I have an interest in this, as I have just voted in a federal election for the first time!Take a look at the recent German election, no party wins enough seats to form a government (as usual with PR)
Historically your statement isn't true, there have been post-war govts with an absolute majority. The scene today, however, is different with more than the old big two and one smaller set of political parties. There are 6 electable ones to choose from now.
There is a mixed system of direct candidates who get a simple majority in each constituency, plus a second vote which is PR and is for the party, who supply a list of candidates who will get in depending on the overall share of the vote. Less than 5% and you don't get in, which as happened to the hard left (Linke) this time. There is also a system of 'overhang' MP's - don't ask, Germans can't explain it either, but I think it is intended to ensure no vote is 'wasted'.
This system undoubtedly makes coalitions more likely, as you don't get a situation where say the Greens would get 2 or 3 million votes but one MP as can happen in the UK. I think coalitions are now a permanent feature of the landscape.
That can happen, although negotiations on a common programme I would not classify as murky secret meetings. The difficulty this time round is the liberals and the Greens are fairly far apart in their programmes, and it will be difficult to find enough common ground to form a stable government. Both have had coalitions with the social democrats in the past. A stable government of three parties is certainly a challenge!so there follows months of murky secret meetings and deal making.
Con - Lib - Green is also a possibility.
The amount any one party's programme can be implemented will in effect be in proportion to their share of the vote in the election. There is tactical voting as well to try to get the best coalition. I voted liberal with the second vote in part to prevent a red - red - green coalition, where the remnant of the old eastern communist party would gain some influence over the government.The electorate has no say in who comes out of the horsetrading on top.
Strangely enough there are Con - Green governments in some of the states, an unlikely combination but on two occasions have been re-elected. Some Greens think they can get more out of a Con coalition than one with the SPD.
Any government that emerges at least has to have the majority of the population behind it, even if it is not exactly what everyone who voted for a particular party would like. Compromises have to be made, there is no winner takes it all.
The constitution doesn't stipulate any limit on how long the negotiations can take - last time it was ages, as a multi-party coalition was unsuccessful and a grand coalition had to be negotiated. Until then the existing government and chancellor carry on on a caretaker basis.I also wonder about the interregnum.
Does the existing government carry on as a lame duck, or is the Fatherland left without leadership until all the deals have been done?
By common consent what happened last time needs to be avoided, so I think a new government will be arrived at fairly quickly.
It's not a perfect system, and personally I don't think FPTP is 'undemocratic', but some PR at least means more of the electorates wishes can be reflected in a parliament.
There is a trade off between a smallish vote enabling disproportionate majorities of the Thatcher ear, and the tail wagging the dog where a smaller coalition party can threaten to being down a government thereby gaining disproportionate influence.
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