A very short guide to STV and AV elections

The Liberton/Gilmerton by-election is to be fought using the Single Transferable Vote (STV) voting system. From canvassing, I know that a significant proportion of the electorate aren’t aware of this. The council is putting 1000 leaflets about STV in community centers and public places; I did suggest to them that they leaflet every house in the constituency but they said that would cost too much. So I thought I’d create this guide…

What is STV?

STV is a way of electing more than one candidate. Typically STV is used to elect 2-7 candidates; for larger numbers than that, it starts to get unwieldy. STV aims at electing those candidates such that all the voters’ preferences are most satisfied.  Of course, it would be impossible to elect candidates that completely satisfy this criterion, without every voter being their own candidate, but STV is generally held to be the best system for electing a small number of candidates.

Edinburgh Council is elected in 17 wards. Each ward elects 3 or 4 councillors. There are 58 councillors altogether.

What is AV?

AV — which stands for Alternative Vote — is a way of electing one candidate to a position. I said earlier that STV is for electing 2 or more candidates; that’s not quite true, STV can be used to elect one candidate, and when that is done is it called AV. AV is therefore a special case of STV when only one candidate is being elected.

The Liberton/Gilmerton by-election is an STV election with 1 candidate. This means it is also an AV election.

Incidentally, there will be a referendum in May 2011 on whether to use AV for elections to Westminster; I hope this referendum passes, because AV is much better system than the current First Past The Post (FPTP) system.

How do I vote in an STV or AV election?

That’s easy. You mark a “1” against the candidate you most prefer, “2” against your second favourite candidate, etc, until you have no further preferences for any of the remaining candidates.

How the votes are counted

We’ll consider AV first, because it is slightly simpler.

The first preference votes for all the candidates are counted. If any candidate has over 50% of the total votes, that candidate is elected. If not, the candidate with the least number of votes is eliminated, and all those votes are redirected to their next highest preference. This continues until one candidate has more voters than all the others put together; that candidate is then declared the winner.

STV is the same idea, except that there are multiple winners. So if the election elects N candidates, then you keep eliminating candidates (as with AV) until there at N left.

But sometimes (usually, in fact) a candidate has more than the votes they need to win. For example, consider a 4-seat election where there are 1000 total votes. Four candidates each have 201 votes. These candidates must all be elected, since all other candidates between them can only get 196 votes.  201 is therefore a “magic number” that guarantees that a candidate will be elected (it’s usually called the “quota”).

Every vote above the quota is a surplus vote that could have gone to electing someone else. And in STV, that’s what happens: if a candidate has more votes than the quota, the candidate is elected, and that fraction of each vote that is above the quote is re-allocated to the voter’s next preference. In our example, if the top candidate gets 210 votes, then 9/210 of each vote is re-allocated. STV is usually counted by computer, for speed.

Further Reading

Wikipedia has some good articles on Single Transferable vote, Alternative Vote, and voting systems in general. The Electoral Reform Society is also good.

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7 Responses to A very short guide to STV and AV elections

  1. workingman says:


    But what if I do not like any of the other candidates. I am working in Australia for a bit and I have taken an interest in their election, which uses the AV voting system. It seems that if you do not vote for all candidates then your vote is not counted.


    So if there are 8 votes as in the example I am forced to rank all of them. This means if there is a candidate/party that I do not want to support in anyway that I am still forced to do that, and therefore my forced could have impact on their chances.
    This seems totally wrong to me.

    • Phil Hunt says:

      Australia is unusual in that you have to rank all he candidates. In Britain you don’t have to.

      if there is a candidate/party that I do not want to support in anyway

      Then you should rank them last (this is the best way to vote against a particular candidate in AV).

      could have impact on their chances

      Yes, a negative one. Which is what you want, surely?

  2. Bruce says:

    I just filled in my postal vote ballot for Liberton/Gilmerton, and it’s got me thinking…

    I’m a big fan of STV and AV, and STV is clearly a sensible fair system for selecting four representatives for Lib/Gil in a normal election. But in the case of a by-election, it’s not clear to me that it stays as fair though.

    Let’s look at FPTP first. Each councillor represents a very small geographic ward. Unfortunately, a small party (like the Pirates) who’s members are spread thinly through the city will be unable to get any representatives. When a councillor resigns or dies, it is very clear exactly which voters have been deprived of representation and will be allowed to vote in a byelection — it’s the ones who live in the very small geographic ward — and the byelection can be held under the same system. If voters do not change party allegiance, then they will return a candidate from the same party.

    In STV, we have medium sized geographic wards, with several councillors. An initial election is held under STV, and the councillors will come from a mix of parties. In Lib/Gill we have two labour councillors, one SNP and one LibDem. The two labour councillors represent the roughly 50% of voters who rate labour higher than SNP, libdem and other parties, the SNP councillor represents the roughly 25% of voters who rate SNP higher than libdem, labour and other parties, etc. The SNP supporters are spread too thinly to get a councillor under FPTP, but they get their preferred representative under STV, which is great.

    When a councillor resigns or dies, it is less clear precisely which constituents have lost representation. Consider if we were replacing the SNP councillor rather than the Labour one. All the voters in the medium sized ward are allowed to vote in the byelection under the AV system. If they do not change party allegiance, then they will return a councillor from the most popular party overall. So a minor party councillor is most likely to be replaced by a major party councillor at a byelection. Over time, if several byelections are held, the composition of the council will become biased towards a single popular party.

    If byelections are common in an STV system and voters do not change the party they vote for, then the composition of the council will change through its term. Which is a (slight) flaw.

    • Phil Hunt says:

      You’re right, by-elections are a limitation of STV. They aren’t that common, so arguably not a big limitation.

      One way this could be dealt with would be for all 4 council seats in the ward to be up for election. I’m not sure sitting councillors would like that very much (especially given that a party could trigger a full council election simply by resigning all their councillors).

      Another way would be to have 90% of the seats elected by STV and the other 10% to be top-up seats. Then when one councillor resigns, their seat is allocated to the next person from the same electoral list.

      BTW, did you vote for me?

  3. Pingback: Some improvements to STV | Amused Cynicism

  4. Pingback: Edinburgh Pirate Party - Some improvements to STV

  5. Pingback: Edinburgh Pirate Party - A short guide to STV elections

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