In recent weeks, political analysts and commentators have been waking up to the possibility of the 2015 general election producing a messy outcome – not a hung parliament from which a stable coalition can emerge, but a close result from which a minority administration dependent on multi-party deals is produced.

The arithmetic underpinning this scenario was expertly set out by Peter Kellner in a recent piece. In essence, his argument is that if the Liberal Democrats lose something close to half their seats, and both the SNP and Ukip do well, then neither the Conservatives nor Labour may be able to form a coalition with the Liberal Democrats that has a safe majority. Writing in the Guardian, Martin Kettle adds a twist to this scenario, namely that for tribal reasons both of the major parties might actually want to govern with a minority rather than form a new coalition (He could also have added that if the Liberal Democrats are heavily defeated, they might consider it illegitimate to enter a coalition even if they still hold the balance of power, preferring a confidence and supply arrangement instead.)

Given the current polls, it is not difficult to see the Liberal Democrats reduced to 30 or 35 seats. What is less obvious is whether Ukip can win more than a handful of seats, though Douglas Carswell's byelection victory will give them momentum and it would be unwise, after the European parliamentary election results, to write off their chances of boosting their representation at Westminster. The SNP are also on a roll, having harvested great swathes of Labour's core vote in the Scottish referendum while eyeing up a number of Liberal Democrat seats that are certain to fall next year. It will take a lot for the SNP to overturn Labour's large heartland majorities, but there are plenty of signs that the Scottish Labour party is in serious long-term trouble. If the nationalists can position themselves as guarantors of the deal to deliver new powers to Holyrood at the general election, they may yet consolidate their support in ways that eluded them in 2010 (particularly if Alex Salmond chooses to return to Westminster to head-up the SNP contingent).

If this scenario produces a minority government, how long will it last? The received wisdom in Whitehall appears to be that it wouldn't last long.

A short history of increasingly short-lived minority governments
In most cases, minority governments in 20th-century Britain were short-lived affairs. True, the minority Liberal government elected in December 1910 lasted until 1915 with the support of the Irish nationalists and the infant Labour party, but this government is often considered a progressive alliance rather than a minority administration (and there had been two elections in 1910). Baldwin could not secure the confidence of parliament after the December 1923 election, leading to a minority Labour government that hung on until October 1924. Ramsay MacDonald's second minority Labour government ran from 1929 until 1931 before it famously split. The hung parliament of 1974 produced another election within the year. The 1977 Lib–Lab pact lasted a little over a year. John Major lost his majority in 1997 a matter of months before going to the country.

These precedents do not augur well for a future minority government. However, the recent experience of the SNP minority Scottish government elected in 2007 is more encouraging: it had a major wobble over its 2009 budget, but governed sufficiently well for the SNP to win a majority at Holyrood in 2011 (ironically in large part because of Conservative support). In Scotland, however, the first minister must receive a vote of 'investiture', which helps cement the authority of the new administration. No such provision exists at Westminster, although the vote on the Queen's speech is essentially the test of parliament's confidence.

Martin Kettle argues that the introduction of fixed-term parliaments means that the prime minister cannot cut and run for a second election, as Harold Wilson did in the 1970s, because the legislation now requires a two-thirds majority in the House of Commons for parliament to be dissolved. However, the Fixed Term Parliaments Act 2011 also allows for early elections if a motion of no confidence is passed and no alternative government is confirmed within two weeks. It is conceivable that the sitting prime minister could table a constructive motion of no confidence in his or her administration and dare the opposition parties not to allow the country to go the polls or try to form an alternative government without a fresh mandate, which would be barely conceivable unless there was a national emergency. Conversely, the 2011 Act also gives a determined and united opposition the opportunity – through the no-confidence procedure – of forcing a general election.

So there are probably three plausible scenarios for a 2015 minority administration. One is that the largest party works out – as Alex Salmond did after 2007 – how to last a full term on the basis of a clear strategy for forging the necessary alliances to get its business through parliament. This would probably have to involve a confidence and supply arrangement with the Liberal Democrats or one of the other parties, depending on the closeness of the result (which puts the Conservatives' theft of the Liberal Democrats' plan to raise the personal tax allowance in a new light, as progress towards it could be placed at the centre of each finance bill). The second is that a minority government tables its most popular legislative and budgetary provisions early on its tenure, and then forces a dissolution in circumstances most favourable to itself. This looks tough but not impossible under the terms of the 2011 Act. The third is that a minority government lasts as long as the multi-party opposition is divided – which could be a whole term if the minor parties each put a price on their support for the government.

The upshot? The Liberal Democrats may find, after 2015 that their real power is not to create a government, but to break one.