Warren said: Hmm, oddly enough, this formula actually works despite my "proof" last post based on number theory that it could not. How can that be? Because the two rational functions in the two integrands are not the same, that is why (my sanity check had assumed they were the same!).
I reply: Howabout because you made a fool of yourself again by writing about what you don't understand. Warren continues: OK, good - Ossipoff's method has at least now been promoted into the land of understanding what it is. However, it remains questionable in the sense that the uniform distribution assumption is self-contradictory (as I pointed out last post re 1 and 1.4) and unjustified (as discussed http://rangevoting.org/NewAppo.html). If it really were uniform it'd cutoff at some point, and near that point Ossipoff's formula would no longer be correct. You could still make an apportionment method out of Ossipoff's formula plus another formula for dealing with the high end of the uniform distribution (Ossipoff did not) but even then you'd still have a bogus method because what if a state population just happens to be fairly far ABOVE the high end of the uniform distribution? In that case the way of dealing with such a state would be unspecified. So then we can (which is what Ossipoff presumably did) just ignore all of that and proclaim we are going to use the y = (B^B / A^A)/e formula come hell or high water (including in regimes where the mathematical justification above clearly is invalid). That is fine if all that is asked is to define a method, not to present a justification for how the method got there. I reply: This is the posting in which Warren admits and corrects his errors, but confusion is still the main ingredient of his posting. In this instance, confusion about the range in which a divisor method's rounding rule could need a disstribution assumption. BF only needs its assumption within a cycle, not over the infinite number-line. Confusion and error are evidently Warren's consistent trademark. Mike Ossipoff _________________________________________________________________ The MSN Entertainment Guide to Golden Globes is here. Get all the scoop. http://tv.msn.com/tv/globes2007/?icid=nctagline2 ---- election-methods mailing list - see http://electorama.com/em for list info