In the recently-posted historical census apportionments, BF did worse than Webster in every census apportionment where those 2 methods apportioned differently.
Dan, did you definitely do the Bias-Free that I defined in the posting just before this one? If so, then the only possible explanation is that the free seats required by the seats-for-every-state rule caused so much small-bias that Webster's slight large-bias is needed to cancel it out, resulting in less measured bias with Webster. Bias-Free is genuinely bias-free if the frequency distribution is flat. With a flat distribution, Webster is sliglhtly large-biased. Add a slight large-bias due to the distribution, and both methods' apportionments are large-biased, but Webster moreso, because Webster has some large-bias of its own. So it must be that the free-seat small-bias is making Webster the best one, because it comes closest to exactly canceling out the free-seat small-bias. Of course Bias-Free and Weighted Bias-Free could have their rounding points carefully moved upward in order to very nearly cancel out the free-seat small-bias. The best solution is to make sure that the House is large enough that all the states _qualify_ for at least one seat, in every census. That could be done separately, or a method could carry it out as part of the method's rules. In any case, since that's how the House should be, I claim that it's important to also report correlations based on not having a free-seat rule. Mike Ossipoff ---- election-methods mailing list - see http://electorama.com/em for list info
