# [EM] Webster has a little bias. The Unbiased Rounding method.

MIKE OSSIPOFF nkklrp at hotmail.com
Mon Dec 11 01:28:10 PST 2006

```When I said that my definition of bias, a systematic disparity in seats per
quota, opens up a can of worms when it's applied, what I meant was that it
shows bias for Webster.  Very, very little bias.

Sometimes it's best to open a can of worms.

Is there a quota and roundoff method that's free of bias? For quota and
roundoff methods, such as Webster, Hill, etc., freedom from bias is only
possible with some particular probability density disrtribution for the
states' populations or their numbers of population quotas.

So let's say that that distribution is uniform.

The quota and roundof method that is unbiased is the one that has, as its
roundoff point (between the integers a & b):

(b**b/a**a)(1/e)

The first of its successive roundoff points (to the nearest hundredth) are:

1.47, 2.48, 3.49, 4.49, 5.49, 6.49, 7.49, 8.5, 9.5

These roundoff points are much closer to those of Webster than to those of
Hill, suggesting that Webster is the least biased of the 5 standard quota
and roundoff methods.

Maybe the above-described method has already been described, but if not, or
if it hasn't been named, I'll call it the Unbiased Method, the Bias-Free
method, or (more descriptively) Unbiased Roundoff.

Largest-Remander/Hamilton is the only distribution-independent unbiased
method.

Mike Ossipoff

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