[EM] A few clarifications about allocation bias, and SL vs LR

[Michael Ossipoff]

Bias:

To not have bias, systematic favoring of large or small parties or
districts, it isn't necessary that, for any particular allocation, the
correlation between q and s/q be minimized.

It's ok if it happens that, in a particular allocation, small parties
happen to have somewhat more s/q than large parties--as long as that hasn't
occurred _because_ they're small. It's ok if, by random variation, it turns
out that way sometimes, when using a method for which expected s/q is the
same at the small and large ends of the size-range.

But, if you aren't sure that your method is unbiased with regard to s/q
expectation for parties of all sizes, then, if small parties end up with
more s/q in a particular allocation, you won't know whether or not that's
because they're small parties.

That's when you'd want to use trial and error to find an allocation that
minimizes correlation between q and s/q.

With Webster/Sainte-Lague, you know that the method is only unbiased with a
probability distribution that can't really be accurate, and that there is
probably a slight large-bias in your allocation procedure. With
Weighted-Webster, the distribution you're using can only be a guess.

That suggests that the best way to ensure unbias would be to find, by trial
and error, the allocation that minimizes the correlation between q and s/q.

Systematically, predictably, favoring or disfavoring some parties,
districts or states is obviously the worst thing that an allocation method
could do. That's why I consider unbias to be the important consideration in
allocation.

SL, LR, & Raph's bad-example:

Of course the splitting strategy in that example would be difficult and
risky, but, in principle, it could happen spontaneously too, without any
strategy being used. ...with the districts, states or parties having, by
improbable chance, sizes that would cause some such result.

Suppose it happened by chance, without strategy. In that admittedly
exceptionally unlikely example, achieving SL's standard makes a result that
looks wrong. But, with SL, the s/q are fairly equal. LR's result looks
better, but then the small districts have s/q 1.77 times that of the large
district. SL is more fair, when the result isn't strategic. But LR does
better if the situation is the result of splitting strategy.

That supports my suggestion that LR's value is as a contingency plan in
case it turned out that splitting was a problem in SL, and remained a
problem even with Modified SL, where the first denominator is 2 instead of
1.

SL is used, apparently with no splitting problem, with a first denominator
of only 1.4.

Mike Ossipoff
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