[EM] Warren--BF's apportionment score

[Michael Ossipoff]

Warren said:

Although Bishop failed to find better behavior (by his Spearman measure) for
"Ossipoff"
(it was not said exactly what "Ossipoff" was) versus Webster, Bishop will
definitely
find superior behavior for the scheme advocated at the beginning of
http://rangevoting.org/NewAppo.html
versus Webster - it is merely a matter of wat the best value of the magic
constant "d" is.
Bishop can search for the best value of d with 0<d<1 to optimize his 
Spearman
measure.

I reply:

It goes wilthout saying that anythng can be tweaked, by trial and error.Say 
I wanted to improve BF's results in that census apportionment. I could 
systematically change all the rounding points, maybe by the same factor, 
maybe by adding a constant amount. If Webster did best because its slight 
large-bias is just right for canceling the small-bias resulting from the 
free-seats, thenanyhone could keep adjusing a uniform rounding point to 
achieve that.

But our method, as I said, has a cruder unbias. How can it be otherwise, 
when the rounding point is fixed rather than found by a formula that 
optimizes it for each cycle? For instance, your R is near the midpoint of 
each cycle. Making the lowest-population cycles have s/q = 1 requires lower 
rounding points in those cycles. Your method will give the lowest cycles 
less s/q. That's biased by anyone's definition.

Mike Ossipoff