Myth Busting: It’s too complicated

Often said of STV (The Single Transferable Vote).  The name is initially the hardest bit; but it says it all:

“I have a single vote and I can instruct the returning officer how to transfer it so as to best elect my choice of candidates.  I do this by putting a “1” against my first choice, a “2” against my second choice, a “3” against my third choice and so on until I am indifferent as to further preferences.”

For the voter it is as simple as that. For the returning officer it is a bit more complicated.  The instruction above can continue in more detail:

Please transfer my vote in the following two situations:

  1. If my first choice is so popular that he or she does not need all my vote, please transfer the unneeded part of my vote to my second choice.
  2. If my first choice comes bottom of the poll, please transfer my entire vote to my second choice.

STV works in multi-member constituencies, so with a single vote it is necessary to calculate what “winning” means.

To get elected you need a fraction equivalent to the reciprocal of the number of seats plus one of the vote.

“the reciprocal of the number of seats plus one” I thought you were saying it was not complicated!  Three examples:

3 seats in a constituency – you need 1/4 of the vote to get one seat

4 seats in a constituency – you need 1/5 of the vote to get one seat

5 seats in a constituency – you need 1/6 of the vote to get one seat

So if you introduce a form of Proportional Representation based on constituencies of around 4 seats, you find that for a candidate to get elected he or she has to achieve 20% (1/5th) of the vote across an area the size of four existing constituencies – which is more votes than they would need in a single seat situation.

The maths:

Say that in a single seat constituency approximately 40,000 vote: to get elected under first past the post (FPTP – the current rotten system) you may need about 40% of the vote to get elected – 16,000 votes.

In a multi-member four-seat constituency approximately 160,000 vote: to get elected you need 20% (one fifth) of that 160,000 to get elected – 32,000 votes. It is actually 20% of the vote + 1.  32,001  This is called the “Quota”

The proof: Once 4 people have been elected with 32,001 votes each, a total of 128,004 votes have been used; this leaves 31,996 votes unused – even if they all went to a fifth candidate, he or she would not have more votes than the four successful candidates.  The “plus 1″ bit avoids an unlikely five-way tie from arising.

Remember these calculations are done by the returning officer and only need to be understood by the candidates and their agents.  They would probably use a calculator to do them – but probably only to ensure that mistakes are not made.

The count may take three or four times as long as a First Past The Post count – but you are electing multiple members and the additional time can be thought of as an investment in getting a representative parliament – it’s only once every four or five years!

The steps in a count are fairly simple:

  1. All the ballot papers are sorted and counted according to first preferences (like a First past the Post Count).
  2. If any candidate has got the “quota” (see above) or more:
    1. He or she is declared elected
    2. If they had more votes than required, the unused fraction is calculated, marked on the ballot papers and then they are all transferred (at their unused value) according to the next preference on each ballot paper.
  3. If no candidate has got the “quota”:
    1. The bottom candidate is declared eliminated
    2. All the ballot papers for that candidate are transferred (at full – unused – value) according to the next preference on each ballot paper.
  4. Then the process is repeated until all seats have been filled.

This process is used for many Parliamentary/Assembly elections in Ireland (both Northern Ireland and the Republic) for Local Authorities in Scotland, and for electing ruling councils of many professional and membership organisations.  It is also used further abroad.

The reasons for all this transferring is to maximise the use of the vote and to avoid issues like “wasted votes” and “split votes”.  In an STV election with 4 seats per constituency, 80% of the votes actually elect someone; in First Past The Post, only around 40% of the votes actually elect anyone (In Norwich South in 2010 less than 30% of the vote actually elected anyone with the other 70% being unrepresented).

The other benefits of STV will be detailed on a later post.

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  • By Other benefits of STV | Enfranchise me! on 17 September 2010 at 12:40 am

    […] of the way votes get transferred (see previous post) parties can put up as many candidates as they like.  Whilst it may initially look a little odd, […]

  • By STV as a tug-of-war | Enfranchise me! on 31 July 2014 at 4:24 pm

    […] Initially with all the candidates in play we might have a situation like the one below. (The numbers of little stick-voters pulling on the ropes are indicative – don’t try to count them to do the maths. For details of the “maths” see another short post on this blog.) […]

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