In the wake of Sunday’s German election, I’ve lost count of the number of reports that tell their readers how forbiddingly complicated the German electoral system is. It’s a particular favorite of English media, wanting to present the continental Europeans as weird and alien, but it also seems to come from amateur election experts who want to put on airs.

Not surprisingly, such experts often get it wrong. This BBC report is perhaps the worst, telling us that “Voters rank the candidates in order of preference” and that the overhang seats are “based on the population in each states [sic] and how many votes go to the second-placed party in each.”

But even when the reports are not inaccurate, the impression of complexity is dangerous because it conveys the message that democracy is hard, and that therefore maybe countries would be better off sticking with simple systems that distort the wishes of the people and produce undemocratic results.

And it’s not true: Germany’s system is very straightforward. So for those who are interested, here’s my short explanation. (Most of this also works as an explanation of the New Zealand system; I’ll note the two differences as we proceed.)

Seats in parliament (in the lower house, that is – there’s also an upper house, which represents the states) are allocated proportionally to parties. Voters get two votes, but the one that really counts is (rather unfortunately) called the “second vote”. Every party that gets more than 5% of those votes gets a number of seats equal to their share of the vote.

There are nominally 598 seats, so if two parties split the vote 50-50 between them, they each get 299 seats. You don’t really need to know the mechanics of exactly how that’s done, but since it’s really easy – as long as you’ve got a spreadsheet you can do it in a couple of minutes – we’ll run though it anyway. (If you don’t care, just skip the next two paragraphs.)

It’s called a Sainte-Laguë calculation: in one column of your spreadsheet, list the votes received by all the parties that reached the 5% threshold. Then, in a second column, divide all those figures by some arbitrary number (call it “x”), and round the result to the nearest whole number (be sure to round the actual number, not just the way the spreadsheet displays it).*

Then add up all the numbers in your second column. If the total equals the number of seats to allocate (in this case 598), that’s it, you’re done – those numbers are the seats each party gets. If the total is too small, it means x is too big, so reduce it and try again. Conversely, if your total is too big, your value for x was too small, so increase it and recalculate. Keep doing this, adjusting x up or down, until the total comes out right.

So now we know how many seats each party gets. Half of those (299) are district seats; they go to the candidate that gets the largest number of “first votes” in each constituency. The other half are party list seats; each party nominates beforehand a list of candidates in each state that it wants to get elected if they don’t win district seats.

But the total, of both sorts of seats, is still proportional, and that’s what matters. If a party wins more district seats it gets fewer list seats, and *vice versa*. So, for example, if a party is entitled to 80 seats and it wins in 20 districts, it will get 60 list seats. If it wins in 50 districts it will only get 30 list seats.

Here’s where one of the differences from New Zealand comes in. In New Zealand, if a party wins a district seat then it’s exempt from the 5% threshold: it gets to participate in the proportional allocation of seats regardless of its overall share of the vote. But in Germany, with a much bigger parliament, a party has to win *three* district seats to get that exemption. If it only wins one or two it gets to keep them, but can’t add any list seats.

It’s not very likely that a party with less than 5% of the vote will win in three districts. But it did happen this time: the Left party (*Die Linke*) fell just short of the threshold with 4.9%, but it won three districts on the “first” votes so it got a proportional allocation of seats just like the rest. There’s also a special exemption from the threshold for parties representing national minorities: that allowed the South Schleswig Voters Association to win a seat, even though it only had 0.1% of the vote.

What happens, though, if a party wins more districts than the total number of seats it’s entitled to? New Zealand gives a simple answer to this: that party gets to keep the extra seats, but nothing else changes, and the total size of the parliament expands slightly. So there’s a small unfairness created – or, depending on how you look at it, a bonus for a party that has strong local support.

Germany (this is the other difference) gives a fairer but more complicated answer: the party keeps the extra seats, but then additional seats are awarded to the other parties as well so as to preserve proportionality. That means the size of parliament can grow quite substantially (which is why I said above that 598 was the “nominal” total), with the addition of “overhang” seats.

In Sunday’s election, the CSU (the Bavarian wing of the Christian Democrats) won 5.2% of the vote, entitling it to 34 seats out of 598. But it won 45 districts, an additional eleven seats. That meant the other parties had to all gain seats as well so that no-one was disadvantaged, bringing the total number up to 735. (There’s no reason for anyone to follow the precise method by which that is calculated, which isn’t as simple as it could be, but if you’re really keen you can find the details here.)

So that’s it. While it’s often referred to as a “mixed” system (because there are both district and list seats), that’s really a misnomer; it’s a pure proportional system, since the overall shares of the vote are what determine each party’s representation. Voters get to have local MPs as well, but the “second” votes are the ones that matter.

My view is that the 5% threshold is too high and distorts the process, because it can make such a huge difference whether a party scores just above or just below it. But apart from that I think it’s an excellent system, and it’s been a key ingredient in keeping Germany such a peaceful and prosperous country for the last 70 years (and, more recently, New Zealand as well).

But regardless of your view of its merits, don’t let anyone tell you it’s too complicated to understand.

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** Bonus point: if, instead of rounding to the nearest whole number, you round down to the number below (that is, you just ignore the remainders), then you get a D’Hondt calculation instead of Sainte-Laguë. A lot of other countries use D’Hondt; it gives very similar results, but it’s slightly more favorable to major parties. If it had been used in Germany the South Schleswig Voters Association would have missed out and the Social Democrats won an extra seat instead.*

So, what do you think would be a suitable threshold? or would you advocate dispensing with a threshold altogether? (Any threshold at all means a huge difference between scoring just above it and just below it.)

A high threshold puts a limit on party fragmentation. A low threshold, or none, doesn’t guarantee a lot of fragmentation, but it does make it possible. In the Netherlands there’s no threshold. I don’t know enough to say that the Dutch system is generally worse than the German one–the Dutch seem to have scrubbed along well enough for the most part–but at this year’s election it allowed for the kind of partisan fragmentation which a German-style 5% threshold would make impossible (or next to it), and the way consequent events are playing out doesn’t provide a recommendation.

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My default view is to tinker with electoral systems less rather than more, so my recommendation would be to reduce the threshold to 3%. The 2012 review in NZ recommended 4%. Of course any threshold can make a significant difference at the margin, but the point is that 5% of a 600+ seat parliament is a *lot* of seats. Bringing it down to 3% would reduce that distortion as well as allowing for greater diversity of representation.

I like the Dutch system, but that’s in a much smaller parliament and I can see that it would be too big a shift for the Germans to go along with.

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