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The Sainte-Laguë method (Template:IPA-fr) is a 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.^[1]

The Sainte-Laguë method is used in Iraq, New Zealand, Norway, Sweden, Bosnia and Herzegovina, Latvia, Kosovo, Denmark (for the 40 supplementary seats in the national parliament), and Germany (on federal level for the Bundestag, on state level for the legislatures of Baden-Württemberg, Hamburg, Bremen, North Rhine-Westphalia, Schleswig-Holstein and 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 Constituent Assembly poll of Nepal in 2008. It has been proposed by the Green Party in Ireland as a reform for use in Dáil Éireann elections,^[2] and by the United Kingdom Conservative-Liberal Democrat coalition government in 2011 as the method for calculating the distribution of seats in elections to the country's upper house of parliament.^[3]

Description of the method

After all the votes have been tallied, successive quotients are calculated for each party. The formula for the quotient is^[1]

q u o t = \frac{V}{2 s + 1}

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.^[4] 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.

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	3
Party B	24,000*	8,000*	4,800	3,428	2,666	2,181	1,846	2
Party C	23,000*	7,666*	4,600	3,285	2,555	2,090	1,769	2

The d'Hondt method differs by the formula to calculate the quotients $(q u o t = \frac{V}{s + 1})$ .^[1]

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.^[5] 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.^[1]

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.^[6]

References

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External links

fr:Scrutin proportionnel plurinominal#Méthode de Sainte-Laguë

↑ ^1.0 ^1.1 ^1.2 ^1.3 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. See in particular the section "Sainte-Lague", pp. 174–175.
↑ Ireland's Green Party website;
↑ Template:Cite web
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.
↑ Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010
↑ Norway's Ministry of Local Government website; Stortinget; General Elections; The main features of the Norwegian electoral system; accessed 22 August 2009

[lijphart-1] 1.0 ^1.1 ^1.2 ^1.3 Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010. See in particular the section "Sainte-Lague", pp. 174–175.

[2] Ireland's Green Party website;

[3] Template:Cite web

[4] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010.

[5] Many property agents need to declare for the PIC grant in Singapore. However, not all of them know find out how to do the correct process for getting this PIC scheme from the IRAS. There are a number of steps that you need to do before your software can be approved.

Naturally, you will have to pay a safety deposit and that is usually one month rent for annually of the settlement. That is the place your good religion deposit will likely be taken into account and will kind part or all of your security deposit. Anticipate to have a proportionate amount deducted out of your deposit if something is discovered to be damaged if you move out. It's best to you'll want to test the inventory drawn up by the owner, which can detail all objects in the property and their condition. If you happen to fail to notice any harm not already mentioned within the inventory before transferring in, you danger having to pay for it yourself.

In case you are in search of an actual estate or Singapore property agent on-line, you simply should belief your intuition. It's because you do not know which agent is nice and which agent will not be. Carry out research on several brokers by looking out the internet. As soon as if you end up positive that a selected agent is dependable and reliable, you can choose to utilize his partnerise in finding you a home in Singapore. Most of the time, a property agent is taken into account to be good if he or she locations the contact data on his website. This may mean that the agent does not mind you calling them and asking them any questions relating to new properties in singapore in Singapore. After chatting with them you too can see them in their office after taking an appointment.

Have handed an trade examination i.e Widespread Examination for House Brokers (CEHA) or Actual Property Agency (REA) examination, or equal; Exclusive brokers are extra keen to share listing information thus making certain the widest doable coverage inside the real estate community via Multiple Listings and Networking. Accepting a severe provide is simpler since your agent is totally conscious of all advertising activity related with your property. This reduces your having to check with a number of agents for some other offers. Price control is easily achieved. Paint work in good restore-discuss with your Property Marketing consultant if main works are still to be done. Softening in residential property prices proceed, led by 2.8 per cent decline within the index for Remainder of Central Region

Once you place down the one per cent choice price to carry down a non-public property, it's important to accept its situation as it is whenever you move in – faulty air-con, choked rest room and all. Get round this by asking your agent to incorporate a ultimate inspection clause within the possibility-to-buy letter. HDB flat patrons routinely take pleasure in this security net. "There's a ultimate inspection of the property two days before the completion of all HDB transactions. If the air-con is defective, you can request the seller to repair it," says Kelvin.

15.6.1 As the agent is an intermediary, generally, as soon as the principal and third party are introduced right into a contractual relationship, the agent drops out of the image, subject to any problems with remuneration or indemnification that he could have against the principal, and extra exceptionally, against the third occasion. Generally, agents are entitled to be indemnified for all liabilities reasonably incurred within the execution of the brokers´ authority.

To achieve the very best outcomes, you must be always updated on market situations, including past transaction information and reliable projections. You could review and examine comparable homes that are currently available in the market, especially these which have been sold or not bought up to now six months. You'll be able to see a pattern of such report by clicking here It's essential to defend yourself in opposition to unscrupulous patrons. They are often very skilled in using highly unethical and manipulative techniques to try and lure you into a lure. That you must also protect your self, your loved ones, and personal belongings as you'll be serving many strangers in your home. Sign a listing itemizing of all of the objects provided by the proprietor, together with their situation. HSR Prime Recruiter 2010

[6] Norway's Ministry of Local Government website; Stortinget; General Elections; The main features of the Norwegian electoral system; accessed 22 August 2009

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+{{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''&nbsp;+&nbsp;1 exactly when the divisor equals the population of the region divided by ''s''&nbsp;+&nbsp;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''&nbsp;=&nbsp;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]]

Margin of error: Difference between revisions

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Description of the method

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Margin of error: Difference between revisions

Revision as of 02:46, 23 January 2014

Description of the method

Sainte-Laguë and Webster

Modified Sainte-Laguë method

References

External links

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