LE22: A Proportional Pickle

For a little break from ongoing LE22 data collation (40.3% done at time of writing), let’s delve into an area near and dear to Ballot Box Scotland’s heart – proportionality. If you’ve followed BBS for any length of time you’ll almost certainly have seen me talk about how STV isn’t a particularly proportional system. That often comes as a surprise to people, given that (despite relatively limited global use) it’s often presented as the default form of PR by the likes of the Electoral Reform Society in the UK. 

The fact that proportionality is somewhat limited under STV means that although local elections in Scotland are far fairer than under First Past the Post, they aren’t perfect. Just like FPTP, you end up with oddities like parties winning wildly different numbers of seats for roughly similar votes, and it can still be quite hard for a lay voter to understand. So let’s take a look at what the issue is, and how different things might have looked.

Purely Yet Partly Proportional

What's stopping STV from being truly proportional?

Compared to AMS, which mixes elements of FPTP and PR, STV can be accurately described as “purely” proportional voting system – so long as you have at least two seats up for grabs, it’s automatically more proportional than FPTP. However, that’s not the same thing as being “fully” proportional – and STV definitely isn’t fully proportional! The very simple reason why STV is not a particularly proportional voting system is that it relies entirely on subdivisions of the whole.

It is a basic mathematical fact that the more of something you have, the easier it is to parcel off smaller portions of it. For example, 10% of 4 is 0.4 and, well, you can’t get 0.4 of a councillor. But 10% of 10 is 1, and you can get 1 councillor. The more seats determined by the same set of votes, the more closely the two proportions align. Any voting system based entirely on subdivisions thus risks disproportionality. That means its true of AMS at Holyrood as well, though by using 15-17 seats overall rather than (mostly) 3 or 4 under STV it’s generally more proportional.

You can make STV (or any PR system) more proportional by electing more seats at one time, but that rapidly begins to detract from another key argument for STV, namely the transferrable nature of the vote. The more seats up for grabs, the more candidates will stand. The more candidates that stand, the more onerous it is to rank them, and the less likely voters are to mark “enough” preferences to ensure their vote is used. If massive numbers of votes are exhausting and not transferring, what’s the point of using a transferrable voting system?

I’m only partway through collation for this year’s elections, but preference use already drops off rapidly. Relative to first preferences, voters using their second preferences run to about 88%, third to 65%, and fourth an abysmal 25%. Even with better voter education (I don’t think folk are processing the “and so on” on their ballot paper instructions…), voters are more likely to preference “enough” candidates with 10 on their ballot paper than they are with 15 or 20. 

Who's it hurting?

This kind of disproportionality catches every party in at least one council, but there are a few particularly notable impacts. The Greens especially face difficulties under STV – although they had an expectation-bustingly successful result in May and their vote share continues to grow, the fact it’s quite evenly spread saw them relatively poorly represented. Councils like Aberdeen, East Renfrewshire and West Lothian (all around 5%) or Dundee and East Dunbartonshire (both roughly 6%) and even Midlothian (8.2%) went without Green councillors. Even where they did win councillors they often saw underrepresentation, as in East Lothian (9.9% of votes, 4.5% of seats) and the Borders (8% of votes, 2.9% of seats). 

For similar reasons, the Conservatives also ended up doing more poorly than they should have. In urban areas their vote share is generally high enough to win some seats, but too thinly spread and the party too unpopular an option for transfers to win all of what they should be due. Their one mainland council without seats, West Dunbartonshire, came out at 8.8% of the vote, whilst in neighbouring Glasgow their 10.2% of votes led to measly 2.4% of seats. The likes of Dundee (11% of votes, 3.4% of seats) were similarly unreasonably grim for the party.

Labour have the opposite problem, in that rural areas are their Achilles’ heel. They ended up completely absent from both Aberdeenshire (4%, but that was from contesting 11 of 19 wards) and the Borders (5.2%), whilst their 6% of the Highland vote only translated to 2.7% of seats. The Lib Dems too end up caught out in places like East Lothian (5.2% but no seats) and Aberdeen (14% of votes and 8.9% of seats).

I reckon these kind of disproportionalities are unfair, and it’d be better to avoid them. Local representation is important, yes, but not so important that we should overly-privilege parties with concentrated vote shares compared to those with similar but more diffuse support. So, what could things have looked like? Let’s start with thinking about AMS – after all, we use it for Holyrood, so it would make sense to translate it to councils.

AMS for Locals?

Building the Model

Obviously, it would be far too much work to come up with an AMS model for every council in the country. However, before the election, I pulled together one for Glasgow – as ever, my home city gets the star treatment. For this I applied roughly the same ratio of FPTP to List seats as exists at Holyrood, though rounding a bit to make it prettier, giving a total of 50 FPTP wards and 35 list seats.

I then used data on polling district electorates to create the FPTP wards, aiming for them to fall with 10% of the target electorate size. I was left with even more respect for the various Boundary Commissions after this, as it’s exhausting to pull together six wards then find you’ve left no way to create a seventh and have to undo it all and start again! I managed to get 43 wards within the 10%, leaving 7 outside tolerance (the worst ward is -14.5% from target).

Lastly, these were grouped together into regions. The split along the river is slightly awkward with 31 to the North and 29 to the South, so rather than five regions of 10 wards, one (West) has 11 wards and another (Southwest) has 9. Similarly, West therefore ended up with 8 List seats and Southwest with 6, whilst the other three regions (North and Centre, East, Southeast) had 7.

Then it was just a case of adding the right polling district data together (from my detailed collation here) for the new wards. Of course, unlike actual AMS, I only had a single vote to work with, so it’s doubled both for electing the FPTP and list seats. In reality, people would be able to vote differently between the two types of seat, as they do at Holyrood.

Results for Glasgow 2022 under AMS

This version comes out with the SNP winning 27 of the FPTP wards, compared to 18 for Labour and 5 for the Greens. List seats then fall mostly in 7’s – that’s how many the SNP, Greens and Conservatives get, whilst Labour take twice that with 14. Overall, the SNP and Labour would be worse off than they were under STV, whilst both the Greens and especially the Conservatives make gains. 

Although this is still a little shy of proportionality – the Conservatives would be due a couple more seats – it’s more accurate than STV was. Notably, the Lib Dems don’t make it onto the council with this version either, as their support in Glasgow is just extremely weak. Even their best region of the city came out at just 3.1% of the vote. 

However, whilst this 2022 version is more proportional than STV was, a 2017 iteration may not have been. It’d be too much work to go back and work out 2017 figures, but given the STV ward map of Glasgow was solidly yellow, it’s not impossible they’d have won at least 43 of the FPTP wards, and thus a majority. If STV’s weakness is that it’s acting across areas that are too small, AMS’ is that it still has the very obvious risk that one party so dominates the FPTP seats they throw everything off.

Purely and Fully Proportional

The BBS ideal is always that elections should be as purely and fully proportional as possible, within reasonable bounds. The general form of what I’d advocate for is outlined in this briefing on a “Scandinavian Style” voting system. In short this involves combining localised representation with allocation of some seats based on overall vote, for all parties winning at least 3% of the vote. 

Modelling that in a truly accurate form would be very time consuming, and this is meant to be a short diversion from collating detailed LE22 data, not its own massive data generating exercise. However, for simplicity we can just use the votes as-cast to get a rough idea.

In the three cases (Greens in North Lanarkshire, Labour in Shetland, Conservatives in Eilean Siar) that a national party won a seat without winning at least 3% of the vote due to gaps in their nominations, I assume they’d actually have won exactly 3%. Similarly, the two micro parties (Rubbish and British Unionist) are treated as Independents. Speaking of Independents, I’ve specifically used Sainte-Laguë so that they have the best chance of still being elected and this system doesn’t just throw them out.

Seats As Elected

Just quickly to enable comparison with the below, the above chart shows total seats for each party as elected under STV in the 2022 elections. 

Notional More Proportional

And this one shows what the more fully proportional version comes out at. All of the gaps identified earlier on, for example Greens in Aberdeen, Labour in Aberdeenshire, Conservatives in West Dunbartonshire and Lib Dems in East Lothian, are filled in.

The net effect is a substantial gain for both the Conservatives (+31) and Greens (+30), plus modest improvement for the Lib Dems (+9). That comes at the expense of the SNP (-28), Labour (-26) and Independents (-13). Many more voters would be represented by their preferred party, which surely has to be a good thing.

Notable Quirks

Of course, if we did use such a system, we wouldn’t have the same kind of contesting gaps that exist under STV. That’d result on some further differences, which it’s worth quickly touching upon for each party, at least for the mainland where it’s easier to gauge how parties would do. For the Conservatives there’d be little to no difference, beyond what they’d lose to others gaining, since they had a full mainland slate, but the SNP’s two absences in the Borders are likely to add another seat to their tally there.

Labour have seats on every mainland council under this model, but their rural ward gaps are substantial enough to add at least another seat in each of Highland, Aberdeenshire, Perth and Kinross and Moray in a real-world implementation. The Borders, Angus and Argyll and Bute are also possibilities on that front.

Moving to parties with more absences still, the Lib Dems could reasonably expect that a lack of gaps in the Borders, Inverclyde, South Lanarkshire, and Dumfries and Galloway could gain them a further seat in those areas. However, of the councils they’re still absent from entirely above, only South Ayrshire (2.6% from 6 of 8 wards) is a clearly unjustified miss. Clackmannanshire is close but not quite there, as their two missing wards are by far their weakest, whilst areas like Falkirk, Glasgow, North Lanarkshire, North Ayrshire and East Ayrshire are absolute no-hopers for Lib Dem councillors.

For the Greens, they could expect additional seats in Highland, Moray, Argyll and Bute, and both Lanarkshires. With every voter in the area able to vote Green, they’d also easily enter onto Aberdeenshire, North Ayrshire and Renfrewshire councils. If they found a candidate for Inverclyde then based on Holyrood performance I’d actually say they’d be likely to pick up a seat there, leaving East and South Ayrshires as the only councils they’d likely fail to win seats on entirely.

Finally, what about Alba? Supporters of that party clung rather desperately in the aftermath of the election to the fact they had a relatively limited contest rate to explain their very low vote share. However, where they did stand their shares were so low that even extrapolated across the whole council area they’d still be well short of crossing the 3% threshold. In Aberdeenshire, for example, their total across contested wards was only 2.3%, and in fully-contested Dundee it was 2.4%. The one question mark is North Lanarkshire, where they had three wards above 5%, and 3.9% across the wards they contested. There’s a chance that could have been their one success in this system.

Scotland is very fortunate indeed to use forms of PR for most elections, and STV means our councils look a lot more like the electorate than is the case in England and Wales, where they persist with FPTP. This piece very much is not an attack on STV – it’s simply another look at how we could make things still more representative. 

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