The method was first described in 1832 by American statesman and senator Daniel Webster. In 1842, the method was adopted for proportional allocation of seats in United States congressional apportionment (Act of 25 June 1842, ch 46, 5 Stat. 491). The same method was independently invented in 1910 by the French mathematician André Sainte-Laguë.
Motivation
Proportional electoral systems attempt to distribute seats in proportion to the votes for each political party, i.e. a party with 30% of votes would receive 30% of seats. Exact proportionality is not possible because only whole seats can be distributed. Different apportionment methods, of which the Sainte-Laguë method is one, exist to distribute the seats according to the votes. Different apportionment methods show different levels of proportionality, apportionment paradoxes and political fragmentation.
The Sainte-Laguë method minimizes the average seats-to-votes ratio deviation[2] and empirically shows the best proportionality behavior[3] and more equal seats-to-votes ratio for different sized parties[1] among apportionment methods. Among other common methods, the D'Hondt method favours large parties and coalitions over small parties.[1][4][5][6] While favoring large parties reduces political fragmentation, this can be achieved with electoral thresholds as well. The Sainte-Laguë method shows fewer apportionment paradoxes compared to largest remainder methods[7] such as the Hare quota and other highest averages methods such as d'Hondt method.[8]
Description
After all the votes have been tallied, successive quotients are calculated for each party. The formula for the quotient is[9]
where:
V is the total number of votes that party received, and
s is the number of seats that have been allocated so far to that party, initially 0 for all parties.
Whichever party has the highest quotient gets the next seat allocated, and their quotient is recalculated. The process is repeated until all seats have been allocated.
The Webster/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.[10]
Often there is an electoral threshold; that is, in order to be allocated seats, a minimum percentage of votes must be gained.
Example
In this example, 230,000 voters decide the disposition of 8 seats among 4 parties. Since 8 seats are to be allocated, each party's total votes are divided by 1, then by 3, and 5 (and then, if necessary, by 7, 9, 11, 13, and so on by using the formula above) every time the number of votes is the biggest for the current round of calculation.
For comparison, the "True proportion" column shows the exact fractional numbers of seats due, calculated in proportion to the number of votes received. (For example, 100,000/230,000 × 8 = 3.48.)
round
(1 seat per round)
1
2
3
4
5
6
7
Seats won
(bold)
Party A quotient
seats after round
100,000
0+1
33,333
1
33,333
1+1
20,000
2
20,000
2
20,000
2+1
14,286
3
3
Party B quotient
seats after round
80,000
0
80,000
0+1
26,667
1
26,667
1
26,667
1+1
16,000
2
16,000
2+1
3
Party C quotient
seats after round
30,000
0
30,000
0
30,000
0
30,000
0+1
10,000
1
10,000
1
10,000
1
1
Party D quotient
seats after round
20,000
0
20,000
0
20,000
0
20,000
0
20,000
0
20,000
0+1
6,667
1
1
The 8 highest entries (in the current round of calculation) are marked by asterisk: from 100,000 down to 16,000; for each, the corresponding party gets a seat.
The below chart is an easy way to perform the calculation:
Denominator
/1
/3
/5
Seats won (*)
True proportion
Party A
100,000*
33,333*
20,000*
3
3.5
Party B
80,000*
26,667*
16,000*
3
2.8
Party C
30,000*
10,000
6,000
1
1.0
Party D
20,000*
6,667
4,000
1
0.7
Total
8
8
Party
Popular vote
Party-list PR — Sainte-Laguë method
Number of seats
Seats %
Party A
43.5%
3
37.5%
Party B
34.8%
3
37.5%
Party C
13.0%
1
12.5%
Party D
8.7%
1
12.5%
TOTAL
100%
8
100%
In comparison, the D'Hondt method would allocate four seats to party A and no seats to party D, reflecting the D'Hondt method's overrepresentation of larger parties.[9]
Properties
When apportioning seats in proportional representation, it is particularly important to avoid bias between large parties and small parties to avoid strategic voting. André Sainte-Laguë showed theoretically that the Sainte-Laguë method shows the lowest average bias in apportionment,[2] confirmed by different theoretical and empirical ways.[3][11]: Sec.5 The European Parliament (Representation) Act 2003 stipulates each region must be allocated at least 3 seats and that the ratio of electors to seats is as nearly as possible the same for each, the Commission found the Sainte-Laguë method produced the smallest standard deviation when compared to the D'Hondt method and Hare quota.[12][13]
Proportionality under Sainte-Laguë method
The seats-to-votes ratio for a political party is the ratio between the fraction of seats and the fraction of votes for that party:
The Sainte-Laguë method approximates proportionality by optimizing the seats-to-votes ratio among all parties with the least squares approach. First, the difference between the seats-to-votes ratio for a party and the ideal seats-to-votes ratio is calculated and squared to obtain the error for the party . To achieve equal representation of each voter, the ideal ratio of seats share to votes share is .
Second, the error for each party is weighted according to the vote share of each party to represent each voter equally. In the last step, the errors for each party are summed up. This error is identical to the Sainte-Laguë Index.
It was shown[14] that this error is minimized by the Sainte-Laguë method.
Modified Sainte-Laguë method
To reduce political fragmentation, some countries, e.g. Nepal, Norway and Sweden, change the quotient formula for parties with no seats (s = 0). These countries changed the quotient from V to V/1.4, though from the general 2018 elections onwards, Sweden has been using V/1.2.[15] 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 makes it more difficult for parties to earn only one seat, compared to the unmodified Sainte-Laguë's method. With the modified method, such small parties do not get any seats; these seats are instead given to a larger party.[9]
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 (former counties) depends on the population and area of the county: each inhabitant counts one point, while each km2 counts 1.8 points. Furthermore, one seat from each constituency is allocated according to the national distribution of votes.[16]
History
Webster proposed the method in the United States Congress in 1832 for proportional allocation of seats in United States congressional apportionment. In 1842 the method was adopted (Act of June 25, 1842, ch 46, 5 Stat. 491). It was then replaced by Hamilton method and in 1911 the Webster method was reintroduced.[11]
Webster and Sainte-Laguë methods should be treated as two methods with the same result, because the Webster method is used for allocating seats based on states' population, and the Sainte-Laguë based on parties' votes.[17] 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 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.
In 1980 the German physicist Hans Schepers, at the time Head of the Data Processing Group of the German Bundestag, suggested that the distribution of seats according to d'Hondt be modified to avoid putting smaller parties at a disadvantage.[18] German media started using the term Schepers Method and later German literature usually calls it Sainte-Laguë/Schepers.[18]
Threshold for seats
An election threshold can be set to reduce political fragmentation, and any list party which does not receive at least a specified percentage of list votes will not be allocated any seats, even if it received enough votes to have otherwise receive a seat. Examples of countries using the Sainte-Laguë method with a threshold are Germany and New Zealand (5%), although the threshold does not apply if a party wins at least one electorate seat in New Zealand or three electorate seats in Germany. Sweden uses a modified Sainte-Laguë method with a 4% threshold, and a 12% threshold in individual constituencies (i.e. a political party can gain representation with a minuscule representation on the national stage, if its vote share in at least one constituency exceeded 12%). Norway has a threshold of 4% to qualify for leveling seats that are allocated according to the national distribution of votes. This means that even though a party is below the threshold of 4% nationally, they can still get seats from constituencies in which they are particularly popular.
Some cantons in Switzerland use the Sainte-Laguë method for biproportional apportionment between electoral districts and for votes to seats allocation.[24]
The method belongs to the class of highest-averages methods. It is similar to the Jefferson/D'Hondt method, but uses different divisors. The Jefferson/D'Hondt method favors larger parties while the Webster/Sainte-Laguë method doesn't.[9] The Webster/Sainte-Laguë method is generally seen as more proportional, but risks an outcome where a party with more than half the votes can win fewer than half the seats.[29]
When there are two parties, the Webster method is the unique divisor method which is identical to the Hamilton method.[30]: Sub.9.10
^Lijphart, Arend (1990). "The Political Consequences of Electoral Laws, 1945-85". The American Political Science Review. 84 (2): 481–496. doi:10.2307/1963530. JSTOR1963530. S2CID146438586.
^ abcdLijphart, Arend (2003), "Degrees of proportionality of proportional representation formulas", in Grofman, Bernard; Lijphart, Arend (eds.), Electoral Laws and Their Political Consequences, Agathon series on representation, vol. 1, Algora Publishing, pp. 170–179, ISBN9780875862675 See in particular the section "Sainte-Lague", pp. 174–175.
^Badie, Bertrand; Berg-Schlosser, Dirk; Morlino, Leonardo, eds. (2011), International Encyclopedia of Political Science, Volume 1, SAGE, p. 754, ISBN9781412959636, 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.
^"Implications of Iraq's New Election Law". Arab Gulf States Institute in Washington. 2023-05-19. Retrieved 2024-09-26. With the reimplementation of the Sainte-Lague proportional representation system, candidates on lists ... will have a distinct advantage.
Cet article est une ébauche concernant un peintre italien. Vous pouvez partager vos connaissances en l’améliorant (comment ?) selon les recommandations des projets correspondants. Liberale da VeronaLiberale da VeronaNaissance 1441VéroneDécès 1529VéronePériode d'activité 1465-1526Activités Peintre, enlumineurMaître Vincenzo di Stefano da VeronaMouvement École véronaisemodifier - modifier le code - modifier Wikidata Liberale da Verona (1441 - 1526) est un peintre italien et enlu…
Questa voce sull'argomento contee dell'Illinois è solo un abbozzo. Contribuisci a migliorarla secondo le convenzioni di Wikipedia. Contea di ChampaignconteaLocalizzazioneStato Stati Uniti Stato federato Illinois AmministrazioneCapoluogoUrbana Data di istituzione1833 TerritorioCoordinatedel capoluogo40°08′24″N 88°12′00″W / 40.14°N 88.2°W40.14; -88.2 (Contea di Champaign)Coordinate: 40°08′24″N 88°12′00″W / 40.14°N 88.2°W40.1…
Strada A360 LenaLocalizzazioneStato Russia DatiClassificazionestrada federale InizioJakutsk FineSkovorodino Lunghezza1235 km Percorso Manuale Strada statale A360 «Lena» La strada federale A360 «Lena» (in russo Федеральная автомобильная дорога А360 «Лена»?) è una strada federale nella Repubblica della Sacha-Jacuzia che collega la città di Jakutsk con il corridoio della ferrovia Transiberiana vicino a Skovorodino, nell'Oblast' dell'Amur (Circond…
Philippe VRaja SpanyolBerkuasa1 Nopember 1700 – 14 Januari 1724(23 tahun, 74 hari)PendahuluCharles IIPenerusLouis IRaja SpanyolBerkuasa6 September 1724 - 9 Juli 1746(21 tahun, 306 hari)PendahuluLouis IPenerusFerdinand VIInformasi pribadiPemakamanLa Granja de San IldefonsoWangsaWangsa BourbonAyahLouis, Dauphin dari PrancisIbuMaria Anna Victoria dari BayernPasanganMaria Luisa dari SavoyElisabeth FarneseAnakRincianLouis I dari SpanyolFerdinand VI dari SpanyolCharles III dari S…
Time Inc.JenisPublikKode emitenNYSE: TIMENasib Bergabung dengan Warner Communications(asli) Akuisisi oleh Meredith Corporation(spin off) Didirikan 28 November 1922; 101 tahun lalu (1922-11-28)(asli) 9 Juni 2014; 9 tahun lalu (2014-06-09)(spin off) PendiriHenry LuceBriton HaddenDitutup 10 Januari 1990; 34 tahun lalu (1990-01-10)(asli) 31 Januari 2018; 6 tahun lalu (2018-01-31)(spin off) Time Inc. adalah anak perusahaan dari raksasa media Time Warner, perusahaan yang diben…
Colombian Catholic bishop (1919–2019) In this Spanish name, the first or paternal surname is Pimiento and the second or maternal family name is Rodríguez. His EminenceJosé de Jesús Pimiento RodríguezArchbishop Emeritus of ManizalesChurchRoman Catholic ChurchArchdioceseManizalesAppointed22 May 1975Term ended15 October 1996PredecessorArturo Duque VillegasSuccessorFabio Betancur TiradoOther post(s)Cardinal Priest of San Giovanni Crisostomo a Monte Sacro Alto (2015–2019)OrdersOrdinat…
Domesticated animal used for transportation For other uses, see Donkey (disambiguation). Donkey In Clovelly, North Devon Conservation status Domesticated Scientific classification Domain: Eukaryota Kingdom: Animalia Phylum: Chordata Class: Mammalia Order: Perissodactyla Family: Equidae Genus: Equus Species: E. africanus Subspecies: E. a. asinus Trinomial name Equus africanus asinusLinnaeus, 1758 The donkey is a domesticated equine. It derives from the African wild ass, Equus africanus,…
A house destroyed during a battle to control Hawzen, Tigray.[1] All sides of the Tigray War have been repeatedly accused of committing war crimes since it began in November 2020.[2][3][4] In particular, the Ethiopian federal government, the State of Eritrea, the Tigray People's Liberation Front (TPLF) and Amhara regional forces have been the subject of numerous reports of both war crimes and crimes against humanity.[5][6][7][8] Gove…
Balaguer OffensivePart of the Spanish Civil WarAerial view of Balaguer and the Segre RiverDateApril & May 1938LocationBridgehead over the Segre, CataloniaResult Francoist victoryBelligerents Spanish Republic Nationalist SpainCasualties and losses high moderate vteSpanish Civil War Background List of battles July 1936 uprising Melilla Seville 1st Barcelona Cuartel de la Montaña Gijón Oviedo Cuartel de Loyola 1936 German intervention Guadarrama Andalusia Alcázar Extremadura Convoy de la Vic…
Gli Annali di Clonmacnoise (in irlandese Annála Chluain Mhic Nóis) sono una traduzione in lingua inglese, dell'inizio del XVII secolo, di una cronaca irlandese perduta, che copriva gli eventi in Irlanda dalla preistoria al 1408. L'opera è talvolta nota come Libro di Mageoghagan, dal nome del suo traduttore Conall lo storico. [1] Indice 1 Traduzione 2 Provenienza della cronaca originale 3 Contenuti 4 Edizione 5 Note 6 Bibliografia 7 Voci correlate 8 Collegamenti esterni Traduzione…
English inventor This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: William Bickford 1774–1834 – news · newspapers · books · scholar · JSTOR (September 2021) (Learn how and when to remove this message) William BickfordBorn1774Ashburton, Devon, England, United KingdomDied1834 (aged 60)NationalityBritishOccup…
During World War I, the Kingdom of Romania was a source of various types of military equipment. Either directly, or indirectly through Romanian-born people designing military equipment abroad. Munitions and related equipment Romanian soldiers during a training exercise. The rifle is the Mannlicher M1893, the standard service rifle of the Kingdom of Romania at the time. Between 1914 and 1916, 59 Romanian factories along with numerous private contractors produced a total of 400,000 artillery round…
Act of reducing, limiting, or abolishing weapons, usually on a national scale Let Us Beat Swords into Plowshares in the United Nations garden (1957) Disarmament is the act of reducing, limiting, or abolishing weapons. Disarmament generally refers to a country's military or specific type of weaponry. Disarmament is often taken to mean total elimination of weapons of mass destruction, such as nuclear arms. General and Complete Disarmament was defined by the United Nations General Assembly as the e…
For other uses, see Taille (disambiguation). Former land tax on Ancien Régime French peasants This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed.Find sources: Taille – news · newspapers · books · scholar · JSTOR (September 2007) (Learn how and when to remove this message) Ancien Régime Structure Estates of the realm Great Off…
Part of England's switch to Protestantism Queen Elizabeth I Part of a series on theHistory of the Church of EnglandWestminster Abbey (1749) by Canaletto Middle Ages (597–1500)Anglo-Saxon ChristianityReligion in Medieval EnglandConvocations of Canterbury and YorkDevelopment of dioceses Reformation (1509–1559)Reformation ParliamentDissolution of the MonasteriesThomas CranmerBook of Common Prayer (1549)Edwardine OrdinalsBook of Common Prayer (1552)Forty-two ArticlesMartyrsMarian exiles Elizabet…
This article needs to be updated. Please help update this article to reflect recent events or newly available information. (February 2022) CanadaThe Maple Leaf has always appeared on the uniformAssociationCanada BandyHead coachTeam colors Home colours Away colours First international Canada 0–4 Norway (Roseville, Minnesota; February 14, 2006)Women's Bandy World ChampionshipAppearances7 (first in 2006)Best result4th (2007, 2010, 2012, 2016) Canada women's national bandy team Me…
Place in Tamil Nadu, IndiaAlathurCoordinates: 10°47′03″N 78°44′48″E / 10.784231°N 78.746612°E / 10.784231; 78.746612Country IndiaStateTamil NaduDistrictTiruchirappalliPopulation (2019) • Total1,300Languages • OfficialTamilTime zoneUTC+5:30 (IST) Alathur is a village in Tiruchirappalli taluk of Tiruchirappalli district, Tamil Nadu. It was merged with the Tiruchirappalli Corporation in 2011.[1] Demographics As per the 20…
هذه المقالة تحتاج للمزيد من الوصلات للمقالات الأخرى للمساعدة في ترابط مقالات الموسوعة. فضلًا ساعد في تحسين هذه المقالة بإضافة وصلات إلى المقالات المتعلقة بها الموجودة في النص الحالي. (مارس 2018) لمعانٍ أخرى، طالع مقاطعة بيكر (توضيح). مقاطعة بيكر الإحداثيات 44°43′N …