Editing D'Hondt method (section)

==Jefferson and D'Hondt==
The Jefferson and the D'Hondt methods are equivalent. They always give the same results, but the methods of presenting the calculation are different.

The method was first described in 1792 by Statesman and future US President [[Thomas Jefferson]], in a letter to [[George Washington]] regarding the apportionment of seats in the [[United States House of Representatives]] pursuant to the [[1790 United States census|First United States Census]]:<ref name=":0" />

{{blockquote|For representatives there can be no such common ratio, or divisor which ... will divide them exactly without a remainder or fraction. I answer then ... that representatives [must be divided] as nearly as the nearest ratio will admit; and the fractions must be neglected.}}

Washington had exercised his first veto power on a bill that introduced a new plan for dividing seats in the House of Representatives that would have increased the number of seats for northern states.<ref>{{cite web | url=https://founders.archives.gov/documents/Madison/01-14-02-0233 | title=Founders Online: Proportional Representation, &#91;22 March&#93; 1792 }}</ref> Ten days after the veto, Congress passed a new method of apportionment, now known as Jefferson's Method. It was used to achieve the proportional distribution of seats in the [[United States House of Representatives|House of Representatives]] among the states until 1842.<ref>{{cite web |url=http://www.maa.org/press/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-jeffersons-method-of-apportionment |title=Apportioning Representatives in the United States Congress – Jefferson's Method of Apportionment |first=Michael |last=Caulfield |work=Mathematical Association of America |access-date=25 June 2017 |archive-url=https://web.archive.org/web/20160307203834/http://www.maa.org/press/periodicals/convergence/apportioning-representatives-in-the-united-states-congress-jeffersons-method-of-apportionment |archive-date=7 March 2016}}</ref>

It was also invented independently in 1878 in Europe, by Belgian mathematician [[Victor D'Hondt]], who wrote in his publication {{lang|fr|Système pratique et raisonné de représentation proportionnelle}}, published in Brussels in 1882{{Citation needed|date=January 2024}}:

{{blockquote|To allocate discrete entities proportionally among several numbers, it is necessary to divide these numbers by a common divisor, producing quotients whose sum is equal to the number of entities to be allocated.}}

The system can be used both for distributing seats in a legislature among states pursuant to populations or among parties pursuant to an election result. The tasks are mathematically equivalent, putting states in the place of parties and population in place of votes. In some countries, the Jefferson system is known by the names of local politicians or experts who introduced them locally. For example, it is known in [[Israel]] as the '''Bader–Ofer system'''.

Jefferson's method uses a quota (called a divisor), as in the [[largest remainder method]]. The divisor is chosen as necessary so that the resulting quotients, disregarding any fractional [[remainder]]s, sum to the required total; in other words, pick a number so that there is no need to examine the remainders. Any number in one range of quotas will accomplish this, with the highest number in the range always being the same as the lowest number used by the D'Hondt method to award a seat (if it is used rather than the Jefferson method), and the lowest number in the range being the smallest number larger than the next number which would award a seat in the D'Hondt calculations.

Applied to the above example of party lists, this range extends as [[integer]]s from 20,001 to 25,000. More precisely, any number n for which 20,000 < n ≤ 25,000 can be used.