methods that equalize s/q even  without flat distribution. That’s what CW, 
AR, & WW are for.

But, as I said, there’s a good case for saying that the 
_distribution-caused_ measured bias, when Webster is used, isn’t unfair in 
the sense that _method-caused_ measured bias is unfair.

Mike Ossipoff