I'm posting some comments from Warren Smith, and my replies. I emphasize that Warren's angry tone was there from the start, entirely unprovoked. I had never criticized Warren. This discussion is on-topic, because it's about the electoral system, even if it reveals someone's anger. How we discuss, and what motivates us, are relevant on this list. I believe that it's a good thing to find out whom you've been correspoinding with. Warren said: Re your formula involving a^a and b^b, let me just simply say: I don't believe you. Specifically, whatever integral it is you claim to have done, I claim you did it wrong and got a totally bogus, albeit cute looking, formula out. Re "cycles", I did not disparage that idea, in fact I thought it was interesting, and credited you with it. (Basically this entire thing was me trying to make sense of what you'd been saying, failing, and then redoing it myself trying to preserve the good or interesting ideas you had, but getting rid of the wrong execution of them, unclear stuff, etc.) I reply: But Warren never showed the "failing" or the "wrong execution, etc. Warren continues: Specifically, you executed wrong in the following ways: 1) you did your integral or integrals wrong, getting bogus formulas. I reply: Warren seems to believe that sufficiently frequent repetition is a substitute for substantiation of his claims. Warren continues: 2) your probabilistic model was inappropriate (uniform distribution); Bias-Free, even with its uniform distribution assumption, is less biased than Webster. Warren continues: exponential distribution is appropriate if any simple one is. This is well known to mathematicians for various reasons probably unfamiliar to you, but I'll probably try to write them down later. (Dirichlet... Poisson... Binomial Combinatorics... to mouth some buzzwords in a manner which is probably meaningless, but it is too much of a pain for me to explain it right, right now, and I'm not sure even if I did so, that you would appreciate it...) I reply: ...or maybe yoou're just parroting some terminology from a class in which you got a "D" or worse, or from other source, on topics about which you're as clueless as you are about the derivation of Bias-Free. In any case, it's better to not make so many unsupported statements. Your misunderstandings and confusions about the other things you've discussed make it unlikely that you were doing other than parroting and posturing, in the above quote. Warren continues: Incidentally, computer simulation by a modification of Bishop's sim program http://rangevoting.org/BishopSim.html indicates my new method is indeed an improvement over Webster and all the classical divisor methods. A computer simulation of your method would indicate it was a total failure, because your formulas are bogus. I reply: Bias-Free has been applied to censuses, and, in 2 apportionments, it agreed with Webster, then wilth Hill. On the bias signed-number-line, Bias-Free is between Hill and Webster. In the long run it will be less biased than eilther. Mike Ossipoff _________________________________________________________________ Your Hotmail address already works to sign into Windows Live Messenger! Get it now http://clk.atdmt.com/MSN/go/msnnkwme0020000001msn/direct/01/?href=http://get.live.com/messenger/overview _________________________________________________________________ Your Hotmail address already works to sign into Windows Live Messenger! Get it now http://clk.atdmt.com/MSN/go/msnnkwme0020000001msn/direct/01/?href=http://get.live.com/messenger/overview ---- election-methods mailing list - see http://electorama.com/em for list info