# [EM] A numerical example with Bias-Free and Hill

MIKE OSSIPOFF nkklrp at hotmail.com
Thu Dec 14 12:13:07 PST 2006

```I did a simplel example, with only 10 states, 55 people, and 82 seats. I
chose 82 seats because I wanted about 1.5 seats per person.

State #1 has one person. State #2 has 2 people...on up to state #10 with 10
people.

Bias-Free:

Population: 1    2    3    4    5    6    7  8    9    10
Seats:        2    3    4    6    7    9   11 12  13   15

Hill:

Population: 1    2    3    4    5    6    7    8    9    10
Seats:        2    3    5    6    7    9    10  12  13   15

Hill has taken a seat from #7 and given it to #3

Hill is 3 times as biased as Bias-Free in this example:

For each of the 2 allocations, determine the averate seats-per-person for
the largest 5 states and for the smallest 5 states. Determine the difference
and the ratio by which those averages differ for each allocation.

With Hill, the difference is 3 time greater, as the percent by which they
differ.

Maybe someone would like to determine the probability of that difference of
the means under the null assumption of no bias. Maybe someone would like to
apply other tests for bias.

Mike Ossipoff

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