en>ArnoldReinhold: ce intro to clarify

2015-01-12T19:50:41Z

ce intro to clarify

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en>Pigman: /* References */clean up using AWB

2014-02-17T01:58:56Z

References: clean up using AWB

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66.25.206.181: /* See also */ redundant

2014-01-23T01:46:08Z

See also: redundant

← Older revision		Revision as of 03:46, 23 January 2014
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	~~Howdy! I am Dalton~~. ~~Acting~~ is ~~without~~ a ~~doubt~~ a ~~thing that~~ ~~totally addicted~~ to. ~~Vermont could be~~ where ~~my home~~ is. ~~Managing everyone~~ has been my 24-~~hour period job~~ for a ~~while~~ but ~~I plan inside changing it~~. I've been ~~jogging~~ on ~~my website~~ to ~~produce some time now~~. ~~Check it out here:~~ http://~~prometeu~~.~~net~~<br>~~<br>Feel free to visit my website~~ :: [http://~~prometeu~~.~~net Hack Clash Of Clans~~]		{{Electoral systems}}

			The '''Sainte-Laguë method''' ({{IPA-fr\|sɛ̃t.la.ɡy}}) is a [[highest averages method\|highest quotient method]] for allocating seats in [[party-list proportional representation]] used in many [[voting systems]]. It is named after the French mathematician [[André Sainte-Laguë]]. The Sainte-Laguë method is quite similar to the [[D'Hondt method]], but uses different divisors. In most cases the [[largest remainder method]] delivers almost identical results. The D'Hondt method gives similar results too, but favors larger parties compared to the Sainte-Laguë method.<ref name="lijphart">{{citation\|contribution=Degrees of proportionality of proportional representation formulas\|first=Arend\|last=Lijphart\|authorlink=Arend Lijphart\|pages=170–179\|title=Electoral Laws and Their Political Consequences\|volume=1\|series=Agathon series on representation\|editor1-first=Bernard\|editor1-last=Grofman\|editor2-first=Arend\|editor2-last=Lijphart\|publisher=Algora Publishing\|year=2003\|isbn=9780875862675}}. See in particular the section "Sainte-Lague", [http://books.google.com/books?id=o1dqas0m8kIC&pg=PA174 pp. 174–175].</ref>

			The Sainte-Laguë method is used in [[Iraq]], [[New Zealand]], [[Norway]], [[Sweden]], [[Bosnia and Herzegovina]], [[Latvia]], [[Kosovo]], [[Denmark]] (for the [[Folketing#Constitutional_requirements\|40 supplementary seats in the national parliament]]), and [[Germany]] (on federal level for the [[Bundestag]], on state level for the [[legislature]]s of [[Landtag of Baden-Württemberg\|Baden-Württemberg]], [[Elections in Hamburg\|Hamburg]], [[Bürgerschaft of Bremen\|Bremen]], [[Landtag of North Rhine-Westphalia\|North Rhine-Westphalia]], [[Landtag of Schleswig-Holstein\|Schleswig-Holstein]] and [[Landtag of Rhineland-Palatinate\|Rhineland-Palatinate]]). It was also used in [[Bolivia]] in 1993, in [[Poland]] in 2001, and in the elections to the [[Palestinian Legislative Council]] in 2006. A variant of this method, the modified Sainte-Laguë method, was used to allocate the [[proportional representation]] (PR) seats in the [[Nepalese Constituent Assembly election, 2008\|Constituent Assembly poll of Nepal]] in 2008. It has been proposed by the [[Green Party (Ireland)\|Green Party]] in [[Ireland]] as a reform for use in [[Dáil Éireann]] elections,<ref>[http://www.greenparty.ie/news/latest_news/political_reform_vital_to_ireland_s_prosperity Ireland's Green Party website;]</ref> and by the [[United Kingdom]] [[United Kingdom coalition government (2010–present)\|Conservative-Liberal Democrat coalition government]] in 2011 as the method for calculating the distribution of seats in elections to the country's [[House of Lords\|upper house]] of parliament.<ref>{{cite web \|url=http://www.cabinetoffice.gov.uk/sites/default/files/resources/house-of-lords-reform-draft-bill.pdf \|format=PDF \|date=May 2011 \|title=House of Lords Reform Draft Bill \|publisher=Cabinet Office \|page=16}}</ref>

			==Description of the method==
			After all the votes have been tallied, successive [[quotient]]s are calculated for each party. The formula for the quotient is<ref name="lijphart"/>

			:: <math>quot = \frac{V}{2s+1}</math>

			where:

			* ''V'' is the total number of votes that party received, and
			* ''s'' is the number of seats that party has been allocated so far, initially 0 for all parties.

			Whichever party has the highest quotient gets the next seat allocated, and their quotient is recalculated given their new seat total. The process is repeated until all seats have been allocated.

			The Sainte-Laguë method does not ensure that a party receiving more than half the votes will win at least half the seats; nor does its modified form.<ref>{{citation\|contribution=Election inversions under proportional representation\|url=http://userpages.umbc.edu/~nmiller/RESEARCH/NRMILLER.PCS2013.pdf\|first=Nicholas R.\|last=Miller\|date=February 2013\|title=Annual Meeting of the Public Choice Society, New Orleans, March 8-10, 2013}}.</ref> For example, with seven seats available and the votes split 53,000, 24,000 and 23,000, the allocation would be three, two and two seats respectively.

			{\|class="wikitable"
			! ''denominator'' \|\| /1 \|\| /3 \|\| /5 \|\| /7 \|\| /9 \|\| /11 \|\| /13 \|\| Seats won (*)
			\|-
			\|\| Party A \|\| '''53,000''' \|\| '''17,666''' \|\| '''10,600*''' \|\| 7,571 \|\| 5,888 \|\| 4,818 \|\| 4,076
			\| align="center" \| '''3'''
			\|-
			\|\| Party B \|\| '''24,000''' \|\| '''8,000''' \|\| 4,800 \|\| 3,428 \|\| 2,666 \|\| 2,181 \|\| 1,846
			\| align="center" \| '''2'''
			\|-
			\|\| Party C \|\| '''23,000''' \|\| '''7,666''' \|\| 4,600 \|\| 3,285 \|\| 2,555 \|\| 2,090 \|\| 1,769
			\| align="center" \| '''2'''
			\|-
			\|}

			The d'Hondt method differs by the formula to calculate the quotients <math>\left( quot = \frac{V}{s+1}\right)</math>.<ref name="lijphart"/>

			==Sainte-Laguë and Webster==
			The Sainte-Laguë method is equivalent to the Webster method (named after its proponent, the U.S. senator [[Daniel Webster]]) in that they always give the same results, but the method of calculating the apportionment seems to be quite different.<ref>{{citation\|title=International Encyclopedia of Political Science, Volume 1\|editor1-first=Bertrand\|editor1-last=Badie\|editor2-first=Dirk\|editor2-last=Berg-Schlosser\|editor3-first=Leonardo\|editor3-last=Morlino\|publisher=SAGE\|year=2011\|isbn=9781412959636\|page=754\|url=http://books.google.com/books?id=t0JZp-jrotQC&pg=PA754\|quotation=Mathematically, divisor methods for allocating seats to parties on the basis of party vote shares are identical to divisor methods for allocating seats to geographic units on the basis of the unit's share of the total population. ... Similarly, the Sainte-Laguë method is identical to a method devised by the American legislator Daniel Webster.}}</ref> Webster invented his method for legislative apportionment (allocating legislative seats to regions based on their share of the population) rather than elections (allocating legislative seats to parties based on their share of the votes) but this makes no difference to the calculations in the method.

			Webster's method is defined in terms of a [[Droop quota]] as in the [[largest remainder method]]; in this method, the quota is called a "divisor". For a given value of the divisor, the population count for each region is divided by this divisor and then rounded to give the number of legislators to allocate to that region. In order to make the total number of legislators come out equal to the target number, the divisor is adjusted to make the sum of allocated seats after being rounded give the required total.

			One way to determine the correct value of the divisor would be to start with a very large divisor, so that no seats are allocated after rounding. Then the divisor may be successively decreased until one seat, two seats, three seats and finally the total number of seats are allocated. The number of allocated seats for a given region increases from ''s'' to ''s'' + 1 exactly when the divisor equals the population of the region divided by ''s'' + 1/2, so at each step the next region to get a seat will be the one with the largest value of this quotient. That means that this successive adjustment method for implementing Webster's method allocates seats in the same order to the same regions as the Sainte-Laguë method would allocate them.

			==Modified Sainte-Laguë method==
			Some countries, e.g. [[Nepal]], [[Norway]] and [[Sweden]], change the quotient formula for parties that have not yet been allocated any seats (''s'' = 0) from ''V'' to ''V''/1.4. That is, the modified method changes the sequence of divisors used in this method from (1, 3, 5, 7, ...) to (1.4, 3, 5, 7, ...). This gives slightly larger preference to the larger parties over parties that would earn, with small margin, only a single seat if unmodified Sainte-Laguë's method were used. With the modified method, such small parties do not get any seat; these seats are instead given to a larger party.<ref name="lijphart"/>

			Norway further amends this system by utilizing a two-tier proportionality. The number of members to be returned from each of Norway's 19 constituencies (counties) depends on the population and area of the county: each inhabitant counts one point, while each square kilometer counts 1.8 points. Furthermore, one seat from each constituency is allocated according to the national distribution of votes.<ref>Norway's Ministry of Local Government website; [http://www.regjeringen.no/en/dep/krd/kampanjer/the-municipal-and-county-election/the-norwegian-electoral-system.html?id=456636 Stortinget; General Elections; The main features of the Norwegian electoral system]; accessed 22 August 2009</ref>

			==References==
			{{reflist}}

			==External links==
			* [http://staatsrecht.honikel.de/en/sainte-lague-schepers-verfahren.htm Seats Calculator with the Sainte-Laguë method]
			* [http://www.cut-the-knot.org/Curriculum/SocialScience/Webster.shtml Java implementation of Webster's method] at [[cut-the-knot]]
			* [http://www.elections.org.nz/voting-system/mmp-voting-system/sainte-lagu%C3%AB-allocation-formula Elections New Zealand explanation of Sainte-Laguë]

			{{DEFAULTSORT:Sainte-Lague method}}
			[[Category:Party-list PR]]

			[[fr:Scrutin proportionnel plurinominal#Méthode de Sainte-Laguë]]

24.36.85.227: /* Calculations assuming random sampling */ removed spurious factor of 2

2012-08-25T15:15:17Z

Calculations assuming random sampling: removed spurious factor of 2

New page

Howdy! I am Dalton. Acting is without a doubt a thing that totally addicted to. Vermont could be where my home is. Managing everyone has been my 24-hour period job for a while but I plan inside changing it. I've been jogging on my website to produce some time now. Check it out here: http://prometeu.net<br><br>Feel free to visit my website :: [http://prometeu.net Hack Clash Of Clans]

Margin of error - Revision history

en>ArnoldReinhold: ce intro to clarify

en>Pigman: /* References */clean up using AWB

66.25.206.181: /* See also */ redundant

24.36.85.227: /* Calculations assuming random sampling */ removed spurious factor of 2