# [EM] Same goal, opposite results. Examine the differences.

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Dec 14 10:30:42 PST 2006

```Say, for a particular census, we do allocations bv Hill and by Bias-Free.
Say your measure of proportional disparity is the _ratio_ of s/q, rather
than its difference. So, by that standard, any trransfer of a seat, starting
with the Hill allocation, will put the two affected states more disparate in
their s/q.

But say, as should usually be the case, the Bias-Free allocation is less
biased, by some tests for bias.

How to choose between those two allocations and their justifying standards?

1) The Hill transfer property is about your state's s/q disparity with a
particular state, whichever one is involved in the disagreement between the
2 allocations. Bias-Free's unbias is overall.

2) There's a difference in _when_ the s/q disparity is looked at. With
Hill's transfer property, the disparilty is looked at after the count,
juding the s/q disparity of those two states in hindsight.
Bias-Free's unbias means a uniform s/q expectation for _all_ states, as
judged before the apportionment and the census. And of course, the time when
you're deciding which method to advocate or adopt is a time before the
census, and certainly before the allocation. So it makes the most sense to
choose the method that gets rid of s/q expectation disparity as judged at a
time _before_ the census and allocation.

Mike Ossipoff

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