[EM] apportionment and some random Ossipoffness

[Warren Smith]

My "credentials" as a "professor" have been attacked.
I am not a professor and do not recall claiming to be one.
However in many ways I resemble a professor:
I do have a math PhD from Princeton, I have written and published a lot of math papers,
I worked for various research places for a lot of years, I taught math in 2 universities
at various times, and I acquired pseudo-tenure at this pseudo-academic place I worked for
(that was trying to claim to be academia-like and award "tenure," even though
it was not academic) but I have not been anointed "professor" at any time so far (albeit
that may happen).   I also have a web page at Temple U. Math. Dept, which is because they gave me
a permanent web page there as part of my employment deal at one time.
There are a bunch of academic titles which, frankly, I usually do not actually 
understand, but which anyhow you only get if they are awarded, and 
in my case the title "professor" was never awarded.

Second, while I happen to think Mike Ossipoff has some talents,
and indeed in the present case it turns out that his "bias free method" can
indeed be derived and explained
in a semi-reasonable way (albeit, at first I thought it was arrant nonsense)
his ability to explain mathematics clearly, often falls short.  
If you have an algorithm to present, then by all means do so. Step 1, step 2, etc.
Do not leave the algorithm to the reader to divine by mindreading, do not 
assume the reader knows what letters mean or what words mean and therefore nowhere define them.
If you do this about 6 times in a row it becomes very likely whatever you say cannot be 
understood - and even if there is some sense behind it, it is highly likely that any reader 
will assume anybody who can only explain things that badly, has to be senseless.
Writing math is about precision and clarity, not ambiguity and mindreading.

Third, in his recent series Mike has made some errors, for example asserting the wonderfulness
of the probability density  1/(Ax+B)   over the domain x>0;   whereas in fact this is not
a probability density for any A,B because it cannot be normalized.
There are, in fact, numerous reasons to focus on exponential densities in preference
to all other simpleminded densities, for this prupose, and some of those reasons are
explained in     http://rangevoting.org/NewAppo.html .

Fourth and finally, I rather object to Mike's apparent notion that it is my responsibility to
find flaws in derivations he nowhere gives, and then if I nevertheless do find flaws, he
is free to declare he meant something else and therefore was flawless (which can be
a wholy defensible stance by Mike, because he nowhere ever explained what he meant, and then he 
blames the critic for not understanding what he meant, because said critic was 
obviously deficient in mindreading ablity).  On the other hand if the critic does manage 
to mind-read, Mike then attacks the critic as having
only done so with some kind of assistance from Mike,
thus demonstrating the ineptitude of the critic once again.  Well, quite.

In any event, concerning apportionment methods, it seems to me that (and always has seemed
to me that) Mike's underlying spiritual idea, that of trying to devise a method
with zero "bias" of some quantity in some probabilistic model, is a good one.
There are a potpourri of such methods that you can derive from different probabilistic 
models and different kinds of unbias demands.  
It is not clear to me which one is the "best" (if any) and the one I
happen to have advertised in
 http://rangevoting.org/NewAppo.html
was mainly chosen, not because of any great belief by me that it eas the "best,"
but rather, mainly becuase it results in an extremely simple algorithm, which is clearly 
at least as good (by any measure of "goodness" whatever) as Webster, Adams, or Jefferson, 
and therefore, to the extent you buy Balinski & Young's claim Webster is the best they know, 
at least as good as any previous method.

It is probably a good idea to write down more elements of the potpourri and I hopefully
will do so soon.  I suspect some others are objectively better, but I also suspect no others
come close to my method's simplicity and all others are probably just too messy to
hope for adoption by Joe Public.  If so, then my method is probably the best possible
method with realistic adoptability chances.

Warren D Smith
http://rangevoting.org