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

[Dan Bishop]

MIKE OSSIPOFF wrote:
> 
> 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 computed apportionment based on the 1790 census 
(http://www.thirty-thousand.org/pages/first_veto.htm), considering the 
five divisor methods (Jefferson, Webster, Hill, Dean, and Adams) plus 
Hamilton (both Hare and Droop Quota versions).

For a historically-accurate House size of 105, these seven methods 
produce only three unique apportionments:

(1) Hamilton (Droop), Hamilton (Hare), and Webster give the apportionment

Connecticut: 7
Delaware: 2
Georgia: 2
Kentucky: 2
Maryland: 8
Massachusetts: 14
New Hampshire: 4
New Jersey: 5
New York: 10
North Carolina: 10
Pennsylvania: 13
Rhode Island: 2
South Carolina: 6
Vermont: 2
Virginia: 18

Most underrepresented state: Vermont (42,766.5 persons/district)
Most overrepresented state: Delaware (27,770 persons/district)
Greatest representation disparity ratio: 1.5400

Large-state bias (Pearson): -0.0111
Large-state bias (Spearman): +0.0857

(2) Hill, Dean, and Adams give the apportionment

Connecticut: 7
Delaware: 2
Georgia: 2
Kentucky: 2
Maryland: 8
Massachusetts: 14
New Hampshire: 4
New Jersey: 5
New York: 10
North Carolina: 10
Pennsylvania: 12
Rhode Island: 2
South Carolina: 6
Vermont: 3
Virginia: 18

Most underrepresented state: Pennsylvania (36073.25 persons/district)
Most overrepresented state: Delaware (27,770 persons/district)
Greatest representation disparity ratio: 1.2990

Large-state bias (Pearson): -0.3842
Large-state bias (Spearman): -0.2786

(3) Jefferson's method gives the apportionment

Connecticut: 7
Delaware: 1
Georgia: 2
Kentucky: 2
Maryland: 8
Massachusetts: 14
New Hampshire: 4
New Jersey: 5
New York: 10
North Carolina: 10
Pennsylvania: 13
Rhode Island: 2
South Carolina: 6
Vermont: 2
Virginia: 19

Most underrepresented state: Delaware (55,540 persons/district)
Most overrepresented state: New York (33,158.9 persons/district)
Greatest representation disparity ratio: 1.6750

Large-state bias (Pearson): +0.4963
Large-state bias (Spearman): +0.6250