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Sainte Laguë Formula Explained
The MP for the electoral district is the candidate who wins more votes than any other candidate. He or she does not need to win more than half the votes cast. Under an MMP electoral system MPs for the electoral districts are elected in exactly the same way as they would be under the First-Past-The-Post (FPP) electoral system.
Party List Seats
The number of party votes won by each registered party which has submitted a Party List is used to decide how many seats overall each party will have in Parliament.
If, for example, the party vote for the Grandstand Party entitled it to a total of 54 seats in Parliament and it won 40 electorate candidate seats, it would gain 14 further seats which would be drawn from the Party List of the Grandstand Party. Candidates may stand for Parliament both in an electoral district and on their Party’s List. As a result, the first 14 candidates on the Grandstand Party’s rank-ordered Party List who had not been elected to Parliament to represent an electoral district would be declared elected as Party List MPs.
A procedure, known as the Sainte Laguë formula (after its founder) is used to decide the order in which political parties are awarded seats in Parliament.
Allocating 2005 General Election Parliamentary Seats using the Sainte-Laguë Formula
To determine the precise order in which all the seats in Parliament are allocated to the various political parties, the Electoral Act 1993 prescribes that a mathematical formula, called the Sainte-Laguë formula, be applied. The nationwide party vote of each of the parties which qualified for representation in Parliament is divided by successive odd numbers starting with 1 (ie divided the party votes by 1, 3, 5, 7, 9, 11, 13, etc). The 120 highest numbers (which are called quotients) determine both the number of seats for each party and the order in which they are allocated. The following explains how the process works:
The Chief Electoral Officer draws up a table showing the name of each party shown on the party side of the ballot paper, the number of party votes it won, the percentage of all party votes it won and the number of electorate seats it won. For the purposes of this explanation minor parties are combined under the heading ‘OTHER’.
The Chief Electoral Officer then excludes parties that are not eligible for Party List seats by deleting any party that has not won at least 5% of the total number of party votes and has not won at least one electorate seat (commonly termed the threshold). Although ACT New Zealand, United Future, Jim Anderton’s Progressive and the Maori Party each gained less than 5% of the party votes they did win electorate seats, so are included.
Because the parties not reaching the threshold have been disregarded the percentage share for each of the remaining parties has increased.
The Chief Electoral Officer then divides the total party votes for each eligible party by a sequence of odd numbers starting with 1 (1, 3, 5, 7, 9, 11, 13, 15, etc), until enough quotients had been found to allocate all 120 seats. In the table on the following page the italic numbers beside the highest 120 quotients indicate their order from highest to lowest.
The Chief Electoral Officer then counts the number of quotients each party has in the highest 120.
The Chief Electoral Officer then determines how many electorate seats each party has won, and allocates enough Party List seats to each party to bring the total number of seats up to the number to which it is entitled.
The Chief Electoral Officer then examines the list of candidates each party submitted on its Party List before the election, and deletes the names of any candidate who has won an electorate seat. He then allocates each Party's list seats to its list candidates, starting at the top of the list and working down until he has allocated all the list seats to which that party is entitled. He then declares these candidates elected to Parliament and advises the Clerk of the House of Representatives of their names.
There are four further points to note about the process.
 An overhang occurred at the 2005 general election with the Maori Party winning more electorate seats (4) than it was entitled to based on its share of the party vote (3). Accordingly, the size of Parliament increased to 121 seats.
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