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 _________________________________________________________________ Get live scores and news about your team: Add the Live.com Football Page www.live.com/?addtemplate=football&icid=T001MSN30A0701 ---- election-methods mailing list - see http://electorama.com/em for list info
