In my last post I talked about PR within the UK and how the Houses of Parliament would change if we moved to a pure PR system. To briefly recap this is the way things look right now.

And this is the impact that you’d see from a pure PR system.

On a facebook thread someone suggested investigating how this would change if we used the German parliamentary rules instead. You’d think this would be relatively simple, but I’ve discovered that it’s not the easiest system to work out, even with the help of a few German friends. The following article will work through a German approach to UK polling numbers to work out how parliament would change if we used the Bundestag rules. If you’d like more detail feel free to check out the wikipedia article on the German Electoral System which I’ve used heavily!

**Two Votes**

First up everybody in Germany gets two votes. These are known as the “vote for person” (fur die Wahl eines Wahlkreisabgeordneten) and the “vote for party” (fur die Wahl einer landesliste (Partei)). German words rule. These two votes are equally important for the overall result but operate completely differently.

The first vote directly elects constituency MPs in the same way that a vote in a UK parliamentary election would. Half of the seats in the Bundestag are settled like this. The second vote sets the proportion of MPs from each party who will sit in the Bundestag when all votes are settled. The second half of the seats are then filled using the PR system, with MPs nominated from a party list.

Let’s break down how this would work in a hypothetical German UK election.

**Vote For Person**

The UK parliament currently has 650 constituencies. Let’s cut that down to half, leaving us with 325 constituencies. This leads to the following number of MPs being elected from the first round…

The first calculated column allows for half-MPs, but I’m guessing that most people would accept that cutting MPs in half would be a little unfair. Instead I removed all the half-MPs and redistributed the 3 seats to the Speaker, and the two largest parties who suffered from the rounding (Plaid + SDLP).

That was painless right?

**Vote For Party**

The second vote the Germans get sets the proportional weightings for the Bundestag. This also has an interesting filter to prevent representation for parties who poll less than 5% of the vote. Amusingly in the UK this would eliminate the SNP, but sadly, there’s another rule that parties with 3 Constituency MPs from round 1 then get to take part in the PR round. So the SNP qualify for round 2.

In total 5 parties qualify from 3 seats or more. The Conservatives, Labour, The Libdems, The SNP and The DUP. Additionally UKIP qualify by getting 12.7% of the popular vote. Rather sadly, the Green party only polled 3.8% of the national vote in 2015, and so they don’t get to take part in the PR round.

Now we’re down to 6 parties, lets work out what the PR system gives each party.

This time round you’ll notice that the total number of MPs is 650. That’s because the second round is used to calculate the total number of seats a party should get across the entire parliament.

**Fractional Seats**

You’ll also notice that we’ve got some pesky fractions again. In my last article I rounded all numbers to integers. We’ll call that the Penfold Method. There are two seperate methods that have been used in German elections. Up until 2008 these fractional seats were resolved using the Hare-Niemeyer method. In that case the seats are awarded in order of the party that has the largest fraction.

Since 2008 the Germans have used the Sainte-Lague/Schepers method. That ensures that the fractions are awarded in such a way to equalise the number of voters who are represented by each party. The mathematical details of this are amusing and deep, so I won’t detail them, but this is the number of seats each party gets according to the three methods.

So you can see that despite the complexity of the SL/S method, it ended up with exactly the same attribution of MPs as the H-N method, and they both ended up with the same result as rounding the numbers. That’s a bit of a fluke, in most elections this doesn’t happen!

**Final Seat Allocation**

To work out the final seat allocation we now have to take the proportional seats that each party has received, and work out how many seats are allocated from the party list. To do this we take the PR number, subtract the seats from round 1, and then allocate the remaining seats from the party list.

That gives us the following number of seats allocated from round two.

You’ll notice that we have a few negative numbers here. That’s because the smaller parties haven’t been allocated any seats from the Votes for Party. These remaining constituency seats are known as Overhang seats, and remain allocated from the vote.

In this case then, all those constituency seats remain, and we now end up with a slightly enlarged parliament of 658 seats split up in the following way.

This time round the UKIP/Tory block has 349 seats, requiring 329 to form a majority thanks to the Overhang seats. This is a bit of a clearer margin of victory than under the PR system where the parties end up with exactly 325 seats. A hung parliament!

The biggest proportional loser under the German system, ironically, is the Green party. They go from 1 seat under current rules, and 25 under true PR, to exactly zero under the German voting system. Ho-hum.

Here’s a summary of the wins/losses under each system for each party.

**Party List Revisited**

The assumption I’ve made above is that all voters would pick their party vote to match up to their constituency vote. In practice people often vote tactically in a UK election to block certain constituency MPs. If we had a two vote system there would be no point to tactically voting with the second vote, and so typically you get a more diverse set of parties represented under the party vote.

In the last German election the two main parties CDU and SDP received 8.1% and 12.4% less votes on the Party list than on the constituency list. Meanwhile the Human Environment Animal Protection party polled an enormous 3063% more votes on the Party list. In terms of comparable parties to UKIP you have the AfD increasing their party list vote by 153.66%. The greens also receive a boost on the party list of 16.15%.

**So should we?**

There’s a deep part of me that can’t accept that a German system might give a better result than a British system. If you’re like me, then don’t worry, it turns out the Brits came up with the German system after the war*. So actually, we’ve just experimented with it on the Germans for 70 years. After a successful period of testing we can now conclude that this is indeed a better system and implement it back at home**.

There are a number of significant positives from the German system. First off, around 20% of the electorate are barely represented in parliament right now (Libdem + UKIP) and under this modified system those individuals would finally have a voice in parliament. A further positive in my view is the reduced weight given to regional nationalists. For the future of the United Kingdom it’d be good to see this happen.

On the negative side I’m not keen on the Green Party slipping out of parliament entirely. I guess we’d have to hope that the Greens would see a significant uplift on the party vote. I’m also concerned that while regional nationalists would be reduced, the UK wide nationalist vote would increase.

Overall it’s hard to argue against better representation for voters. Ultimately if I did want a LibDem in parliament, or a UKIP MP (!), then it’d be nice to feel that my vote mattered…

** – as far as I can tell it isn’t actually true that the Brits came up with the German MPP system. What actually happened was that there was a conference in London involving France, the UK, USA, Luxembourg, Holland and Belgium. During this conference it was decided that the three sections of Germany held by the UK, FR and US should be merged into a West German state. The Frankfurt documents were written containing an outline of the approach that should be taken to form the West German state. These documents were then handed to the Germans who came up with the basic election system currently known as MPP. But it’s a good yarn…*

*** – it turns out that MPP is already used to elect the devolved assemblies of Scotland and Wales.*