Leveling seat
Leveling seats (, , , , ), commonly known also as adjustment seats, are an election mechanism employed for many years by all Nordic countries (except Finland) in elections for their national legislatures. In 2013, Germany also introduced national leveling seats for their national parliament, the Bundestag. Leveling seats are seats of additional members elected to supplement the members directly elected by each constituency. The purpose of these additional seats is to ensure that each party's share of the total seats is roughly proportional to the party's overall shares of votes at the national level. Denmark. In 1915, Denmark became one  of the first countries in the world to introduce leveling seats in their parliamentary elections. Since then, all parliamentary elections in Denmark have allocated these adjustment seats as a substantial fraction of the seats in the parliament. The parliamentary seats currently comprise 135 county seats and 40 leveling seats, with a further 4 "North Atlantic seats" elected separately by proportional representation in the Faroe Islands and Greenland (which are not treated as an integral part of the Danish election system). The leveling seats are supplementary to the normal seats which are allocated by proportional votes within each county. All parties  which achieve at least 2% of the national votes are granted as many leveling seats as required to achieve proportional representation at the national level. Iceland. Leveling seats have been a part of the election procedures for all Icelandic parliamentary elections since 1934. Sweden. Since 1970, Sweden used leveling seats in its elections for both the Riksdag and county councils, for parties having qualified with a total share of votes above a 4%-limit in parliamentary elections and 3%-limit in county council elections. Sweden did not use leveling seats for municipal elections prior to 2018. With the new election law (effective  from the election 2018), leveling seats are used in municipalities with more than one electoral district. Of the 349 seats in the Riksdag, 310 are fixed seats and 39 are adjustment seats. The 310 fixed seats are distributed among the 29 electoral districts () according to the largest remainder method with the Hare quota. The distribution of seats between the parties then takes place in four stages. Leveling seat allocation. In the first stage, the fixed seats are distributed within each district according to the modified Sainte-Laguë method ("jämkade uddatalsmetoden") with the first divisor adjusted to 1.2 (1.4 in elections  before 2018). Only parties that have received at least 4 percent of the vote nationally or 12 percent of the vote within the district can participate in this distribution of seats. In the second stage, the 349 seats are distributed through a calculation based on the total number of votes summed up across the entire country. In this distribution only parties that have received more than 4 percent of the national vote are included. Parties that fall below 4 percent nationally but have been awarded fixed seats in districts where they have had more than 12 percent of the vote  are disregarded, and their seats are subtracted from the calculation. If a party has received 2 seats in this fashion, for example, the calculation will be made with 347 seats. Again the modified Sainte-Laguë method is used. In the third stage, a summary is made of the fixed seats that the parties have achieved, and this is compared to the outcome of the nationwide distribution above. If a party has received more fixed seats than its share of the total 349-seat distribution, district seats allocated to that party are retracted and given to the party with the second  'highest quotient'. The parties are then awarded a number of adjustment seats sufficient to cover the gap between their number of fixed seats and their share in the nationwide distribution. Finally, the adjustment seats that each party has received are distributed among the districts. The application of the Sainte-Laguë number gives each party a quotient ('comparison number', "jämförelsetal") in each district, which is its number of votes in the district divided by (2"n"+1), where "n" is the number of seats it has been awarded. The district where the party has the highest quotient is awarded an adjustment seat, and  a new quotient is then calculated for that district, before the next adjustment seat is distributed. In theory, a district can thus receive more than one adjustment seat. If a party is yet to receive a seat in the district, its quotient simply is the number of votes it received. When the fixed seats were distributed among the parties in the district, this number was divided by 1.4, which made it harder for a party to achieve its first seat. Now, however, no such division takes place. The method used is thus pure and not modified Sainte-Laguë. In local  elections. In elections to the county councils, the same principles are followed, with the following differences: only parties that have received more than 3 percent of the vote in the county are able to participate in the distribution of seats. There is no 12 percent clause or other possibility for parties that fall below this threshold to gain seats. Finally, the number of adjustment seats is one tenth of the number of seats in the county council. If one tenth is a fractional number (which it always is, since the number of seats in a county council is required to  be odd), the fraction is always adjusted upwards, so a county council with 51 seats would have 45 fixed seats and 6 adjustment seats. Norway. Leveling seats were introduced in Norway in the 1989 parliamentary election when there were 8 such seats. Since 2005, there are 19 leveling mandates, one for each county. Its current form is based on the following principles: In the 2005 elections, the average number of votes on a national level was largely similar across party lines. The largest party, the Norwegian Labour Party, required the fewest votes per representative with 14,139; the party that needed  the most votes was the Christian Democrats, with 16,262. On a county by county basis, however, there were greater disparities: Sogn og Fjordane needed only 3,503 votes to elect one representative from the Liberal Party, while Akershus needed 22,555 to elect one representative from the Socialist Left Party. The arrangement has gone through several adjustments through the years and is the result of legislative action. Allocation of leveling seats. The allocation of leveling seats is a fairly complex process. First the leveling seats are distributed among the parties. The second part is distributing them among the counties. Allocating among counties . To determine the county that each party will receive its leveling seats in, the following process is done: Peculiarities. The method for assigning leveling seats usually results in the first leveling seats being given to candidates that did fairly well in the county. However, the last leveling seats may be awarded to candidates that received few votes in the county that they will represent. (In theory it is even possible for a party to receive a leveling seat in a county where they received no votes, or even in a county where they did not field any candidates, a scenario  that the election law has no contingency for.) An illustration of this came in 2005 when Vera Lysklætt of the Liberal Party received the last leveling seat, in Finnmark, with 826 votes. Thus, the Liberal party gained 20% of Finnmark's seats with about 2% of the vote there. In the 2009 election, a programming fault in the software calculating the allocation prognosis for one county made their leveling seat go to another party. That changed the outcome in two other counties, and it took over a week and a recount until the distribution of leveling seats was finally decided . Mette Hanekamhaug got the final seat. Germany. In February 2013, following a decision of the Federal Constitutional Court which demanded a reform of the electoral law for proportional representation, Germany added a provision to create national leveling seats as needed in a case of negative vote weight occurring in its mixed member proportional system, in addition to the traditional leveling seats that already existed in many state elections.