[EMAIL PROTECTED] wrote: > > From: [EMAIL PROTECTED] > > > > The examples dramatize Hill's bias, but would could be more dramatic than > > this?: > > > > If we dildn't have the 1-free-seat-for-each-state rule, Hill would give > > everyone a seat anyway, but Hill's own rules. It would give a seat to any > > state that contains at least one person. How do you like that for > dramatic > > bias. > > That is pretty cool, it will comply with the 1 seat per State rule > 'natively'. > > Pity about the additional bias for higher numbers of seats. > > > If you had any doubt about Hill's bias, that should settle the matter. > > Someone might say, "But that doesn't happen, due to the free seats". > > Right. Also, how small is the smallest State ?
Wyoming has about half a million people. > > While Hill's round-up point between 0 and 1 is at 0, Bias-Free's round-up > > point in that range is near .38 That is, 1/e. Webster's round off > point in > > that range, of course, is at .5 So, though Webster is biased, it's bias > > isn't of the dramatic nature of Hill's bias. > > Recognising that all States get 1 seat anyway, the critical point is for > numbers greater than 1. I guess Webster is 1.5 and Hill is lower than > that ? Correct. Hill's cutoff is sqrt(2) = 1.4142135623730951. Not that far from the Webster cutoff; in fact, as I've mentioned before, Webster and Hill give identical apportionments this decade. > > Unbias is absolutely essential for House apportionment. That means that > > Hamilton and Bias-Free are the only methods that can be considered for > > apportionment. > > It seems to me that they are all reasonably close. Unless you get rid of > the 2 Senators per State rule, slight biases in the House apportionment > are not very significant. Furthermore, you could get a much better improvement in proportionality by increasing the size of the House than by changing the apportionment method. > If you are going to settle for Webster, then settling for Hill isn't a major > additional compromise. Agreed. ---- election-methods mailing list - see http://electorama.com/em for list info
