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District Health Board Elections
Single Transferable Voting

DHB elections use the Single Transferable Voting (STV) system to elect candidates to boards. Under STV, voters rank their desired candidates in order of preference. Candidates are elected when they reach a specific level of support from voters (‘the STV quota’).

How do you vote in an STV election?

When casting an STV vote, voters write a ‘1’ beside the candidate they most prefer, a ‘2’ beside the candidate they next prefer, and so on. Voters can rank as many or as few candidates as they wish: their vote will be valid as long as a unique first preference appears on the voting document.

An STV voting document may look something like this.

Example of the STV voting document.

The way the voter has completed the sample voting document above means they are saying, ‘I prefer Etevise Eggplant the most so I’ll put a “1” beside her name, then my next preferred candidate is Christine Carrot so I’ll put a “2” beside her, then I like Belinda Banana next so I’ll put a “3” beside her’, and so on. The voter decided to stop ranking candidates at Gerald Grape (who the voter marked ‘8’), remembering that voters can express preferences for as many or as few candidates as they wish – it’s not necessary to rank all the candidates on the voting document.

How does the STV quota work?

In order to be elected, candidates must reach the STV quota. The STV quota is calculated as follows (an extra billionth of a vote is added to the STV quota to remove the small risk that two or more candidates may be tied for a position):

Image of the STV quota formula.

Text description:
STV quota = the number of valid voting documents divided by the number of vacancies + 1.

The STV quota is constructed this way to ensure that only the required number of candidates are elected. For example, when just one vacancy is being filled, a candidate needs slightly more than half the votes to be elected. If a candidate has more than half the votes, then no other candidates can have as many votes.

Similarly, if two vacancies are being filled, then any candidate with more than one-third of the votes remaining in the count will be elected. This is because there can be at most one other candidate (who can fill the other vacancy) who will receive as many votes.

As an example, in a DHB election with 80,000 valid voting documents cast and seven positions on the board, the STV quota would be:

Image of a STV quota formula calculation example.

Image of a STV quota formula calculation example.

Text description:
STV quota = the number of valid voting documents divided by the number of vacancies + 1 = 80,000 divided by 7 + 1 = 10,000

Therefore, based on a DHB election with the above figures, candidates would need to receive just over 10,000 votes to be elected to the board. This works out to be a little over 12.5 percent of the vote.

How are STV votes counted?

The Department of Internal Affairs has developed computer software which counts STV vote preferences. This software is used by DHB electoral officers to calculate the election results.

The process for counting vote preferences under STV (as performed by the calculation software) is as follows:

Flowchart of the counting process - see text below the image for an explanation of the flowchart.

Flowchart of the counting process - see text below the image for an explanation of the flowchart.

This method means that candidates with enough support to be elected do not keep more votes than they need to be elected. Rather, the excess votes they receive are redistributed, in order of voter preference, to help elect other candidates.

At the other end of the scale, where no candidate has sufficient support to achieve the quota and there are still vacancies to fill, the least popular candidate is removed from the count and, again, their votes are used to assist other candidates in being elected. This is done on the basis that it is impossible for that candidate to be elected, even if all the remaining votes were transferred to them.

The cycle stops when all available positions have been filled. In the case of DHBs, there are seven elected member vacancies per board.

Page last updated: 2 August 2007