Constituencies & Lists: The Whole Truth

The latest factoid doing the rounds in the bubble that is indy social media is the correlation being implied that the more constituency seats the SNP wins, the ‘less likely’ it is to win list seats.

The implication made is that the Additional Member System (AMS) d’Hondt algorithm somehow prevents a party overwhelmingly successful in the constituencies winning many, if any, list seats. (This is akin to the false assertion that AMS is designed to prevent a majority government.)

This notion is eagerly seized upon by list party advocates as a justification to vote for their fringe list party of choice (currently AFI or ISP).

Again, confusion abounds, and a vital factor in the process is always omitted (maybe unintentionally, maybe not).

Attention is only ever paid to the fact that the starting position in the list calculations is the list vote divided by the number of constituency seats won, plus one.

There are two relevant points here:

(1) list votes aren’t ever ‘wasted’ — AMS is designed to produce a parliament more or less proportional to the parties’ percentage share of the list vote (this being a crucial aspect of the electoral system that we shall return to).

and (this is the vital factor mentioned above):

(2) no reference is ever made to the SNP’s percentage share of the list vote.

You see, the number of list seats a party wins isn’t solely determined by the number of constituencies won, it also depends on that party’s result in the list, as the overall number of seats at Holyrood is based on that second vote.

Those who have never been able to see beyond the ‘four seats of 2016’ result singularly fail to understand that the reason for the reduced number of SNP list seats was because of leakage from the SNP’s list vote: from 1.2% in 2011 to 5% in 2016. If #BothVotesSNP had been followed through in 2016 as in 2011, the SNP would have doubled its list seats and won an overall majority.

The crucial importance of the size of the SNP’s list vote is revealed by recent polling: one poll from Survation pointed to a 11% gap between the SNP’s constituency and list vote, leading to a reduced seat projection on one seat. A 5% gap tends to produce about four seats, whereas a 1% gap will double that.

Since we are examining an assertion about the workings of the AMS algorithm, as always we can ascertain the truth behind the factoid with some modelling. (We are not looking to model a realistic election outcome here, the focus is purely on examining the claim that the SNP is ‘less likely’ to win list seats — and importantly to see the effect of the SNP’s list vote share on the outcome.)

Here’s our starting point, the projection from the last Panelbase poll:

Let’s keep the SNP constituency percentage at 55%, as determined by the polling company. The projection is for the SNP to win 70 out of the 73 constituencies (the Lib Dems would win two seats, and the Tories one).

This poll had the SNP’s list vote at almost 50%, but let’s now make that equal to the constituency share (remember, this is an exercise purely to determine the arithmetical facts about how ‘less likely’ it is for the SNP to win on the list, and the importance of the list vote).

With this #BothVotesSNP scenario, the list result would look like below.

With #BothVotesSNP, the SNP now has won 11 list seats to add to its 70 constituency seats, giving a total of 81 of the 129 seat in Holyood, a supermajority of 63%. (No fringe list parties needed.)

Purely to demonstrate how the size of the list vote affects the list seat outcome, let’s increase SNP2 higher to almost 60%:

The SNP has now amassed 15 list seats, over three times the starting value of four.

It wouldn’t matter if the SNP won every single constituency — if the SNP’s list share is high enough, it will win seats on the list too.


Modelling with the algorithm used for AMS clearly demonstrates that the claim that ‘the more constituencies the SNP wins, the harder it is to win list seats’ is yet another misleading factoid pushed by list party advocates that misses out an entirely crucial part of the equation, the SNP’s list vote share.

The actual size of the SNP’s list vote in 2021 is obviously a matter of real world political campaigning and getting across the importance of #BothVotesSNP, but it can certainly be said that this factor is crucial to the SNP’s success in the list, and it is not simply a case of ‘more constituencies won = less list seats’, however much list parties would like to portray it as such.

There is nothing inherent in the d’Hondt algorithm itself that prevents the SNP winning list seats because it has swept the constituencies. This claim is demonstrably false.

When you next see this assertion on social media, you’ll now be aware of the rest of the story they’re not telling you.

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