Sainte-Laguë method

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results The Webster method, also called the Sainte-Laguë method (French pronunciation: [sɛ̃t.la.ɡy]), is a highest averages apportionment method for allocating seats in a parliament among federal states, or among parties in a party-list proportional representation system.

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.

The same method was independently invented in 1910 by the French mathematician André Sainte-Laguë.

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.

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.

[1][4][5][6] While favoring large parties reduces political fragmentation, this can be achieved with electoral thresholds as well.

[10] It also does not ensure that a party with a minority of the vote will not win a majority of the seats, for roughly the same reason.

Often there is an electoral threshold; that is, in order to be allocated seats, a minimum percentage of votes must be gained.

For comparison, the "True proportion" column shows the exact fractional numbers of seats due, calculated in proportion to the number of votes received.

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.

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.

This makes it more difficult for parties to earn only one seat, compared to the unmodified Sainte-Laguë's method.

[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.

In 1842 the method was adopted (Act of June 25, 1842, ch 46, 5 Stat.

[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.

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.

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.

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.

The Webster/Sainte-Laguë method is currently used in Bosnia and Herzegovina, Ecuador, Indonesia,[19] Iraq,[20][21] Kosovo, Latvia, Nepal,[22] New Zealand, Norway and Sweden.

In Germany it is used on the federal level for the Bundestag, and on the state level for the legislatures of Baden-Württemberg, Bavaria, Bremen, Hamburg, North Rhine-Westphalia, Rhineland-Palatinate, Saxony and Schleswig-Holstein.

[25] Some cantons in Switzerland use the Sainte-Laguë method for biproportional apportionment between electoral districts and for votes to seats allocation.

The United Kingdom Electoral Commission has used the method from 2003 to 2013 to distribute British seats in the European Parliament to constituent countries of the United Kingdom and the English regions.

[27][28] The method has been proposed by the Green Party in Ireland as a reform for use in Dáil Éireann elections,[29] 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 House of Lords, the country's upper house of parliament.