Law Thirty-Six

You gotta go with what works

Electoral Maths

| 0 comments

So the election is over, and depending on your political view point we’re destined for five years of good government, five years of bad government, or five years of it doesn’t really matter because they’re all as bad as each other.

As the results started to come through, it became clear that UKIP’s share of the vote wasn’t going to turn into a significant number of seats. Commentators started making a comparison with the SNP – UKIP got 3.9 million votes and turned this into 1 seat; the SNP got 1.5 million votes and 56 MPs.

The problem with this comparison is that the SNP only contested the 59 seats in Scotland, where they got 50% of the vote, over double Labour’s share in the region. UKIP contested 41 out of 59 seats in Scotland and got 1.6% of the vote. But even if you look just at Scotland, 50% of the votes for 95% of the seats.

The Independent put together a chart of what the make up of Parliament would have looked like under “a proportional voting system”:

There are a number of different proportional representation systems, and the model above simply assigns seats according to the national share of the vote. For those who can remember 2011, the UK had a referendum on a different form of PR – Single Transferable Vote, where you rank candidates in order and if your first choice candidate comes bottom of the list, your votes are transferred to your second choice candidate. The result of the referendum was this – a fairly categorical decision that the country did NOT want to use STV:

But let’s continue anyway, reminding ourselves that if the election was being held under a PR system, people may have voted differently, so the analysis that follows is likely to be about as accurate as an opinion poll. Based on how STV works, we don’t have the data to be able to work out what might have happened under that system, but with UKIP coming second in 118 constituencies, it’s possible that they would have done well under an STV system.

The Independent’s chart accounts for 626 of the 650 seats, which made me wonder what the impact might be on the smaller parties. For comparison, this is what we got on the First Past the Post (FPtP) system:

FPtP

And this is what we would have got if you take the national vote for each party and apply it using a simple Proportional Representation (PR) model:

 

PartyFPtPPRChange
Conservative

331

240

-91

Labour

232

198

-34

UKIP

1

82

+81

Lib Dem

8

51

+43

SNP

56

31

-25

Green

1

25

+24

DUP

8

4

-4

Sinn Fein

4

4

=

Plaid Cymru

3

4

+1

SDLP

3

2

-1

Ulster Unionist

2

2

=

Alliance Party

0

1

+1

TUSC

0

1

+1

National Health Action

0

1

+1

Traditional Unionist Voice

0

1

+1

Respect

0

1

+1

Others

1

2

+1

 

The Conservatives and Labour do much worse under this model; the Liberal Democrats are in fourth place but have a substantial number of MPs. UKIP and the Greens do very well out of the deal. And the SNP ends up as a significant player but with its number of MPs nearly halved. When you look at the smaller parties, the DUP does badly but the other parties in Northern Ireland are more or less unchanged.

Among the very small parties, we end up with more ‘Others’, notably George Galloway, who did enough in his ballot to get a seat based on his share of the vote. My approach here was to allocate seats to the parties whose vote gave them less than 1 seat in descending order of votes until I ran out of seats.

So where did the seats for the SNP and DUP ‘go’? Notably, these are both parties the stand in a limited number of constituencies within a specific region. And this simple PR approach has done something subtle here – instead of allocation 40 seats to Wales, 59 seats to Scotland and 18 seats to Northern Ireland, we’re allocating seats based on number of votes cast – which will be a product both of the size of the electorate in each region and the turnout. In this election we saw an above average turnout in Scotland but a below average turnout in Northern Ireland.

It turns out that during this election, Wales and Northern Ireland both lose out under this model:

EnglandWalesScotlandNorthern Ireland
Number of seats – FPtP

533

40

59

18

Size of electorate

38811622

2282297

4094784

1236683

Turnout – 2015

25571209

1498433

2910465

718103

Turnout – 2015 (%)

66%

66%

71%

58%

Number of seats – PR

541

32

62

15

Change

+8

-8

+3

-3

 

You can reduce the impact of this by calculating your seats on a regional model instead – taking the share of the vote in England and apportioning its 533 seats accordingly, then doing the same for the other three regions.

 

PartyFPtPPR (Nat)PR (Reg)Change (Nat)Change (Reg)
Conservative

331

240

239

-91

-92

Labour

232

198

198

-34

-34

UKIP

1

82

81

+81

+80

Lib Dem

8

51

51

+43

+43

SNP

56

31

29

-25

-27

Green

1

25

24

+24

+23

DUP

8

4

5

-4

-3

Sinn Fein

4

4

4

=

=

Plaid Cymru

3

4

5

+1

+2

SDLP

3

2

3

-1

=

Ulster Unionist

2

2

3

=

+1

Alliance Party

0

1

2

+1

+2

TUSC

0

1

2

+1

+2

National Health Action

0

1

1

+1

+1

Traditional Unionist Voice

0

1

0

+1

=

Respect

0

1

1

+1

+1

Others

1

2

2

+1

+1

 

The Northern Ireland parties see a slight improvement under this model. The SNP does slightly worse because it no longer gets an advantage from Scotland’s higher turnout. And of course if we were doing this ‘properly’, we’d break England down into regions rather than considering all 533 seats in one lump.

Either of the PR systems ends up requiring a coalition to form a government – and based on historical voting in general elections, that would be the norm. Since 1880, there have only been four elections where a single party achieved over 50% of the vote (in 1886, 1900, 1931 and 1935).

If these votes had been cast in a PR-based election, the Conservatives would still have been the largest party and constitutionally would have been the ones to try to form a coalition first. The third largest party would have been UKIP, and their combined seats would have been just short of the 325 MPs needed, so they’d need some further support from one or more of the other parties, but potentially could have formed a government. Instead of resigning as his party’s leader, Nigel Farage would probably be Deputy Prime Minister. Labour, on the other hand, would not have enough seats even if it managed to assemble a coalition with SNP, the Lib Dems, and the Greens.

Would that be a better result? Well, that’s what the Comments box is for below – you decide!

Leave a Reply

%d bloggers like this: