Tag Archives: D’Hondt

So what about that second vote?

This all started on Twitter. Some people were talking about how best to use their second vote in the forthcoming Scottish parliamentary elections and since I didn’t actually understand how the voting system worked I just lurked until it dawned on me that they didn’t know how the system worked either. I asked a couple of people offline. They didn’t know either. So this post is my attempt to explain how the Scottish electoral system works. In a subsequent post I’ll attempt to understand what this example tells us about the second vote.


The Scottish Electoral Systems

There are two different electoral systems used to elect representatives to the Scottish Parliament.

It all begins with the constituency votes. There are seventy-three constituencies in the Scottish elections (different from the Westminster boundaries) and each of these constituencies elects a single representative based on a first-past-the-post system (FPTP). The FPTP system is just one of several of what are known as ‘plurality systems’.

The electoral system used for the regional ballot for the Scottish Parliament is called the Additional Member System. This is a variant of the D’Hondt system with the the number of seats won in the local constituency FPTP vote taken into account in the calculation. So although the number of votes for each constituency candidate has no bearing on how regional members are elected, the number of constituency seats that each party gains in a region plays an important part.

Before going any further, this BBC video gives a good explanation of the standard D’Hondt system.

Right, back to Scotland, where it’s done a little bit differently.

There are currently eight regions in Scotland. These are :-

  • Central Scotland
  • Glasgow
  • Highlands and Islands
  • Lothians
  • Mid Scotland and Fife
  • North East Scotland
  • South Scotland
  • West Scotland

Each of these eight regions provides seven regional, or list, MSPs (a total of 56 if you didn’t do the arithmetic) which when added to the 73 constituency MSPs gives us a grand total of 129.


North East Scotland, 2007

So since Pol asked.

In the 2007 North East Scotland region, the constituency results were:-

  • Labour – 1 seat
  • Liberal Democrats – 2 seats
  • SNP – 6 seats

It’s only when we know the constituency results that we can start to calculate the regional results.

The number of votes cast on the regional list in North East Scotland in the 2007 election were:-

  • SNP 105,265
  • Labour 52,125
  • Conservative 37,666
  • Liberal Democrat 40,934
  • Scottish Green 8,148
  • SSP 1,331
  • Solidarity 2,004
  • Scottish Senior Citizens 3,874
  • BNP 2,764
  • Scottish Christian 1,895
  • UKIP 1,045
  • Christian Peoples 941
  • Scottish Voice 569
  • Scottish Enterprise 569

For the sake of simplicity I’m going to disregard any party below 4,000 votes. This makes no difference to the calculation or the overall result. In the spreadsheet I’ve included the Greens, the SSP and Solidarity because I want to do some analysis in a later post.
So for now we’re only dealing with:-

  • SNP 105,265
  • Labour 52,125
  • Liberal Democrat 40,934
  • Conservative 37,666
  • Scottish Green 8,148


Getting Started with D’Hondt

Round 1

Before we can actually say who has won Round 1 we need to apply the standard D’Hondt formulation to the regional votes of the parties that won constituency seats. The standard D’Hondt formula is

q = V / (s+1)

where

  • the quotient q is the number of votes to be accounted for in the first round of AMS;
  • V is the number of regional votes for the respective party;
  • s is for the total number of seats; and
  • (s+1) which is known as the ‘divisor’

So because the SNP did particularly well in gaining 6 constituency seats their regional vote tally is reduced by the divisor (6+1) to 15,038, and the same is then done for the Liberal Democrats (2 seats) and Labour (1 seat) because they were the only other parties that won constituency seats.

Screenshot 2015-09-20 at 07.41.35

image

And, hopefully the chart shows the formula has used the constituency seats to provide a more regional average.
Technically, the formula is applied to the vote share of every other party on the regional list even if they didn’t win a constituency seat. The Greens can be used as an example

q = V / (s+1)
q = 8148 / (0+1)
q = 8,148

And it’s because they didn’t win any constituency seats that they have 0 entered into the formula. This means that unlike the parties that won constituency seats the Greens enter the first round of the regional vote with all their regional votes. And that’s the same for the Tories and every other party on the list that didn’t win a constituency seat.

So here we go.
In the first round the North East Scotland regional tallies were:-

SNP 15,038
Labour 26,062
Conservative 37,666
Liberal Democrat 13,644
Scottish Green 8,148

Result: the Tories have the highest share, and so win the first round, and gain a seat.

Round 2

Before we can work out who has won Round 2 we need to apply the D’Hondt formula to the winner of Round 1 which as we’ve just seen was the Tory vote.

So for the Tory vote going into Round 2, their tally is reduced using the formula to 18,833

q = 37666 / (1+1)
q = 18,833

The tallies of the unsuccessful parties in the previous round are unchanged for this round.

So, here we go again.
In the second round the North East Scotland regional tallies were:-

SNP 15,038
Labour 26,062
Conservative 18,833
Liberal Democrat 13,644
Scottish Green 8,148

Result: Labour now have the highest share and so they win their first regional seat, and increase their overall number of seats to 2.

Round 3

Before we can work out who has won Round 3, we again need to apply the D’Hondt formula to the winner of Round 2 which as we’ve just seen was Labour.

So their tally going into Round 3 is reduced, using the formula, to 17,375
q = 52,125 / (2+1)
q = 17,375

The tallies from the unsuccessful parties in the previous round are again unchanged from the previous round.

So, here we go again
In the third round the North East Scotland regional tallies were:-

SNP 15,038
Labour 17,375
Conservative 18,833
Liberal Democrat 13,644
Scottish Green 8,148

Result: the Tories again have the highest share, and so win their second regional seat, and increase their overall number of seats to 2.

Round 4

Once again, before we can work out who has won Round 4 we need to apply the D’Hondt formula to the winner of Round 3 which was the Conservatives.

So the Tory share going into Round 4 is reduced, using the formula, to 12,555
q = 37,666 / (2+1)
q = 12,555

The tallies of the unsuccessful parties in the previous round are again unchanged for this round.

So, here we go again,
In the fourth round the North East Scotland regional tallies were:-

SNP 15,038
Labour 17,375
Conservative 12,555
Liberal Democrat 13,644
Scottish Green 8,148

Result: Labour again have the highest share, and so win their second regional seat, and increase their overall number of seats to 3.

Round 5

Hopefully you’re starting to see the pattern here.
Once again, before we can see who has won Round 5 we need to apply the D’Hondt formula to the winner of Round 4 which was the Labour.
So going into Round 5, the Labour tally is reduced using the formula to 13,031

q = 52,125 / (3+1)
q = 13,031

The tallies of the unsuccessful parties in the previous round are unchanged for this round.

So, here we go again.
In the fifth round the tallies in the North East Scotland region were:-

SNP 15,038
Labour 13,031
Conservative 12,555
Liberal Democrat 13,644
Scottish Green 8,148

Result: the SNP have the highest share, and so win their first regional seat, and increase their overall number of seats to 7.

Round 6

Once again, the D’Hondt formula is applied to the winner of the previous round which was the SNP. So going into Round 6 the SNP tally is reduced, using the formula, to 13,158
q = 105,265 / (7+1)
q = 13,158

The tallies of the unsuccessful parties in the previous round are again unchanged for this round.

So, here we go again.
In the sixth round the tallies in the North East Scotland region were:-

SNP 13,158
Labour 13,031
Conservative 12,555
Liberal Democrat 13,644
Scottish Green 8,148

Result: the Lib Dems have the highest share, and so win their first regional seat, and increase their overall number of seats to 3.

Round 7

For the last time, the D’Hondt formula is applied to the winner of Round 6 which was the Lib Dem, and their tally is reduced, using the formula, to 10,234

q = 40,934 / (3+1)

q = 10,234

The tallies of the unsuccessful parties in the previous round are, you guessed it, unchanged for this round.

So, here we go again for the last time
In the seventh and final round, the votes in the North East Scotland region were:-
SNP 13,158
Labour 13,031
Conservative 12,555
Liberal Democrat 10,234
Scottish Green 8,148

Result: the SNP again have the highest share and win their second regional seat. They now increase their overall number of seats to 8

North East Scotland region summary

SNP – 2 seats

Labour – 2 seats

Conservative – 2 seats

Liberal Democrat – 1 seat

Scottish Green – 0 seats

And that’s how it works. Once the total number of regional votes are collated, the parties that won constituency seats have their regional vote tally reduced using the D’Hondt formula. As parties start to win regional seats their tally is in turn reduced using the formula. This continues for seven rounds until all the seats are won.

As I said at the start there is no political analysis in this post. I was simply trying to explain how the AMS works in Scottish parliamentary elections. That isn’t to say that having an understanding of the system’s mechanics doesn’t lend itself it to some conclusions, but these will be in another post.

When all three posts are online I’ll put a Google Sheet which might make it easier to see what’s happening. I’ve tried to make it as easy to follow as possible.

This is the first of three posts looking at the second vote and its potential effect.

The second is So what would have happened if the SNP had voted Green?

The third has yet to be put online.

References

Scottish Parliament

Wikipedia
Wikimedia Commons
YouTube
D’Hondt Explainer, YouTube, https://www.youtube.com/watch?v=6CU3F3ToIIg