After the 1880 census, C. W. Seaton, chief clerk of the United States Census Bureau, computed apportionments for all House sizes between 275 and 350, and discovered that Alabama would get 8 seats with a House size of 299 but only 7 with a House size of 300. In general the term Alabama paradox refers to any apportionment scenario where increasing the total number of items would decrease one of the shares.
A simplified example with three states and 10 seats, following the Largest remainder method, is as follows:
| State | Size | Fair share | Seats |
|---|---|---|---|
| A | 6 | 4.286 | 4 |
| B | 6 | 4.286 | 4 |
| C | 2 | 1.429 | 2 |
With 11 seats:
| State | Size | Fair share | Seats |
|---|---|---|---|
| A | 6 | 4.714 | 5 |
| B | 6 | 4.714 | 5 |
| C | 2 | 1.571 | 1 |
Observe that state C's share decreases from 2 to 1.
This occurs because increasing the number of seats increases the fair share faster for the large states than for the small states. In particular, large A and B had their fair share increase faster than small C. Therefore, the fractional parts for A and B increased faster than those for C. In fact, they overtook C's fraction, causing C to lose its seat, since the Hamilton method examines which states have the largest fraction.
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Last updated on Tuesday April 08, 2008 at 10:19:13 PDT (GMT -0700)
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