The Alabama paradox was the first of the apportionment paradoxes to be discovered today on 11/10/06. After the 1880 census, C. W. Seaton, chief clerk of the U.S. Census Office, 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. To apportion is to divide into parts according to some rule, the rule typically being one of proportion. ... 1880 (MDCCCLXXX) was a leap year starting on Thursday (see link for calendar). ... 1870 US Census for New York City A census is the process of obtaining information about every member of a population (not necessarily a human population). ... The United States Census Bureau (officially Bureau of the Census as defined in Title ) is a part of the United States Department of Commerce. ... US Congressional apportionment for states in 2000 The membership of the United States House of Representatives changes each decade following the decennial United States Census. ... Seal of the House of Representatives The United States House of Representatives (or simply the House) is one of the two chambers of the United States Congress, the other being the Senate. ... Official language(s) English Capital Montgomery Largest city Birmingham Area  Ranked 30th  - Total 52,419 sq mi (135,765 km²)  - Width 190 miles (306 km)  - Length 330 miles (531 km)  - % water 3. ... Apportionment, or reapportionment, is the process of determining representation in politics within a legislative body by creating constituencies. ...

A simplified example with four states and 323 seats, following the Hamilton method, is as follows: The Hamilton method is a version of the largest remainder method for allocating seats proportionally for representative assemblies with party list voting systems. ...

With 324 seats:

Observe that state C's share decreases from 14 to 13.

The reason this occurs starts with the fact that increasing the number of seats increases the fair share faster for the large states than for the small states. Hence, large A and B had their fair share increase faster than small C. Therefore, the decimal parts for A and B increased faster than those for C. In fact, they overtook C's decimal part, causing C to lose its seat, since the Hamilton method examines which states have the largest decimal part.

See also

• New states paradox
• Paradox
• Population paradox

The new states paradox occurs when adding a new state to the United States of America causes another state to get more congressional representatives than it had before the new state was added. ... Robert Boyles self-flowing flask fills itself in this diagram, but perpetual motion machines cannot exist. ... The population paradox occurs when two states of the United States of America have populations increasing at different rates and the state with the greater growth rate loses a congressional seat to the state with the lower growth rate. ...

Reference

• Methods of apportionment (in PDF format), from a University of Maryland, College Park website