STV - the Quick Explanation

Unlike elections to the UK Parliament, but similar to Scottish Parliament elections, Local Elections in Scotland use a system of proportional representation (PR), as is the norm in democracies across the world. Just to confuse matters we don’t use the same form of PR as we do for Holyrood, and instead use a system called the Single Transferable Vote (STV).

In this system, voters rank candidates in order of preference – 1, 2, 3, etc. Each ward elects a small number of councillors, and the preferences allow votes to be transferred between candidates according to set rules. The count therefore takes place over a number of stages.

This can be when a candidate has more votes than they needed to win, in which case the surplus is transferred. Or, more familiarly, it can be when no remaining candidate has enough votes to be elected, so the lowest ranked candidate is removed and their votes transferred.

This makes it very hard for a single party to win every seat in the ward, and thus more accurately reflects the diversity of views amongst voters in that ward. Importantly, later preferences only matter if the candidate your vote is with is elected or eliminated. You cannot “harm” your first preference candidate by marking later preferences.

When STV was first introduced, every ward elected either 3 or 4 councillors. The Islands Act has since expanded the allowable range for a ward including an inhabited island to go from 1 to 4 councillors. Then, the Electoral Reform Act similarly broadened the allowable range for all wards to span from 2 to 5 councillors.

These changes will be seen first in a half-dozen councils in 2022 – Orkney, Shetland, the Western Isles, Highland, Argyll & Bute, and North Ayrshire. The remaining 26 councils will likely have boundaries redrawn according to the Electoral Reform Act ahead of the 2027 elections.

STV - the More Detailed Explanation

To demonstrate how the system works, we can look at the results in Glasgow’s Pollokshields ward in 2017. I’ve deliberately picked a diverse ward for this, so we can see lots of different parties at play.

First Preferences

The first thing that happens is to tally up the total number of first preferences per candidate. In the above chart I’ve also shown combined share for parties with multiple candidates. That’s useful information, as it gives a sense of how close to winning multiple seats the party might be, but doesn’t impact the count by itself. Once we know the total number of valid votes, we can work out what is known as the “quota”.

The Quota

This is the number of votes necessary to be elected, and is defined as the total number of valid votes cast, divided by one more than the number of seats to fill, then add one vote. Applying that formula to the councillor numbers above, we can say in percentage terms this works out roughly as:

  • 1 Seat – 50% +1 vote
  • 2 Seats – 33.33% +1 vote
  • 3 Seats – 25% +1 vote
  • 4 Seats – 20% +1 vote
  • 5 Seats – 16.67% +1 vote

Pollokshields elects 4 councillors, and there were a total of 10288 valid first preference votes. Applying the formula above, that means the quota to be elected is 2058 votes.

Transfers - Overall

When it comes to transferring votes, there is a bit of a difference between what happens when a candidate is eliminated and when they are elected. Eliminations are simple – all votes simply move to their next preference. Surplus votes on the other hand only transfer as a portion of a whole vote.

This chart might look a bit complex at first glance, but it’s just showing how votes transferred at each stage in the count. So let’s break down each stage in turn, to see what was happening.

Stage 1 / First Preferences

This is just the first preference chart again, but removing the “total” value for parties with more than one candidate and showing only the raw number of votes for clarity. It’s also got that quota of 2058 votes added so you can see what people are aiming for.

Right in this first stage, you can see that both the SNP’s first candidate and the Conservative candidate have more votes than the quota, meaning they are elected. That means 2 of 4 seats have been filled. According to our STV rules, we now have to redistribute their surplus votes.

Stage 2 / Surplus Transfers

The surplus transfer value is calculated by dividing the number of votes above quota by the total number of votes that candidate had when they were elected. The SNP’s first placed candidate had 446 of their 2504 votes as surplus – so all votes transfer with a value of 0.178.

As you’d expect, most of the successful SNP candidate’s surplus goes to the second SNP candidate. You can see here how precise the system is about transferring votes, as candidates are getting transfers with decimal places. The actual count data is even more precise than what I’ve shown here!

Note that since the Conservative candidate was also elected, they can’t receive any surplus votes, so we can’t tell from this chart how many of those SNP voters put the Conservatives as their second preference. You can also see a little pile of “Didn’t Transfer” votes, which will grow throughout the process as ballots “exhaust” for lack of available candidates to transfer to.

We’ve still only filled 2 of 4 seats and haven’t redistributed the Conservative’s surplus, so that’s the next step.

Stage 3 / Surplus Transfers

The Conservative surplus was 312 of 2370, so all votes transfer with a value of 0.132. The Lib Dems receive the largest share, though not that much more than the combined total that go Labour – however, more ballots exhaust than go to any individual other candidate.

At this point no one else has reached quota yet, and we’ve still only filled 2 of the 4 seats, so we have to eliminate the lowest placed candidate, which is UKIP.

Stage 4 / Elimination Transfers

Similar to Conservative transfers, the Lib Dems received the biggest boost from UKIP, followed by Labour – but exhausted ballots were the biggest individual chunk. There weren’t enough votes here to take anyone to quota anyway, so we’re still on 2 of 4 councillors elected, and need to eliminate another candidate. This time that will be the Lib Dems.

Stage 5 / Elimination Transfers

The Greens end up taking the largest share of Lib Dem transfers, though followed very closely by Labour. By contrast, the SNP receive barely any of them. Again though, nobody hits quota, we still have 2 seats left to fill, so it’s time for another candidate to crash out. Labour’s second candidate are the lowest placed, so we wave goodbye to them.

Stage 6 / Elimination Transfers

No surprises that if you eliminate one Labour candidate, most of their votes transfer to the other. That catapults the first Labour candidate over the quota, meaning we’ve now elected 3 of 4 councillors for the ward. There’s one seat left to go, and a surplus to transfer that could make the difference.

Stage 7 / Surplus Transfers

Labour’s surplus was 320.8 of 2378.8, so all votes transfer with a value of 0.135. The gap between the Green and second SNP candidate narrows very slightly here, meaning more Labour votes went SNP than Green at this stage. However, the vast majority of ballots exhausted (i.e. nobody marked on them was still in the running to transfer to.)

Neither of the remaining two candidates have reached quota, but of course only one can win the remaining seat, and there are no other votes to transfer from anyone else. We can therefore mathematically say at this point that the Green has been elected, and we know all 4 councillors. However, because Scotland uses machines to do these counts, they strictly follow the rule requiring a quota, and thus eliminate the second SNP candidate anyway.

Stage 8 / Elimination Transfers

Most of those SNP votes do find there way into the Green pile, easily tipping them over the quota. However, remember this round is just the machine being thorough, and it doesn’t really mean anything – the Green was guaranteed election at stage 7. Even if they hadn’t made quota here, they would have been elected as last candidate standing.

Final Outcome

The four councillors elected for Pollokshields in 2017 therefore ended up being 1 SNP, 1 Conservative, 1 Labour and 1 Green. That helped ensure a broad spectrum of views were represented. By contrast, had the ward been split into 4 wards using FPTP, there’s a very good chance all 4 would have elected SNP councillors, leaving most voters without proper representation in the council.