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)|
|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?