30 March 2012

Rank local election wonkery: Glasgow City Council...

Seen as we've Scottish council elections coming up in a month and a bit, it seems appropriate to stray back into obsessive wonkish territory, and indulge ourselves in a closer squint at a) the election system Scotland will be using and b) a few choice examples of contested wards. 

You may recall that 2007 was the first local election to be conducted using the "single transferable vote" under the Local Governance (Scotland) Act 2004. Screwed out of Labour by the Liberal Democrats under their coalition agreement of 2003, the shift from first past the post to proportionate election of local authorities merrily buggered up Labour's councillor base in 2007. Although nationally, Labour took 590,085 first preferences votes to the SNP's 585,885, the net result was a loss of 161 Labour councillors, with the SNP gaining 182 - while the poor auld Liberals contrived to lose nine under their own STV scheme.

Just muse on this example. Under the first past the post poll in 2003, Labour won seventy one of seventy nine seats in Glasgow City chambers: a stonking 90% of the wards on 48% of the vote.  Come STV in 2007, and the party's 43% of first preference votes could only secure them 45 seats, representing 57% of the whole chamber. Twenty six of their councillors were evicted, and the SNP increased its representation in Glasgow from the three (!) councillors elected in 2003, to 23, under a more proportional procedure in 2007. Although going largely unappreciated and uncommented upon, this was a radical shift.  The SNP now have more MSPs representing Glaswegian constituencies than they had councillors in the city as recently as 2003.

Recent meditations on Labour's drubbing in 2011 and the party's prostrate subsequent politics have tended to emphasise Gray's lack of colour before and during the campaign, weak and unmemorable policy positions and a ramshackle national campaign dogged by hostile coverage. A nip back in time to the local results of 2007 suggest another vital factor. The evisceration of the party's councillor base in 2007 - potential locus for organisation and political vitality that they are - seems another important aspect which it would be remiss to neglect. 

So how does STV work in practice? Some of you may be well-aquent with the single transferable vote, and I dare say all of you know, from the resolutely practical perspective of the voter, how to construct a valid ballot paper. I thought it would be helpful - and potentially interesting - to explain with reference to a real world example how the allocation of seats functions.  For my object, I'll take the Pollokshields ward in Glasgow, where I cast my local ballot in 2007.

A few preliminaries. The Pollokshields allocation went through nine rounds in 2007, including two transfers of candidates' surpluses, six candidates excluded and the next preferences expressed on their ballots being transferred to the remaining candidates.  As you can appreciate, this can be lobe-rending stuff, which I cannot but condense a little, aiming at intelligibility. Those interested can see the full transfers and redistributions of surpluses for the ward here

Secondly, unlike first past the post, STV elects multi-member wards. The number of councillors elected per ward is either three or four, depending on regulations. In Pollokshields, three seats on the council were for the filling, and nine candidates put themselves forward: one each from the parties with MSPs in Holyrood - SNP, Labour, Liberals, Tories, Greens - two independents, and vying against one another at the bottom, a candidate apiece from Solidarity and the Scottish Socialist Party.  In the end, Labour, SNP and Tory candidates were elected - but third place was a close run thing.  After the elimination of the Liberal candidate in the eighth round (who by that time was trailing behind the Greens by around 300 votes), the Tory vote exceeded the Greens by just four and a few percentage pips, roughly rendered 1,839 to 1,835. Damn close run indeed.  In terms of first preferences, the 2007 vote in the ward was as follows:
Stage 1: First Preferences
Irfan Rabbani (Lab) 2,575 (26.92%)
Khalil Malik (SNP)  2,057 (21.5%)
David Meikle (Con) 1,435 (15%)
Ian Ruffell (Green) 1,043 (10.9%)
Isobel Nelson (Lib) 863 (9.02%)
Muhammad Shoaib (Ind) 592 (6.19%)
Karin Currie (Ind) 438 (4.58%)
Fatima Uygun (Solidarity) 380 (3.97%)
Ali Ashraf (SSP) 184 (1.92%)
So now what? In terms of allocating seats under STV, the most important concept is the quota.  In the Scottish system, this figure is reached by taking the total number of votes cast and dividing that number by the number of seats available + 1, and adding 1.  The quota remains the same throughout the "rounds" used to shuffle and reshuffle preferences. So, if 100 people voted in a ward, and four seats were to be allocated, the quota for election would be twenty votes.  In Pollokshields in 2007, the quota was 2,392 (9,567 (total turnout) ÷ 4 [3+1] +1). As you can see, Labour's (now the SNP's) Irfan Rabbani already exceeds the quota on the first round by 183 votes, and is accordingly elected Pollokshields' first councillor. If he had not achieved a sufficient level of support to be elected on the first round, we would have immediately proceeded to exclude the candidate achieving the lowest level of support, and redistributing next preferences among remaining candidates. Before we can crack on with eliminating candidates, however, there falls a necessary and modestly complicated interlude.

Transferring "surplus" votes
Here's where things get a little trickier. We have to transfer the surplus secured by Irfan Rabbani - who in this case, received 183 votes above the 2,393 threshold.  To do so is a multi-stage endeavour. Firstly, you have to take the whole body of ballots registering a first preference for the candidate with a surplus, and count up their second preferences. Remember, however, that we don't want to transfer all of Rabbani's second preference votes: only the 183 votes above the threshold. Although initially a bit mind bending, this is done in a simple enough fashion.  We calculate a "transfer value" to each ballot. Here, we do so by dividing the total number of surplus votes by the total number of votes the candidate with the surplus received.

To put this in numerically convenient terms, consider a contest where a candidate in a two-member ward is elected on first preferences. Say the quota for election is 900 votes, and Bob received 1,000 votes. His 100 vote surplus needs to be redistributed between his three competitors. Percival receives 70% of Bob's second preferences, Guthrie receives only 30% while Imelda garners none. Taking the total surplus and dividing that by Bob's total vote (100/1000), the transfer value of each surplus vote would be 0.1. Accordingly, Percival would receive 70 of the 100 surplus votes, Guthrie would receive 30, and Imelda none.  In the real world things aren't quite so neat, and we stray into the domain of figures with five-decimal points. To take Irfan Rabbani's surplus in Pollokshields, this worked out as 183 votes (Rabbani's surplus) ÷ 2,575 (Rabbani's total vote) giving us a "transfer value" for votes of 0.07106. Concretely, this means that every second preference vote on a Rabbani ballot is counted as 0.07106 of a vote, and is transferred to his competitors based on the number of second preferences they received.  

Stage 2: Transferring Rabbani's surplus

Irfan Rabbani (Lab) 2,575 (-183 votes)
Khalil Malik (SNP) 2,057 (+25.01312 votes)
David Meikle (Con) 1,435 (+10.09052 votes)
Ian Ruffell (Green) 1,043 (+17.97818 votes)
Isobel Nelson (Lib) 863 (+20.96270 votes)
Muhammad Shoaib (Ind) 592 (+13.50140 votes)
Karin Currie (Ind) 438 (+3.48194 votes)
Fatima Uygun (Solidarity) 380 (+8.17190 votes)
Ali Ashraf (SSP) 184 (+4.76102 votes)
Non transferable: 1112 (79.01872 votes)
Non transferable due to rounding: 0.02050

For those particularly interested in the politics of who transferred to who in Pollokshields, we can work back from these figures to make the following observations. About 43% of those giving their first preferences to Rabbani recorded no second preference and so didn't transfer votes to his competitors.  Of the remaining 57% of Rabbani's ballots, 13.7% listed the SNP candidate as second preference, 11.5% for the Liberal Democrat, 9.8% for the Greens and just 5.5% for the Tory, behind the 7.4% of the Labour candidate's transfers to the independent candidate, Muhammad Shoaib. You'll notice that even with Rabbani's transfers, no remaining candidate has achieved the quota of 2,393. Accordingly, we have to go on to the next stage of the process: eliminating the candidate with the smallest number of votes.

As an out of turn aside, when Kalil Malik (SNP) was elected in the seventh stage of calculating the Pollokshields vote, his surplus numbered 232.74834. While just over 50% of Malik's surplus would not transfer to the remaining candidates (explanations include a) Malik was his supporters' first and only preference; b) they had only indicated a preference for candidates already elected or c) who had been eliminated), of the half which did transfer, roughly 23% of next preferences went to the Greens, 17% to the Liberals and 9% to the Tories. 

Elimination and transfer

Back to the next stage of the process. In Pollokshields in 2007, the Scottish Socialist candidate received the smallest number of votes, resting on just 188.76102 votes after the transfer of the Labour candidate's surplus. He is now eliminated from the contest, and his ballot papers redistributed to their next recorded preference.  To be absolutely clear, the transferred ballots are only those of the eliminated candidate. For example, say a paradoxical socialist had put the SSP first and Tory second, the ballot would move to David Meikle's pile. And so on till all of the excluded candidate's ballots have been transferred to other candidates, or identified as untransferable.

Since he has already been elected, any second preferences for Rabbani are passed over, for the next preference candidate recorded, if any.  So far, so simple. But the transfers are complicated somewhat by the legacy of transferring Rabbani's (and any previously elected candidate's) surplus. Remember, the SSP candidate gained 4.76102 votes from Rabbani's surplus, in addition to those second preferences, recorded on ballots. Practically, the rule is that ballots carry whatever "transfer value" they currently have, over to the candidate they are transferred to. The candidates with the lowest number of votes are eliminated, one after the other, until a candidate achieves the quota, their ballots and surplus votes then cascading across the field of remaining candidates according to voter preferences.

I don't propose to go through the detail of the exclusions of Ashrag, Uygun, Currie and Shoaib which constituted the third to sixth stages of the 2007 allocation. There is, however, the odd political morsel worth mentioning. Firstly, of the four candidates first excluded, in every case around 25% of ballots didn't express transferable next preferences (and remember, at this stage only Rabbani is being passed over, so we aren't deep in the impenetrable mangroves of this contest, eking out last next preferences). Might this change over time, as Scots become more acquainted with the system, less likely just to scratch an "X" beside their preferred candidates, as they used to do before 2007?

Although results cannot be calculated from the figures, it is also interesting to take a look at the preference numbers*. Just how keen were the folk of Pollokshields to express preferences? Did they sweep through all nine candidates, or make a choice selection of one or two? I knocked the results together on this graph, which shows pretty plainly that while 7% of those who vote diligently complete the whole ballot, for the vast majority, interest sharply fell off in 2007 after the first preference was identified.  Historically, it would be interesting - but no insubstantial task - to see how Pollokshields compares with the rest of the country on this score. Prospectively, we can also speculate on how Scottish voters' use of their local STV ballots change this election year, and whether they avail themselves of the possibility of expressing multiple preferences.


One major change which is likely to have an impact on that is a new phenomenon in Scottish politics: multiple candidates from the same party, standing in multi-member council constituencies. The peril, potentially, is that your vote is split between your candidates, and so neither wins, rather than returning two candidates of the same tribe, as intended. In Glasgow in May, the SNP will be running two candidates in twenty of the twenty one council wards, and as many as three in Govan.  Similarly, Labour is running between one and three candidates in the various wards across the city.

Unlike the closed lists used for our Holyrood elections, voters in Glasgow will be able to single our preferred candidates in their ward rather than simply selecting a party. The Labour voter, for example, who rates one candidate but despises another will be able to direct their electoral support accordingly.  No doubt the headline council results and overall balance of power will receive the greatest attention in the press, but it will be fascinating to see just how far the parties' new multi-member strategies will work out - or precipitate unmitigated electoral disaster - in Glasgow.

*Which the council also publishes (POLLOKSHIELDS-preferences is the relevant page in this .zip file).


  1. It's a complicated beast LPW.

    I am standing for the SNP in the Glasgow North-east ward. Alphabetically you are advantaged/disadvantaged straight away, hence why a labour candidate in England changed her name to be listed above her colleague. We are standing 2 candidates and labour 3, unlike other parts of the city this will be a straight out ruck between labour and us. When we boil it down it is a straight out fight between myself and the 3rd in the list labour candidate. Unless our voter management strategy gave me a ridiculous portion like over 70% of the ward there is nothing short of popular incumbancy to prevent those higher in the list attracting more votes. There is only one incumbant amongst the 5 of us, who also has the alphabet in his favour.

  2. Tony, you're assuming everyone votes alphabetically, top down, but some people are thrawn and will start from the bottom of the paper. Likewise, any party with half a clue who are running multiple candidates in a ward should be tailoring their advertising to suit. This is routine stuff in Ireland.

  3. Angus

    We are well schooled on VMS and have studied the Irish experience, SF in West belfast is a lesson in itself. Thrawn or not the overwhelming majority vote top down. 2007 provided a classic example where a blow in beat a local colleague who was actually a good councillor. Not something that we can truthfully say about many labour councillors, but the alphabetical list beat him. We reckon that if we tell 100 people to vote for someone second in the list a quarter to a third will still vote for the first party candidate alphabetically.

  4. Bloody hell. I reckon one of the reasons for low turnout (less than 14% for Hillhead in November) may be that the voters are very unclear on what STV is. First time they did it they maybe didn't get it right so they don't bother again. No one likes to feel like a prat.

    Labour were pushing hard in Hillhead - I got a phone cal from Ann McKechin to get my arse out - and I know the SNP were also pushing hard. And still less than 14%.

    May is going to throw up some weird results.

  5. I received an election communication that said 'voters in village x vote 1:candidate a, 2: candidate b. Voters in village y vote 1:candidate b, 2:candidate a.' It all makes sense now.

  6. I came to the conclusion recently that I'm not in favour of STV after all. This is not despite being in favour of proportional representation, but because of it.

    In my ward in Aberdeen (a three-member ward), the SNP are only standing one candidate, presumably for the reasons already highlighted about members from the same party cancelling each other out. But this means that the SNP could win 100% of the first preferences - meaning everyone in the ward wants to be represented by the SNP - and yet they cannot get more than 33.333333333333333333333333(okay I've made my point)% of the seats. That doesn't look very proportional to me, and the effect is that in my ward, the SNP would be outnumbered by parties who only got people's second-preference, at best.

    The problem seems to be that STV places emphasis on 1) minimising wasted votes and 2) individual candidates. But here's the thing, you can't get proportionality with individual candidates. When people talk about making elections more proportional, they're talking about making sure each party gets a number of seats proportional to their vote. So we're accepting that people want to vote for parties, not people. That means we can only achieve the proportionality we desire through party lists.

    The criticism of the party list system seems to be that a party can shove some person at the top who their party likes, but who the electorate hate, meaning as long as the party can retain enough popularity, the unpopular candidate becomes a shoo-in. But there is such a thing as open lists, where the electorate can rank the party's list members. Therefore, someone can't rely on his or her party's popularity to see them through. It also means parties don't have to worry about candidates cancelling each other out, because they've already got the vote in the bag. To top it off, the mathematics is far more straight-forward than STV (unless you then use STV in the list rankings...) It also gets around the problem of how to allocate surplus votes, because I don't think the current way of doing it is sufficient (unless, as I've already said, you then use STV for the list rankings.)

    Besides, people may think STV takes the power out of a party's hands, but the very fact parties have voter "management" systems in place rubbishes that idea. By placing someone as the sole candidate from their party in a ward where they know they will get someone elected, a party can almost guarantee a councillor's continued presence. Indeed, I believe this is being put into practice in Aberdeen where the SNP are putting the council leader in a ward as the sole SNP candidate, even though they could feasibly get two candidates elected, in order to avoid the potential embarrassment of losing their leader. In that respect it's no different to a party putting their leader first on the list in Holyrood elections.

    If STV was any good, the Nordic countries would use it. But they don't - Sweden uses open lists, and the rest use variations of D'Hondt and its ilk. Need I say more?

  7. I thought the weighting scores I use on operational spreadsheets were confusing! Quantum mathematics are suddenly become understandable!

    Seriously, one thing that totally buggered my vote up last time around was the ballot paper. Long enough to satisfy an Andrex puppy, I think mine was one of the many thousand that was spoiled, albeit unintentionally. And I design forms!

    The electorate do need to have the ballot papers explained properly, although perhaps not as patronisingly as in the SNP's latest broadcast (remember children, SNP, 1,2 3!).

    Councillor personalities will certainly play a part however. The parties will have to tread carefully.

  8. And you can tell how confused I must be, judging by the rather poor use of language in my first sentence..........

  9. Doug, given the contempt displayed by many towards "second class" list MPs there's unlikely to be much enthusiasm for lists, period. And if some people think STV papers are complex, wait until they see what gets handed out with, for example, Slovakia's (fairly) open list system. How many papers?!?

  10. Angus - yes, I understand Sweden's version of open lists means people get entire pages of a party's candidates to rank. I also understand they allow people to vote for the party but not rank the candidates on the list, and they even allow you to write your party's name on a blank voting paper! However, this is where we have to decide where to draw the line between ensuring the result correctly mirrors what the electorate expect from the ballot, and ensuring the voting process is simple enough for people to understand.

    Where do we draw that line? Well, we won't know until we properly define what it is we expect from the vote: ensuring everyone's vote counts towards electing someone (even if it's their well-he's-better-than-THAT-guy preference), or ensuring that the proportion of representatives from each party roughly mirrors the proportion of the electorate who voted for them. To me, STV is about compromise, rather than ensuring differing voices are heard.

    As for the second-class nature of list MSPs - I think we're perhaps getting away from that a bit, as people get used to the fact that both types of MSP are relevant. It probably helps that 3/5 party leaders in Holyrood are list MSPs, as well as the fact that some of those list MSPs are extremely effective politicians (Humza springs immediately to mind, as does Mark McDonald, who is arguably far more prominent than any constituency SNP MSP in the North East, despite being their sole list MSP in the region). I think two of the positive aspects of the list system is it seems to be an effective way of showcasing the talent of politicians who aren't yet well known, and can help beat the incumbency factor - I would be amazed if Humza didn't stand as a constituency MSP next time, and win easily, something which might not have happened if we did not have a list system.

    But if there is a problem with second-class MSPs, there's a pretty simple solution to that - make them ALL list MSPs!

  11. (Incidentally, I do know you said Slovakia and not Sweden, just in case that's not obvious!)

  12. Thanks for taking the time to explain all this LPW. Some hunches about how this works have become more solidly grounded.

    I have always tended to vote exclusively for the candidate(s) I really want to see elected, under the understanding that it is better that a candidate I dislike gets nothing from me at all. Seems that most voters think the same.

    >>DD: Mark McDonald, who is arguably far more prominent than any constituency SNP MSP in the North East

    Not sure about that. Mark McDonald isn't in Time Magazine's list of 100 most influential people, but another NE MSP is...

  13. I'm glad it proved helpful Craig P. As I say, it is perfectly comprehensible, but there are a few knotty details along the way needing unravelling.

    On the election system generally, I'm quite attached to constituencies and wards of some form - grounded geographical specificities. I think they are beneficial points of contact. Beyond that - an onerous and detailed discussion of preferred electoral models is one for another day, and another blog!

  14. There aren't any Liberals in the Scottish Parliament, they are consistantly outvoted by the Liberal Democrats in all but a small handful of wards.