Proportional Representation

I’m a bit of a geek when it comes to mathematics (you might have noticed if you’ve been here before), but today I wanted to look an an interesting and overlooked aspect of the UK parliamentary system.

The UK operates a first past the post parliament, like many countries around the world. This means that the entire country is split up into small areas called constituencies. Within each constituency the local people can vote for who they’d like to send to parliament to represent them. The candidate with the most votes is sent to Westminster to represent the constituency, and the party with the most MPs ends up forming the government.

This has the advantage that when you’re voting you know who could represent you. It also has some major disadvantages which I’m going to go through now.

Lets start by showing how many MPs were returned to parliament in 2015 and for which parties…


The total number of seats up for grabs was 650. That means 325 forms a government, the Conservatives got 330, and they formed the government.

One of the weaknesses of this system is that if you’re in a constituency where one of the parties has a massive lead there’s practically no point voting for anyone else. For example in my constituency David Lammy got 67.3% of the vote. Second place went to the Conservatives with 12.0%. There is literally no point in voting for anyone except David Lammy. If I’m a Conservative voter I should save the two minutes to walk to the polling station and stay at home. It’s even worse if I’m a Green voter. If I want to return a Green MP my only hope is to move to Brighton.

Proportional Representation

Let’s look at what happens if we change the system to PR. This time round every persons vote across the UK is going to be added up. The total number of votes for each party, will be divided by the total number of voters, and we’ll multiply that by 650 and round to the nearest integer to work out how many seats each party has.

This time round we get a very different outcome.


First off, due to rounding we lost 5 MPs somewhere along the line. We’ll just count that as £400K profit for the new system. Note though that the Pie Chart just changed significantly.

Winners and Losers

So what just happened? It seems like the Conservatives lost a bunch of seats, Labour definitely got smaller, and the SNP seemed to lose quite a few seats too. On the other hand we gained a purple slice that’s pretty damn big, and some smaller green and orange pies. Let’s change from a pie chart to show who won and who lost in this system.


Our biggest losers this time round were the Conservatives who just lost 91 seats. If you’re a Labour supporter that sounds pretty damn good, until you notice that UKIP are the biggest winners, and they just gained 82 seats. Eighty Two Seats!!

That’s right folks, it turns out that UKIP are actually the third biggest party in the country by popular vote.

What about that other noisy nationalist party that we’re fed up of hearing about? You know, the one run by the Krankies. Well under PR the SNP actually lose 25 of their MPs.

Lets look at another party that took a kicking at the last election. The Liberal Democrats got absolutely decimated and ended up with a mere 8 MPs. Under PR they’d have had 51 MPs. Not so bad if you support the LibDems, and the Green Party would have gone from 1 MP to 25 MPs, only 6 less than the SNP! In fact, I’d imagine that under PR these parties would do even better than this. Now there’s no need to pick between the two main parties in your constituency. Instead you can pick whomever you like, and know that your vote has the chance to tip the scales in favour of that party. True democracy!

Voters per MP

I mentioned earlier that UKIP are actually the third biggest party in the popular vote. This is easy to skirt away from as it’s not a supreme example of the democratic process at work. If you look at Westminster right now the third biggest party by some margin are the SNP. The truth is that only 1.45 million people voted for the SNP. UKIP received 3.88 million votes. That’s 2.43 million more people than voted for the SNP, and yet they’re only represented by a single MP.

To highlight how absurd this is, lets chart up the number of voters per MP returned.


The numbers here are mindblowingly big. On average the Conservatives returned an MP for every 34K voters. The SNP managed an MP for every 26K voters. Meanwhile UKIP received one MP for 3.88 million voters. That’s more than the entire voting population of Scotland…

Regional politics

That highlights one of the weaknesses of the FPTP system. Over time regional issues have started to spread into Westminster through the parliamentary voting process. Look at the DUP, Sinn Fein, UUP, SDLP and that lone Independent. These are all MPs returned by Northern Ireland. In this part of the country the troubles cast a long shadow and there are no MPs representing the traditional UK parties (Labour, Conservative, Libdem). Instead all of the MPs represent one side of the independence debate with a smattering of local politics mixed on top.

What happened to Scotland in 2015? Well the SNP are basically a single issue party, being the only major party in favour of Scottish independence. In 2014 the Scottish people had a vote on leaving the UK, which resulted in a win for the union. However the referendum polarised opinion, and the SNP managed to hang on to the independence voters at the main Westminster election. As the unionist vote in Scotland is fractured between the major parties it’s almost impossible for Scotland to return anything but SNP MPs. This will only change if the Scottish people stop caring about independence, or if a unionist party turns up in Scottish politics. In that case MPs would be returned based on their position on Scottish Independence instead of their ability to represent the Scottish people at Westminster. A never ending Independence Referendum, exactly what the SNP want!

What’s odd about this is that the FPTP system itself is embedding structural instability within the Union. We can’t starve the SNP of Oxygen as they have a huge platform at Westminster. We can console ourselves by knowing that UK-wide extremists like UKIP are successfully being kept out.

Who’d run the country?

Regional politics aside, who’s actually going to run the country? Let’s go back to the chart that shows how many seats people have under a true PR system.


I guess the two natural alliances I’d see here would be Tory/UKIP and Labour/LD. These two alliances would end up with 322 and 249 seats respectively. The Tory/UKIP alliance would be close, but they’d end up having to bring in some of the NI parties to hit the finish line.

This sounds like a pretty unstable situation. We know that minority governments often struggle to get anything done. Could you imagine the current mess if UKIP formed 25% of the government? Forget worrying about triggering article 50, the entire system would be collapsing around our ears.

And that’s probably the strongest argument against PR. Our tried and tested method of selecting governments tends to lead to relative stability. Even when Cameron threw his strop and left office, Theresa May was back at the helm within a few weeks. In other countries like Italy the government has been paralysed for years, unable to get anything done while the economy stumbles along in neutral. We have to be careful what we wish for.

Summing up

Will we ever move to a PR system? I very much doubt it. Look at the three main losers if we move to PR. The three main political parties. Why would they ever bring forward legislation that weakens their position in this way?

The other aspect of PR that I think is exceedingly damaging is the increased platform for extreme views within the UK. We might see people standing on extreme right or left platforms making their way into the house of commons. In most countries they avoid this by giving no seats to parties with less than 3-5% of the vote. If we did that, we might get rid of the SNP, but we’d still be stuck with a powerful UKIP voice.

I’m sad that the Greens and Libdems don’t have a stronger voice in UK politics, and the SNP seem to get a huge amount of airtime. But perhaps that’s a price we have to pay for a relatively stable government.

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2 Responses

  1. Roger Lipscombe says:

    There is an argument that, precisely because “fringe” votes count for nothing, people vote for the more extreme parties as a protest vote, and to ensure that those positions are considered by the mainstream parties. The argument goes that: if UKIP *really* had a chance of power, people would go “hold up”, and vote for someone less extreme.

    I’m not sure I believe that argument (it’s too simplistic), and even if I did, that’d imply that (e.g.) the Greens were seeing the same benefit from protest voting, and really would be unrepresented once everyone mainstreamed-up.

    On the other hand, democracy could be argued to be about the art of the compromise — pissing off the smallest number of people — and that coalition governments are the right way to encourage that, even if — by whatever measure — they’re less stable.

    Two random thoughts: (1) stable ~= stagnation; (2) we’re simply seeing a chaotic system with two attractors.

  2. Dom Penfold says:

    I’m pretty sure you’re right Re: Greens and UKIP getting the same boost. It’s got to be possible to get a read by looking at elections in other countries where PR is more popular. Pretty sure this kind of thing worked well for the Nazis though.

    1) Not sure about that. The lack of a stable government can also lead to a stagnant economy (Italy)

    2) Yes this. :)

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