[EM] BF and the no-minimum census apportionments

Michael Ossipoff mikeo2106 at msn.com
Wed Jan 24 14:54:14 PST 2007

Even without the 1-seat minimum,. Bias-Free, in the census apportionments, 
still nearly always does worse than Webster when the two dilffer.

There are two possible explanations:

1. Maybe, though I've believed that the frequency distribution causes 
large-bias, I was mistaken and it actually instead causes small-bias. In 
that case, Webster may have just enough intrinsic large-bias to nearly 
cancel the distribution's small-bias. Bias-Free, with no intrinsic bias 
wouldn't do as well.

(It goes without saying that Cycle-Webster and Adjusted-Rounding would still 
do better than any other methods, since their unbias is unconditional).

2. Maybe the use of correlation between _states'_ q and s/q instead of 
_cycles'_ q and s/q gives sufficiently different results as to give the 
result shown. Maybe, in large simulations, the s/q disparities caused by 2 
states being in different parts of their cycles would cancel out, and then 
the two correlations, the state correlation and the cycle correlation would 
give the same result.

Probably the 2 kinds of correlation don't give very different results, and 
that that canceling tendency is present even in a few census 
apportionmentss. So I rather suspect that explanation #1 is the correct one.

Note that someone could fix the correlation, reduce it, by tweaking roundoff 
points up or down. They coudl even tweak a fixed rounding point in that way, 
a rounding point that is at the same part of each cycle. That would make the 
correlation come out lower, but would it actually eliminate bias, as I've 
defined it, and as we mean it?

Mike Ossipoff

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