Reality Check: Does the largest party form the government?

In olden times - last decade and for more than 70 years before that - it was usually expected that either Labour or Conservative would win most of the seats in the House of Commons.

So long as the party leader and prime minister kept the loyalty of backbenchers, and so long as they didn't lose that majority through by-election losses, then that's the way it stayed until the next election.

But things have changed. There is a low expectation of either Conservative, Labour or anyone else winning a majority on 7 May. The two main parties are closely tied in polls showing the share of the popular vote, having lost ground to smaller parties.

That's why the question has arisen of how a government gets formed. Jim Murphy, for Scottish Labour, has been saying the largest party gets to form the government (so he's telling voters to ensure Scottish Labour is the largest party).

Nicola Sturgeon knows she can't possibly get a majority for the SNP (it's standing candidates in 59 out of 650 constituencies), so she says she wants to ensure Ed Miliband is installed as prime minister and then "kept honest" on some sort of loose arrangement for SNP support.

Other parties, including the Lib Dems, Greens, UKIP and Northern Irish parties, can boost their relevance in this election campaign if they talk up the power they could exert if the numbers become tight.

Hung parliament

So how would it work if there's a hung parliament - that is, no single-party majority?

First of all, there's a simple bit of arithmetic. There are 650 seats in the House of Commons. A majority requires half plus one, or 326.

Keep that number in mind. That is what a Tory or Labour leader needs to reach (with one exception, which I'll come back to).

Not having a written constitution, the rules for forming a government are down to convention, and a limited amount of choice over the timing for the Queen.

If parliament is "hung", the prime minister stays in place, and has the first opportunity to put together enough votes to reach the 326 mark.

In this case, that's David Cameron. He might appeal to unionists from Northern Ireland, or he could go back to the Lib Dems to see if they're up for another deal, following the one struck between David Cameron and Nick Clegg in 2010.

That two-party agreement was enough to get past the 326 vote threshold.

Open to agreement

What if David Cameron can't get enough support from other parties? Then he has to resign, and the Queen asks Ed Miliband to form a government.

It doesn't matter if Labour wins more seats than the Conservatives - convention says the incumbent prime minister should get the first shot at putting together a new administration. So on that count, at least, Jim Murphy is wrong.

So Ed Miliband can then try to get past 326 votes. The SNP says it would be open to an agreement with him. The SDLP in Northern Ireland might offer a small number of votes.

The Lib Dems might prefer to push their former Conservative partners out of office as well. Pundits reckon that Ed Miliband may have more options open to him than David Cameron, but it all depends on the arithmetic when the result is clear on 8 May.

Confidence and supply

To get past 326 votes, the parties don't need a formal coalition. It is enough to ensure that the government wins a vote of confidence, whenever the opposition chooses to force one.

The other parties could agree to vote for the government, in return for one or several of their priorities being accepted into the government's programme for legislation or spending.

They could have a "confidence and supply" agreement. That means promising to vote with the government when its survival is in doubt - a vote of confidence forced by the opposition, or another issue on which the prime minister has staked his job.

It would also mean a pledge to back the government's budget, known as "supply" in parliamentary jargon.

Or they could have a looser agreement still. A smaller party could vote in the new government and then force it to keep winning support on a vote-by-vote basis. That is how the SNP ran the administration between 2007 and 2011.

Abstinence

With the SNP hoping to have a decisive role, both "confidence and supply" and "vote-by-vote" options have been discussed, while a formal coalition (with an agreed programme for government and ministerial jobs for the smaller party) looks very unlikely.

There's one other option - abstaining, which means it is not necessary to get to 326 votes. If, for instance, the SNP chose not to vote to support Labour but to abstain, then Labour would need a smaller number of MPs supporting it, if it is to beat its opponents.

That can mean smaller parties have a lot of power. The catch is that smaller parties can be punished by voters if they use that power recklessly. And a clever prime minister can put together shifting alliances of different parties.

MPs don't usually want to bring forward the date of another election by bringing down the government, as voters tend to punish those who bring about that collapse. Also, remember that elections are very expensive to fight.

History lesson

Given that this is down to convention, four elections are worth a look.

In 1923, the incumbent Conservatives held on to 258 seats. Labour increased its seats to 191, and the Liberals to 158.

The Liberals supported Labour in taking office, but Ramsay MacDonald's Labour administration only survived in power for 10 months before another election was called.

In February 1974, Labour won five more seats than Conservatives. But because Conservative leader Edward Heath was prime minister, he had first opportunity to form a government.

He remained in office for four days, failed to get support from Liberals, and Labour's Harold Wilson was invited to form a government. That Wilson government stayed in power until he called another election eight months later, which Labour won with a precarious majority.

Constitutional convention

In 2007, the Scottish Parliament election produced a knife-edge result. Neither Labour's Jack McConnell nor Alex Salmond's SNP had a majority. Nor could they form a majority by allying with any other single party, apart from each other.

Labour won 46 seats, the SNP won 47, Conservatives had 17 and the Lib Dems had 16. A Holyrood majority requires 65.

Alex Salmond got the support of the two Green MSPs, following an agreement which later crumbled. He beat Labour's Jack McConnell to become first minister by 49 to 46 votes, because Conservative and Liberal Democrat MSPs abstained.

In 2010, Gordon Brown wanted to form an alliance with Lib Dems to remain in power. But Nick Clegg asserted that the party with most seats and votes should have the initial say. That was the Conservatives, with whom he then formed a five-year coalition.

That was the assertion of the Lib Dem leader at that pressured moment. It's not firmly established as constitutional convention.

What Nick Clegg did not make so clear is that there's another part of the calculation, which was also a factor in 2007. If the momentum is clearly with the challenger rather than a tired or tainted incumbent, it can be easier to secure support from smaller parties.

Momentum is a vital component in politics. You can't measure it. But you know it when you see it.

Election 2015 - Reality Check

What's the truth behind the politicians' claims on the campaign trail? Our experts investigate the facts, and wider stories, behind the soundbites.

Read latest updates or follow us on Twitter @BBCRealityCheck