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 Im sticking with CW, AR, WW and W. They meet one of your standards, dont 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. Thats what CW, AR, & WW are for.
But, as I said, theres a good case for saying that the _distribution-caused_ measured bias, when Webster is used, isnt unfair in the sense that _method-caused_ measured bias is unfair.
Mike Ossipoff
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