As we continue our foray into the dense ticket of myths, misunderstandings and misinformation about the Additional Member System (AMS) used for elections to the Scottish Parliament, another factoid that frequently arises is the notion that, to garner more indy seats, it is more ‘efficient’ to vote for a small indy list party instead of the SNP. In order words, the SNP has all but ‘maxed out’ on the list, and thus the only viable way to increase seats for the pro-independence contingent in Holyrood is to vote for one of the new minor list only parties (obviously only the one particular party supported by the person making said claim!).

Again, this is typically stated as a fact on social media, with no attempt made to establish to what degree it is true, if at all.

The assertion is usually made in conjunction with the claim that the four list seats won by the SNP in 2016 was a ‘waste of votes’ (which will be addressed in a subsequent article) and accompanied by superficially appealing calculations of ‘votes per seat’ (which naturally ignores the fact that list seats are allocated in order to effect a proportional overall result: the obvious consequence of this is that if the SNP list percentage was lower, these seats would start to fall prey to unionists instead).

Thus, on the assumption that it is all but ‘impossible’ for the SNP to gain (many) more list seats (which we will see is simply not true, as the seats won will increase with the list percentage: the lower number of SNP seats won in 2016 was precisely because its list share was 5% lower than its constituency percentage), then the only viable option for adding to the tally of indy list seats is to vote for an indy list party, right?

Again, this is an assertion that sounds perfectly logical, has the hallmark of truth, and is thus readily swallowed by swathes of indy social media without a second’s thought.

To dare question this assertion, or even the very notion that a fringe indy list party is the Golden Ticket to Independence, is seen as perverse, or indisputable evidence that you are fifth columnist who is trying to sabotage independence (I kid you not). The fringes of the online Yes movement are descending into a paranoia driven madness.

Thankfully, data analysis does allow us the ability to identify the truth behind the rhetoric: to separate the numerical reality from the baseless assertion: we find that, like all the other claims from ‘tactical voting’ to target ‘only unionist’ seats, to instant ‘indy supermajorities’, when you actually look at the facts (analyse the data and model various scenarios) the castle of sand collapses.

However, some list party devotees see the ISP not as an SNP ally, but overtly as an opponent of both the treacherous SNP and the nefarious Greens, as they both are Not Committed to Independence, you see:

Certainly not exactly a message to inspire SNP voters to defect…

The List

As mentioned, the list seats are awarded to try to make Holyrood more proportional — parties which fail in the constituencies will gain seats on the regional lists so as to ensure their representation in parliament more or less reflects their vote share (it’s not perfectly proportional, as less than half of MSP seats are elected through the list, and the regional basis of these lists effectively imposes a threshold of 5–6% to elect a single MSP, thus excluding minor parties).

The 2016 result has proved to be singularly catastrophic in terms of indy supporters’ understanding of the working of the AMS electoral system. The mantra of ‘four seats on 953,587 votes proves SNP2 is a wasted vote’ has led not only to a complete fossilisation of mindsets, but a failure to enquire — or to even want to enquire — ‘behind the headline’ and accept the situation is not as clear cut as it may seem.

‘Just Four Seats’

The number of list seats won by the SNP will be examined in greater depth in my next article: in summary, in 2016, the SNP won ‘only four seats’ because its list vote was about 5% below its constituency percentage. It won four seats precisely because its list percentage was too low. Had the SNP’s list vote percentage matched its constituency percentage, then it could have more than doubled the number of seats won — 9 instead of 4 — giving the SNP an overall majority (of one):

And if the SNP list vote continues to rise, it will win more list seats to reflect that — there is no ‘limit’ on the number of list seats the SNP can win other than that given by its percentage share of the vote.

The Panelbase poll of June-July 2020 again predicts the SNP will win four seats — and again because its list percentage is 5% below the constituency percentage. If the SNP’s list percentage matched its constituency one, then more seats would be projected: a dozen by my modelling, in every region bar Lothian, proving that the SNP’s list hopes are not confined to just a couple of regions.

What’s a Seat ‘Worth’?

Given that the factoid of ‘a million votes for four seats’ is something many indy supporters seem incapable of getting past, let’s take this on face value for the moment.

Looking at Scotland as a whole, using predictions form the latest Panelbase poll, the calculation of ‘votes per seat’ would be as below (obviously this is an entirely facile interpretation of the Additional Member System, which fails to take into account the fact that list seats compensate for lack of representation in the constituencies, but we’ll overlook that for the present).

Thus, ranked from least to most ‘votes per list seat’, we have:

GREENS — 18,057
LABOUR — 20,747
CONSERVATIVE — 46,858
SNP — 285,376

(Again, this is abolutely not the calculation we should be focusing on — it’s whether the percentage of seats a party has in parliament reflects its percentage share of the list vote: thus it is inevitable that parties which succeed in constituencies will have a much larger ‘voters per seat’ ratio than those which don’t.)

But the reason we are looking at these votes per seat ratios is this: for Yessers who place value in this determination of a vote’s ‘value’ (how many votes on average a party needs to win a single list MSP), then a corollary of that is we can model exactly how many more votes it takes to elect additional indy MSPs.

In other words, since we are making predictions based on the most recent poll, how many more votes would the SNP need to win extra seats, compared to how many votes fringe indy list parties would need to win seats?

The assertion made by supporters of the list parties is that it is much more ‘efficient’ to vote for them — i.e., your vote is much more likely to translate into a seat than if you just added on more votes for the SNP.

But is this actually true? Thankfully, using the latest polls, we can model scenarios where we can calculate exactly how many more votes would be required for both SNP and one or more fringe list parties to gain seats, and see which really is more ‘efficient’.

Extra Seats for the SNP

To get a benchmark for the SNP, let’s see exactly how many more votes are required to win extra list seats, using the latest Panelbase poll. Keeping the unionist vote as predicted (so as not to give the SNP an easier time of it) let’s just increase the SNP vote from the indy alternatives, adding in RISE and Solidarity and we find that a swing of 5.5% of the Green vote is required to add on the first seat:

We’ll continue our modelling until we gain five extra seats for the SNP:

Here’s a summary table showing how many extra votes are needed for each additional seat, together with the increase in the share of the vote:

We can see, as would be expected due to the balance of votes among the parties, that the increments in the vote needed to gain these extra seats varies widely (we will see this will also be true of list parties). This is why we need to pay attention to the mean votes per extra seat figure.

We can also see that the mean votes per extra seat decreases as the SNP vote rises, showing that the SNP has far from ‘maxed out’. Indeed, as we will see in a future article, the apparent ‘plateau’ of four list seats for the SNP (leading to the ‘million votes for four seats’ factoid) is a direct consequence of the SNP’s list percentage share being below the constituency percentage share.

I can already hear the comments — but what about the 285,000 votes per seat for the four seats the SNP is starting with? The answer is simple: this is the position where we are starting from, not where devotees of minor list parties would like us to start from. The point at issue is — from the status quo — which is the more ‘efficient’ way to gain extra seats for the independence bloc?

That said, you’ll also notice, taking the SNP’s seats in total, that the mean votes per seat has more than halved, from 285,376 to 135,646.

One List Party

Now we have an idea of how many votes it will take to win extra seats for the SNP (using the Panelbase poll as our model), and the votes per seat for each, let’s do the same for minor indy list parties.

Let’s start with just one (larger) minor list party (in reality, we now have a plethora of fringe indy list parties vying with each other to be The One which will usher in the fabled indy supermajority).

We’ll call it Party X (the identity is irrelevant, as we’re just modelling the arithmetic).

How many votes are needed for Party X to win its first seat, and so on, up to five? And how does the mean votes per seat ratio vary — and compare to the SNP?

To investigate this, we’ll again keep the unionist parties intact and transfer votes from the SNP (we are looking purely at the seat results for Party X, and the expected loss of SNP seats as votes are removed is not pertinent here).

Obviously, voters have no way of knowing in advance of the results in which region this first seat will come. With modelling based on this poll, the first seat for Party X comes after 103,807 votes:

We continue on (as with the SNP) until we get to our five seats. (I am limiting the discussion to five seats since, to win more, Party X would no longer be a ‘minor’ party, but polling with the Lib Dems and Greens at 5% and beyond.)

Here is a summary of the votes, percentage vote share increases, and the important mean votes per extra seat (starting from zero in this case):

Given the existence of the effective regional list ‘threshold’ of about 5%, we can see that Party X needs over 100,000 just to win its very first seat. Then, as we would expect, the mean votes per seat decreases (the increment being eratic as with the SNP).

So 127,734 extra votes have won five seats for Party X, putting the indy bloc just two seats ahead.

But, we need to ask, what could the SNP have done with 127,000 extra votes? Let’s see:

Eight extra seats instead of five. (Yes, the indy bloc is two seats down, as I have left the unionist parties intact and used Green votes only as a source of SNP votes for the algorithm, but the focus of this article is vote ‘efficiency’.)

Two List Parties

The above example reflects a situation where there is only one significant additional indy party — in fact, to gain its first seat, it is almost level pegging with the Lib Dems, so it can’t be considered a ‘minor’ (sub 5%) party any more. Should any new party attract such levels of support, polling will naturally reflect it: until then, it cannot be considered a serious proposition.

But we have now a situation where RISE/SSP and Solidarity have been joined by the AFI and ISP (leaving aside a putative ‘Wings Party’). Thus we have perhaps four fringe indy list parties of various hues scrabbling for votes at the bottom of the barrel, and potentially wasting votes that could otherwise help the SNP or Greens win seats.

For our next scenario, let’s assume that RISE hasn’t risen, Solidarity are stuck on the 0.6% of 2016, and that instead we have two larger minor parties (AFI and ISP) competing against each other (as well as against, obviously, everyone else).

I’ll spare you each step, but, as you’d expect, with two minor parties, it takes even more votes between them to gain seats. As SNP votes are split almost evenly between them, we simply cannot know till ‘the results are in’, which of the two parties, if any, win seats and in which regions. Therefore we have to sum the votes for the two parties in order to see how ‘efficient’ it is if you take a gamble on either the AFI or ISP, with no possible prior knowledge of which is likely to come out ahead and where.

We see that with indy votes no longer going to a stronger Party X, and instead being split between Parties X and Y (AFI and ISP here), it takes even more votes until a first seat is won.

Remember, the SNP won its first ‘extra’ seat with 35,175 more votes, while Party X needed 103,807 to cross the ‘threshold’: here we see that, with two parties, over 200,000 votes are needed just to gain one of the two parties its first seat!

In order words, it would take 17.5% of the actual SNP list vote for the two competing indy list parties to enable just one of them to gain a single seat!

And remember from earlier, the SNP could win an extra eight list seats with 127,000 votes: just imagine what it could do with 200,000 extra votes!

Now let’s look at the mean votes per seat figures. As expected, these decline as more seats are added, but even when five seats are gained, the figure for two minor parties is over three times that of the SNP to gain its extra five seats: 48,217 compared to 15,862.

With our modelling complete, let’s look at a summary of just how many extra votes it will take to win extra indy seats. Which is the most ‘efficient’?

At every stage — from the first extra seat to the fifth — it takes fewer votes to elect an additional SNP list MSP than it does to elect one from Party X, or one from two competing minor parties X and Y.

To elect just the first Party X MSP would take almost three times the vote required to elect one more for the SNP (103,808 against 35,175).

To elect the first MSP from two competing minor parties would take almost six times the vote needed for that one extra SNP seat (200,562 against 35,175).

These huge gaps still persist when we get to five seats, with Party X needing over 60% more votes than the SNP, and Parties X and Y needing over three times the votes needed by the SNP (241,086 against 79,308).

We can thus readily see that the assertion that a list party is a more ‘efficient’ way of gaining pro-indy seats is just another social media factoid that crumbles to dust the moment it is tested.

It’s bad enough with one extra list party, but having two or more is a potential strategic disaster. Remember, it took over 200,500 votes split between two competing list parties just to gain one seat: this means that potentially 200,000 indy votes could be binned on fringe indy list parties for nothing, zilch, nada. No, correct that, even worse than that, as it would mean the SNP or Greens ‘losing’ seats they could potentially have won, had indy votes not been wasted on parties that stood no chance. Only unionist parties would be the winners here.

Conclusion

We can see that AMS favours larger parties: a larger party has to add a much lower number of votes to gain an additional seat, compared to a minor party looking to gain its very first.

Obviously the calculations above will vary from poll to poll, but the bigger picture is that the orders of magnitude in terms of votes needed to gain additional seats will remain on a par: it will always take more votes for one or more minor list parties to get off the ground than for the SNP to add to its tally.

This in-built bias in AMS that effectively rewards larger parties and penalises smaller ones can also be seen in the table below, showing the actual percentage shares of votes and seats for every party in every Holyrood election since the first in 1999:

One can see that the winner of every election, whether Labour or the SNP, has been rewarded with a greater percentage of the seats than percentage of the vote actually won (Labour by 7% in 1999 and 2003, the SNP by 4.5% in 2007, almost 9% in 2011 and over 4% in 2016):

Similarly, the ‘losers’ tend to have a reduced share of the seats compared to their percentage share of the vote.

Whether we like it or not, AMS does built in an advantage for the largest party.

Returning to the original topic of this article, Yessers who fixate on and can’t see past the idea of ‘votes per list seat’ need to examine this very simple question:

If you actually stop to think about this for a moment, what exactly would lead to, for example, the Tories increasing their list votes/seat ratio and the SNP lowering theirs?

Answer: the Tories winning constituencies from SNP, which I presume we can all agree is a bad thing?

‘Voter per list seat’ is an utterly irrelevant statistic to focus on: what matters is who wins the most seat.

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