SOME of our coverage of the German election on September 22nd has focused on something that sounds obscure, forbidding and boring to many of our readers around the world: coalition mathematics. For that, blame the voting system for Germany's Bundestag, or lower house, which is either sophisticated or complicated, depending on your point of view. Its basic architecture comes out of Germany's post-war wish to combine the advantages of two systems. One is the "winner takes all" model used in most Anglo-Saxon countries, where voters in each district send a representative to parliament with a simple plurality of votes. This leads to few, large parties and a tight relationship (at least in theory) between voters and their representatives. But it means that votes for the losers are, well, lost. The other is a proportional-representation system. Here no votes are lost, because all parties are seated in relation to their share of the vote. One downside can be political fragmentation, of the sort that Germany experienced during the Weimar Republic of the inter-war years. So how did Germany combine these two voting systems? It devised a method in which voters make two choices. On the left side of the ballot, they vote for an individual in their district (as though voting for an American congressman, say). There are 299 districts, so 299 members of parliament are directly elected. On the right, they vote for a party. Once these "second votes" are tallied, the parties get to fill another 299 seats from candidate lists until each party's share of the Bundestag's 598 representatives matches the proportion of second votes that it won. To deal with the Weimar problem, parties that fall below a threshold of either 5% of second votes, or three directly elected candidates, do not enter parliament at all. (The other parties' shares are then rebased accordingly.)

There was a problem, however. Many voters "split" their ballots, voting for a candidate from one party with their first vote and for a different party with their second. The directly elected candidates (known as direct mandates) entered the Bundestag, but a given party might then have more candidates than its share of the second votes would imply. This also meant that the Bundestag swelled from its theoretical size of 598 seats to 620. The constitutional court in Karlsruhe ruled that this was unfair.

So the parties haggled out a new system, which is in force now. If direct mandates for any party exceed its second-vote ratio, then all the other parties get compensated so that the ratios again reflect the second votes exactly. In practice, that could make the Bundestag bigger again, with perhaps more than 700 seats. Crucially, it also hurts one party by withdrawing an advantage it has enjoyed in the past: most of the excess direct mandates went to the Christian Democratic Union (CDU), the party of Angela Merkel, the chancellor. As a result, the CDU is likely to fare worse than it would have done under the previous system.