[EM] Why my methods are unbiased by accepted definition

Warren Smith wds at math.temple.edu
Mon Jan 22 21:44:52 PST 2007

Mike Ossipoff in the thus-named post failed to provide any definition or any
theorem as usual, while also failing to answer my question about Hamilton's method.

Concerning further issues related to Apportionment:
1. Ossipoff's "bias free" method can be cast in a global optimization framework,
as can many other methods (I now know how) including my own.

2. I conjecture that the or a reason why Bishop's simulation from US census data, failed
to yield good performanxce for O's method, was because he was requiring a 1-seat minimum.
Bishop did not actually describe his methods so we cannot tell.   Anyhow, note that my
method in http://rangevoting.org/NewAppo.html is capable (with a different value of "d")
of handling the 1-seat-min still without "bias"... and you can work out the exact theoretical
value of d to use.   That is because it is based on a valid probabilistic model.
I mentioned before how Ossipoff, in his posts expressing his contempt for probability
theory and the lack of need for valid probability density functions, was thereby exhibiting
"underlying rot" in his thinking.  This is a concrete instantiation of that.  Note that
Ossipoff could NOT similarly obtain a version of his method that was unbiased in the presence
of an imposed 1-seat-minimum, while I can.  That is because I am based on probability
theory and he is not.  This contrast illustrates the wages of sin (mathematical sin that is).
I hope that little lesson sinks in.

3. The book Malkevitch pointed out by the 5 Italians gives some useful theorems that are
capable of yielding a vast profusion of global optimization formulations of divisor methods,
and which also are capable of yielding effcient algorithms equivalent to a considerable set
of (but not all) interesting global optimization formulations you could write down tabula rasa.
I plan to write down some of that later, but haven't yet.  The problem actually is not writing
them down, it is writing nice ones down; there is some component of "art" to the latter.

Warren D Smith

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