STV as a tug-of-war

In a previous post having another go at the horse race analogy used by supporters of FPTP (First Past The Post) electoral systems, I tried to compare AV (The Alternative Vote) to a tug-of-war:

Initially the die-hard supporters of the two established foes (usually Labour and the Conservatives) take an end each. As they start pulling they scream out promises and threats to bystanders to try to persuade

  • their stay-at-home supporters to pick up their end of the rope and pull
  • supporters of minority parties to lend their weight (if only to stop the other side winning)
  • the apathetic to look at how things are going and if they don’t like what they see to also lend their weight.

As all of this happens you may find a few people changing ends, but the result is determined by who has the greatest weight of support and can pull themselves over the line at the close of polls.

Electoral Tug-of-War

Electoral Tug-of-War as an AV analogy

I also suggested that STV (the Single Transferable Vote – usually in multi-member constituencies) might be a multi-dimensional version of this tug-of-war with each candidate having a rope. I have since been trying to visualise this!Suppose we have an election for three representatives. To keep this simple (and within the bounds of a two-dimensional screen!) I shall assume that there are only three parties and they all put up three candidates.

STV Tug-of-War - Target

STV Tug-of-War – Target

Hopefully these three candidates offer greater diversity and are not just clones of their fellow party members.

Each candidate has a rope attached to a target ring; the more voters they can attract to help pull it towards them the more likely they are to get elected. A voter has to choose one rope to pull on (hence the single in single transferable vote).

In the AV example above the tug of war takes place on a ground divided into two areas – each area representing a win for the party pulling towards that area. In a multi-member area the ground is divided into a number of areas representing different possible results.

STV Tug-of-War - Ground - showing possible election results STV Tug-of-War – Ground (aerial view)- showing possible election results

In the centre we have one candidate from each party being elected – all parties have similar numbers of voters. At the top we have three “Red” candidates elected; in the bottom left we have three “Blue” and in the bottom right we have three “Yellow” candidates elected. In between are the other possible combinations – depending on the weight of party support.

Unlike council divisions that elect multiple councillors under FPTP – where there is a tendency for one party (the biggest minority party) to take all the seats, this system permits a diversity of representation roughly in proportion to the opinions within the seat.

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.)

STV Tug-of-War - Initial situation - First Count

STV Tug-of-War – Initial situation – First Count

The target ring is approximately over the centre – representing the approximate equality of support for various candidates – and indicating the likely final result in terms of party allegiance. Notice the maverick yellows initially supporting a particular red candidate! Green supporters (without any candidates) are split between red and yellow, whilst purple supporters are supporting a maverick “blue” candidate. A few non-aligned voters have lent their support.

In a three seat election you need just over a quarter of the vote to get elected. This is called the quota – once three candidates have gathered the quota, there are insufficient votes remaining for any other candidate to have a better claim on a seat than the three who have achieved the quota.

In this situation, no candidate has achieved the quota. So the candidate with the least support is eliminated – and their supporters transfer to lend their weight to another candidate. The destination of each transfer is determined by the preferences expressed by the voter on their ballot paper (1st choice, 2nd choice, 3rd choice etc.). This avoids the concept of “the wasted vote” and explains the transferable in single transferable vote.

This then continues until a candidate achieves the quota.

STV Tug-of-War - First Elimination - of Least popular Yellow

STV Tug-of-War – First Elimination – of least popular Yellow

Most of the support stays with Yellow (although some lends its weight to Red) – so the target barely moves as the proportion of support for each party has barely changed. This demonstrates how voters have choice and do not have to “vote the ticket”. “Voting the ticket” is a major drawback of the closed list system used in most of the UK for electing MEPs – once you have voted for a party you have abdicated your choice to that party. Here one of the voters supporting the minority Yellow candidate has probably decided that they do not like the other Yellow candidates so have been empowered to chose their favourite Red candidate as their second choice.

Still no one has achieved the quota, so the candidate who now has the least votes is eliminated – the least popular Blue in this case.

STV Tug-of-War - Second Elimination - Least popular Blue

STV Tug-of-War – Second Elimination – of least popular Blue

All the support stays in the Blue camp. Notice that this eliminated candidate may have been a “Bit of a Maverick” lacking any support from party members – but appealing to a significant number of voters. STV means that mavericks can’t “split the vote” – because if mavericks can’t get elected,  the chances are their vote “comes home” at an early stage.

Again no one has achieved the quota, so another elimination takes place.

STV Tug-of-War - Third Elimination - of Least popular Red

STV Tug-of-War – Third Elimination – of least popular Red

Again most support – as expected stays with the party, but there is a little leakage (of a non-aligned voter) to a Yellow candidate. Still no one has achieved the quota so the least popular candidate is eliminated.

STV Tug-of-War - Fourth Elimination - of the now least popular Yellow

STV Tug-of-War – Fourth Elimination – of the now least popular Yellow

The effect of the eliminations to date is such that sufficient Yellow support has been concentrated in the remaining Yellow candidate that they have just achieved the quota.They have now got just over a quarter of the voters pulling on their rope.

Since all their vote has been used to elect this Yellow candidate, there is no “unused” vote (surplus) to account for. So another elimination occurs.

STV Tug-of-War - Fifth Elimination - of another Blue candidate

STV Tug-of-War – Fifth Elimination – of another Blue candidate

This now causes the remaining Blue candidate to be elected – with more votes than required to meet the quota. A large chunk of the support is not actually required. So how do we ensure that it is not wasted? “Wasted Votes” can happen not just because people vote for no-hopers (Such as voting Conservative in a die-hard Labour area) but also because in die-hard areas, winning candidates don’t need all their vote (Such as Conservatives in died-in-the wool Conservative areas).

Analogies always break-down – and this one is now under strain!

We want to leave most of the support with Blue (which will give them sufficient votes to achieve the Quota) and transfer the remaining unused “surplus”. But we cannot just take any surplus – we need to transfer in proportion to ensure that the balance of views of the voters behind those votes is respected.

So we split every single vote currently residing with the remaining Blue candidate. and we transfer the surplus according to preferences expressed on the ballot paper. It is still a single vote, but part of it is electing one candidate and the surplus part (which would otherwise be wasted) is going on to try to elect other candidates.

STV Tug-of-War - First Surplus

STV Tug-of-War – First Surplus

Most is left with Blue and the remainder is transferred. We have assumed (to keep this example reasonably easy) that all voters express a full set of preferences – it is not required, you can if you like just express a single preference – your vote is however likely to be less effective. So surplus Blue votes get transferred to one of the remaining candidates. The remaining candidates may be unlikely homes for Blue, but by now we are talking about the difference between eighth and ninth preferences – earlier preferences having been eliminated – or elected.

In this case Blue supporters seem to have marginally decided to prefer one Red candidate over the other (perhaps he or she is more independently minded, or has a good reputation for constituency work).

As a result this Red candidates narrowly achieves the Quota and the other narrowly fails to achieve the Quota.

As a result of this election 3 candidates have been elected (boxed-in voters in the above diagram) and the votes of just over 75% of the voters have actually been used to elect someone who voters prefer over other candidates.

  • 3 seats – Quota is 1/4 of vote (plus one)
  • 3 elected – must have used 3 x 1/4 of the vote (plus 3 x 1)
  • 75%+ of the vote has been used to elect someone
  • 25%- of the vote has not elected anyone and the losing candidate cannot claim more support than any successful candidate.

The Vote Efficiency is over 75% – which compares to between 30% and 40% for first past the post elections. If you like, at the end of the process more than 75% of the voters are still engaged in the tug-of-war and are pulling on a rope.

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