Four weeks after the German elections, the Christian Democrats and their new coalition partners, the Free Democrats (or Liberals), yesterday announced an agreement  on forming a new government, which will be sworn in this week.

There’s the first lesson. Things don’t fall apart if a new government isn’t in place immediately after an election; it doesn’t do any harm, and may do considerable good for the parties to take their time, review their options, and even have a bit of a break after the rigors of an election campaign. If government is worth doing at all, it’s worth doing properly.

In Australia, our politicians seem obsessed with the need to be seen to be going back to work immediately after an election. Instead of taking some time off, they hold party meetings and announce new appointments within the first few days. At best they lose an opportunity to take stock; at worst, they make stupid and avoidable mistakes — think Brendan Nelson.

The German coalition deal is not a surprise. Unlike 2005, when there were multiple possible combinations, it’s been obvious since election night what the eventual outcome would be. The Liberals were Angela Merkel’s preferred allies, and the fact that they won a majority between them basically ruled out anything else.

There’s the second lesson: in most of the world, coalition is a post-election decision, not a permanent state of affairs. Parties have their preferred options, but they don’t rule out the others until they see what the numbers look like. Partnerships can change, and even when their party makeup stays the same, policies can shift in response to their relative electoral strength.

In Australia we often have what are nominally coalition governments, but in reality we have an inflexible two-party system. That’s not entirely a bad thing, since it gives voters a clear choice, but it closes off options that might better suit the new circumstances. It also puts our coalition parties in the fundamentally false position of pretending to be free agents while tied to a permanent alliance.

The new government gives nine ministries to the Christian Democrats and five to the Liberals. The two parties will share the key economic portfolios, and Liberal leader Guido Westerwelle will be foreign affairs minister. One new policy will be the reduction in compulsory military service from nine to six months.

Third lesson: conservatives and liberals can work together, not because philosophically they are natural allies — they’re not — but because politics is the art of the possible. In a particular circumstance a liberal-conservative alliance might be the most sensible combination, and by negotiating in a mature fashion they can agree on a common approach.

Australia’s liberals and conservatives, locked together in the same party for a century, have no such opportunity to exercise the arts of compromise. With only one party, the struggle for control of it takes on a life-or-death dimension; liberals and conservatives would probably have better relations if each had their own party.

There are probably more lessons from Germany — such as the key place of tax cuts in the new government’s program — but three for one day is enough. No sign, unfortunately, that Australia’s politicians are paying the slightest attention.