Editing Apportionment paradox (section)

==History==
An example of the apportionment paradox known as "the [[Alabama]] paradox" was discovered in the context of [[United States congressional apportionment]] in 1880,<ref name=Stein2008/>{{rp|228–231}} when census calculations found that if the total number of seats in the [[United States House of Representatives|House of Representatives]] were hypothetically increased, this would decrease Alabama's seats from 8 to 7. An actual impact was observed in 1900, when Virginia lost a seat to Maine, even though Virginia's population was growing more rapidly: this is an example of the population paradox.<ref name=Stein2008/>{{rp|231–232}} In 1907, when [[Oklahoma]] became a state, New York lost a seat to Maine, thus the name "the new state paradox".<ref name=Stein2008/>{{rp|232–233}}<ref name=Caulfield>{{cite journal |last = Caulfield |first = Michael J. |date = November 2010  |url = https://www.maa.org/publications/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-paradoxes-of-apportionment |title = Apportioning Representatives in the United States Congress - Paradoxes of Apportionment |journal = Convergence |publisher = Mathematical Association of America |doi = 10.4169/loci003163 |doi-broken-date = 1 November 2024 }}</ref>

The [[Hamilton method|method for apportionment]] used during this period, originally put forth by [[Alexander Hamilton]], but vetoed by [[George Washington]] and not adopted until 1852,<ref name=Stein2008/>{{rp|228}} was as follows:

* First, the fair share of each state is computed, i.e. the proportional share of seats that each state would get if fractional values were allowed. 
* Second, each state receives as many seats as the whole number portion of its fair share.
* Third, any state whose fair share is less than one receives one seat, regardless of population, as required by the [[United States Constitution]].
* Fourth, any remaining seats are distributed, one each, to the states whose fair shares have the highest fractional parts.

The Hamilton method replaced a rounding method proposed by [[Thomas Jefferson]],<ref name=Stein2008/>{{rp|228}} and was itself replaced by the [[Huntington–Hill method]] in 1941.<ref name=Stein2008/>