What happens when Webster's method can't narrow down to a working divisor?

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The Politicus
Apr 10, 2022 10:47 PM 0 Answers
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I've been poking around and without trying, managed to bump into some scenarios where Webster's method gives inconclusive results. The fact I managed it more than once without trying implies to me that this is a highly probable situation, though maybe only with small or rounded numbers.

For example, with 20 seats available, and states with populations of: 10000, 5000, 9000, 1000, 3000, 2000, 8000 (total: 38,000)

State Population Standard Q Modified Q Rounded Q (2,000.00000000) Final (2,000.00000000) Rounded Q (2,000.00000001) Final (2,000.00000001)
A 10000 5.263157895 5 5 5 5 5
B 5000 2.631578947 2.5 3 3 2 2
C 9000 4.736842105 4.5 5 5 4 4
D 1000 0.526315789 0.5 1 1 0 1
E 3000 1.578947368 1.5 2 2 1 1
F 2000 1.052631579 1 1 1 1 1
G 8000 4.210526316 4 4 4 4 4
total 38000 20 19 17 21 (too high) 17 18 (too low)

I can't tell what it is about these numbers but the tiniest fraction of a change to the divisor will always swing between the result being too high or too low, with the a perfect result being impossible to hit.

I'm wondering primarily if there's a lesser-known official next-step for dealing with this situation as written in Webster's original algorithm, or a common follow-up or modified step for dealing with this situation that someone else has come up with?

Otherwise, is there a way of telling in advance if the numbers will work or not?

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• April 10, 2022