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An apportionment paradox exists when the rules for apportionment in a political system produce results which are unexpected or seem to violate common sense. To apportion is to divide into parts according to some rule, the rule typically being one of proportion. Certain quantities, like milk, can be divided in any proportion whatsoever; others, such as horses, cannot—only whole numbers will do. In the latter case, there is an inherent tension between our desire to obey the rule of proportion as closely as possible and the constraint restricting the size of each portion to discrete values. This results, at times, in unintuitive observations, or paradoxes. Several paradoxes related to apportionment, also called ''fair division'', have been identified. In some cases, simple adjustments to an apportionment methodology can resolve observed paradoxes. Others, such as those relating to the United States House of Representatives, call into question notions that mathematics alone can provide a single, fair resolution. ==History== The Alabama paradox was discovered in 1880, when it was found that increasing the total number of seats in the House of Representatives would decrease Alabama's seats from 8 to 7. There was more to come: when Oklahoma became a state in 1907, a recomputation of apportionment showed that the number of seats due to other states would be affected even though Oklahoma would be given a fair share of seats and the total number of seats increased by that number. Increasing the house from 386 to 391 members made New York lose a seat while Maine gained one, thus the name "the new state paradox". 〔(Apportioning Representatives in the United States Congress - Paradoxes of Apportionment ), Michael J. Caulfield〕 The method for apportionment used during this period, originally put forth by Alexander Hamilton but not adopted until 1852, 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Apportionment paradox」の詳細全文を読む スポンサード リンク
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