Holyrood: How does the Additional Member system work

Members of the Scottish Parliament are elected by a proportional system know as AMS (Additional Member System).    The official explanation is here but I'm going to try to explain with a minimum of maths and in as simple a way as I can. 

Scotland is divided into 8 regions and as well as 73 constituency MSPs being elected, each Region elects 7 list MSPs.    The constituency MSPs are elected by first-past-the-post, the same system used for UK General Elections.   But in addition voters cast a vote against a Party on the Regional List. 

The list MSPs in each Region are allocated to adjust the total number of MSPs (constituency and list) to reflect the party share of vote as cast in the Regional (list) ballot.  Sometime people refer to the constituency as the first vote and the list as the second.  I think that confuses.  

Now, you'll quickly realise that with only 7 seats to adjust a result, it's pretty likely that the result will only be roughly proportional.  Typically a Region has 8 constituency seats (the pre 1999 Westminster constituencies, but with Orkney and Shetland each having their own MSP) so with 7 List seats, that is a total of 15.  Roughly speaking a party should get a seat if they can gather more than about 6.5% of the vote (100%/15 =6.66%).  So it'll be a bit 'lumpy' and until a party starts getting over the ~6% bar, their votes wont get them a seat even on the list.

But we currently have one party, the SNP running at about 50% for the constituency vote.  That should enable them to make a near clean-sweep of the constituencies.  Most estimates put the actual likely number at 67 to 68.   That would given the 53% of the seats. 

The SNP do not do as well on the Regional list vote.  There is no reason to tactically vote in the Regional list (unless you know your preferred choice will stand no chance of getting more than 6.5% of the vote).  So, we have developed a remarkable sophisticated electorate who are very clear that while they will vote SNP 49% in the constituency, that drops to 43% for the Regional List.  Fr the Greens, only 2% will vote for them in the constituency vote if they are given the option, but that rises to 8% for the Regional vote - reflecting the reality that Regional list seats is where a small party is likely to win.  

Take an average Region (if there is such a thing!).  The SNP win all the 8 constituency seats on 50% of the vote.   That gives them more than their fair share of the seats so they shouldn't be entitled to any of the top up list seats.  These 7 seats then get allocated between the other parties in proportion to the other parties list vote. 

So imagine that the Regional vote is 43% SNP, 25% Labour, 15% Tory, 8% Green, 5% LibDem and 2% UKIP. 

We can ignore the SNP as they already have more than 43% of the seats and therefore shouldn't get any extra. 

So how do we divide the 7 seats between the others? 

Let's just guess at a fair distribution (there is something called Modified D'Hondt that is the mathematical way to do this but I'm not going there).   Let's give Labour 3, Tories 2, and 1 to the Greens. 

Now what % of each Party is needed to get 1 MSP on that distribution?  8.33% Labour, 7.5% Tory, 8% Green.  But we've only allocated 6 of the 7 MSPs available. 

So who gets the 7th?  The answer is whoever it makes the least difference to the % per MSP figure, which in this case would be Labour - who then get 1 MSP for each 6.25% of the vote.  Not too far off the one seat per 6.5% of the vote we calculated above.    

Let's just check the SNP wouldn't be entitled to the 7th list seat 43%/8 = 5.35% already so Labour have higher % per MSP even before a 9th SNP member.  The 9th SNP member would be behind the LibDems in the queue at 43%/9 = 4.8% of the vote.  

The SNP Regional vote doesn't come into the equation.   These votes have no effect on the number of SNP seats gained.   However, they could have an impact if they voted for one of the other parties.

Imagine that enough SNP voters realised this to mean that instead of 8% of the vote, the Greens got 16% of the vote. 

Our first off guess of seat allocation would then be Labour 3 (8.33%), Tory 2 (7.5%), Green 2 (8%) and that neatly uses the 7 seats.   The net effect is to deny Labour a seat and add one to the anti-austerity pro Indy voice to the Scottish Parliament.    

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