[EM] Hamilton beats Hll in the example. Hill shows the most bias of the 3 methods.

[MIKE OSSIPOFF]

After testing Hill and Bias-Free in the 10-state example, it occurred to me 
to also test Hamilton. Hamilton's allocation was about 2.8 times less biased 
than that of Hill. Bias-Free had tested more than 3 times less biased than 
Hill.

I'd said that Bias-Free and Hamilton are the completely unbiased methods. 
The probability that, by chance, Hill would finish last, just as I'd 
predicted, is of course only 1/3.

Though both are unbiased, one would expect Hamilton to probably do not quite 
as well as Bias-Free, due to Hamilton's randomness. The probability that, by 
chance, those 3 methods would finish in the predicted order is only 1/6.

Surely Balinski & Young must have done apportionments for all the historical 
censuses, by Hamilton, Webster and Hill, and compared those allocations for 
bias. Has anyone done such comparisons?

For instance, someone recently posted that Webster and Hill gave the same 
allocation for 2000. But, in the censuses where they differ, how does their 
bias compare? And if anyone is going to do such comparisons, I'd suggest 
testing Bias-Free along with Hamilton, Hill, and Webster.

I've been reporting measured bias as the ratio or difference of the average 
seats per quota (or person) for the largest half of the states and the 
smallest half of the states.

Mike Ossipoff

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