SP21 – A Host of Hypotheticals

We’re now four weeks on from this year’s Holyrood election, and in the period since then I’ve been compiling the results here on the BBS website, and doing some more in-depth looks at what happened this time around. Having done all of that initial analysis work, we can now move onto one of my pet topics – electoral reform!

The current voting system for the Scottish Parliament, known as the Additional Member System (AMS), is reasonably proportional. It’s a massive improvement on the pure First Past the Post (FPTP) system that in a Scottish context only persists for elections to the UK Parliament, giving fairer representation to the diversity of voters across the country. However, there are some aspects of the system which negatively impact proportionality, and where we could implement improvements. This piece is a quick run through a few such suggestions, comparing the Gallagher Index of each – this is a measure of proportionality, with figures closer to 0 more proportional.

Note that some of these operate on the basis of the national vote. Where that’s the case, a 3% threshold applies, with parties below that not winning any seats. Thresholds are very common in PR systems, and across Europe (the bit of the world I’m most familiar with), only the Netherlands’ threshold of “votes equivalent to at least one full seat” would have seen any parties apart from the Holyrood 5 win any seats. As such, all the charts below only account for the votes for those 5 seat winning parties.

You may also note that the Single Transferable Vote (STV) is not one of the alternatives here. That’s only partly due to my well-documented dislike of the system – it’s mostly because STV is so hard to predict the outcome from. For example, if we imagine Dunbartonshire as a 5-member STV constituency, based on 2021 results the SNP had votes for 2.3, Labour for 1.4, Conservatives for 1.2, Greens for 0.47, and Lib Dems for 0.36. Apart from the Conservatives, any one of these parties could win the fifth and final seat in Dunbartonshire. It would depend on how each party’s votes were distributed between their own candidates and where transfers went.

Actual Outcome (7.2)

We don’t need to spend a lot of time on the actual outcome as folk should be pretty familiar with it – just including it for context!

Smallest Changes

AMS with Simple Overhang Correction (6.2)

I’ve written a few times about the concept of “overhang” – here on the BBS website, and in this Twitter thread examining this quirk across all elections up to 2016. In short, overhang is when a party wins more constituencies than the total number of seats it is proportionally entitled to. This leads to a knock-on effect at someone else’s expense.

Since the SNP started winning elections, overhangs have actually been quite small – just two seats in 2007 when those were actually in Labour’s favour rather than the SNP’s, and then just one seat extra for the SNP in both 2011 and 2016. This time around there was a much larger overhang of four seats, though that’s still dwarfed by the the net total of seven in both 1999 and 2003.

Some countries correct, in some way, for overhang. Scotland doesn’t. We could do a very simple correction on (roughly) the same model as New Zealand, where the party that would have lost out due to the overhang is nonetheless given the seat they were proportionally due, without depriving the SNP of their overhang.

That would give Labour an additional seat in each of Central and Mid & Fife regions, the Conservatives one in the North East, and the Greens one in Glasgow, bumping Holyrood up to 133 seats. A side effect of this (and all hypotheticals here) would be that, assuming (now formerly) Green MSP Alison Johnstone had still become the Presiding Officer, there would still have been an outright majority for non-SNP parties, rather than the 64:64 tie that exists now.

Pure List (6.2)

This one is so simple that there isn’t a map accompanying it. This would simply abolish constituencies and the inherent risk of FPTP distortion, but otherwise leave the system unchanged by now electing every seat in each region via List using the D’Hondt method.

This gives the same total number of seats for each party in each region except the four with overhangs listed above. Those would each be down one SNP MSP, given they could no longer induce an overhang, whilst gaining for the parties listed. In terms of overall proportionality, this actually ends up being basically identical to the version correcting for overhang.

Larger Changes

Unsurprisingly, if we only make very small changes to the current system, the results would only have been slightly different. How about if we start trying things that involve more substantial modifications?

AMS with Sainte-Laguë (6.3)

Here, we use the Sainte-Laguë method to allocate seats, rather than D’Hondt, but otherwise retaining the FPTP-List mix of AMS. This isn’t a particularly complex change, really, but it does have a larger impact in terms of shifting seats between parties than the previous two alternatives. Rather than dividing each party’s vote share by one more than their number of seats in that region so far, it does one more than twice their number of seats. Whereas D’Hondt gives a slight edge to larger parties, Sainte-Laguë tilts a bit towards smaller parties.

We see that effect in that the SNP don’t get any list seats in this scenario, and the Conservatives also lose three of theirs. Those are perfectly constitutionally balanced with two more Greens and three more Lib Dems. Labour sit unmoved in the middle, albeit they trade one of their Glasgow seats for a second in Highlands & Islands. When I say Sainte-Laguë is more favourable to smaller parties, that Lib Dem bump is the best example – this is the only alternative beyond the optimally-proportional Scandi-style where they come out with that share.

Though this is a bigger change to the system than either of the previous two, in the case of 2021 it’s actually very marginally less proportional – very marginally!

AMS with National Allocation (6.2)

Again, this keeps the bones of AMS, but allocates list seats to regions not simply on the basis of the votes in those regions, but accounting for the national vote. This attempts to strike something of a balance, whereby List MSPs still represent regions and the votes in those regions shape which parties the local representatives come from, but which eliminates the distorting effect of treating each region individually.

This is somewhat similar to the Sainte-Laguë outcome above, though with just two additional Lib Dems rather than three. At this point though if we go back to that concept of overhang, it’s even worse here – if we’re allocating nationally rather than regionally, the SNP are now seven seats over their AMS ideal share. 

Largest Changes

So although we had two less and two more substantial changes to the system above, based on 2021 votes they all have roughly the same impact on proportionality. The Gallagher Index goes down from 7.2 to either 6.3 or 6.2 with all of those options. That’s better but it’s still, in PR terms, relatively unproportional.

All of the above changes presumed (roughly) the same number of seats at Holyrood as at present and only changed one individual component of the system. The fact they all came out broadly similar emphasises that there are two key drivers of disproportionality under AMS: the imbalance of constituency (73) vs list (56 seats) in favour of the former, and the self-contained nature of regional seat allocation.

Of these, the constituency imbalance had clearly the larger effect in this election, as the SNP start with 48% of seats already in any option that preserves constituencies. That may match their constituency vote, but remember that is utterly immaterial to the proportionality. So, we’d need to do some even bigger shakeups to really fix that.

AMS with 145 Seats (4.7)

For this one, I’ve (roughly) equalised the list seats (72) with constituencies (73) by simply adding two more list seats to each region. That bumps Holyrood up to 145 seats in total, which is what makes this such a big change.

Even though this therefore still maintains self-contained regions, the boosting of the proportional side of things really helps to balance things out more. The SNP only pick up two of these additional 16 seats. However, we still see the effect of regionalisation, because both the Greens and especially the Lib Dems are still under-represented for their vote shares.

Scandinavian Style (3.0)

Long standing followers of BBS will know this is my favoured electoral system, and I’ve written extensively about it in the past. Whereas everything else in this piece tweaks AMS in some form, this wipes the whole thing away and starts over – it has no constituencies, the regions are different, and part of the allocation of seats is done based on the national vote share.

With no FPTP seats to inflate their share, the SNP are quite substantially down, and everyone else gains. Whilst it’s true that voters would make slightly different decisions if we had this system in reality, it’s worth noting the SNP’s performance in local and EU elections lately has been closer to their list vote than their constituency vote. That suggests that it’s not just their seat share that is inflated when FPTP is involved.

Overall, this as close to maximum proportionality as we can get with the threshold, giving us a Gallagher Index of 3.0. That’s really quite good, and is why I quite like this system! But it’s not without some oddities of its own. My eye was immediately drawn to the lack of Green MSP in Highland South – that’s the party’s 4th best area, but based on 2021 figures they get their full allocation of seats elsewhere due to the small number of seats in that district.

That kind of thing is a bit like how under AMS highly placed list candidates can still fail to be elected if their party unexpectedly wins a lot of constituencies. The example per excellence of this would be Shirley-Anne Somerville who lost her seat in 2011 despite placing 3rd on the list, because the SNP won shock victories in seats like Edinburgh Pentlands.

Final Notes

This piece has looked at six different ways we could change Scotland’s voting system to improve proportionality. Apart from the last option, these all involve just making one change at a time – you could actually mix’n’match many of these proposals into innumerable further alternatives. For example, you could do Sainte-Laguë and Overhang Correction. That’d be a lot of work to go through every possible alternative though!

The main reason I do these hypothetical comparisons is that I’m a massive nerd who enjoys playing with voting systems. However, this was a second Holyrood election in a row in which there was a lot of discourse surrounding the flaws of AMS and possible reforms. Four weeks on from the election and we’re still seeing those kinds of discussions, and I wonder if there is perhaps space now for some kind of reform.

I’ve therefore got one more alternative to discuss – but rather than do so in this piece, it’s worth talking about it as a stand alone item. Whereas some of the hypotheticals here are too small to make much difference, and others are likely too dramatic to be adopted, this one involves a number of changes that I think could credibly be adopted, without massively overhauling the system.

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