[EM] Adjusted Rounding--Webster by cycles
MIKE OSSIPOFF
nkklrp at hotmail.com
Tue Dec 19 10:08:58 PST 2006
Webster individually puts each state as close as possible to one seat per
quota, but we've seen how optimization for states and pairs of states
doesn't do much for overall unbias, uniform s/q expectation.
The important thing is that each _cycle_ be as close as possible to 1 seat
per quota. So why not do Webster by cycle instead of by state?
For each cycle, each interval between integers, choose the round-up point so
that the overall s/q of the states in that cycle will be as close as
possible to 1.
It occurred to me that, in my 10-state example, population distribution was
uniform, and that Hamilton's and Bias-Free's justification assumes that.
But, if that isn't so in real apportionments, then the s/q of the biggest
half of the states might systematically differ form that of the smallest
half of the states. In particular, if the population-density distribution is
single-peaked at the middle, maybe normally distributed, one would expect
small states to be favored by methods optimized for uniform population
distribution. Of course one could make a Bias-Free version for normal
distribution, but Adjusted Rounding seems a more adaptable solution.
I haven't abandoned Bias-Free or Hamilton. I haven't done any apportionments
based on censuses. Maybe Adjusted Rounding isn't needed, if Bias-Free and
Hamilton do well in actual censuses. On the other hand, Adjusted-Rounding is
easier to convince people of than Bias-Free, and won't put off people who
don't like mathematical formulas.
Mike Ossipoff
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