Who will win the 2015 general election?

As voting begins after one of the longest campaigns in memory, opinion polls suggest that the UK general election remains too close to call. Nearly all the polls published in the last two days have Labour and the Conservatives tied, with only a handful giving one or the other a narrow advantage.

The lead has ebbed and flowed in the week's before the election, almost always remaining within the margin or error. That means it is as likely to have been caused by statistical vagaries as by real voting trends.

The bookies are convinced that the Conservatives will end up with more seats than Labour, but they too are little help when it comes to predicting who will be PM: many are offering the same odds on Ed Miliband and David Cameron.

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Who's going to win?

The most likely outcome is that that no-one will win, at least not with a majority. It looks like being the tightest general election for decades, and some polls are even suggesting that there could be a dead heat, with Labour and the Conservatives ending up with the same share of the vote.

Election odds: who the bookies think will win

What do the polls say?

And how would that translate into seats?

Under the first-past-the-post system, national polling only tells part of the picture. A party whose support is concentrated in certain areas will pick up far more seats than a party with the same number of votes spread evenly around the country. Several polling companies attempt to translate polling data into seats, with significantly different results:

Electoral Calculus models polling across individual constituencies, and claims to have been the most accurate forecaster before the last election.

* Plaid Cymru and Northern Irish parties.

Elections Etc's model works on similar principles, but its calculations are more cheering for the Conservatives.

* Not specified

Nate Silver made a name for himself by correctly predicting the result of all 50 states in the last US election. His model combines polls, historical results and census data.

* Plaid Cymru and Northern Irish parties.

YouGov offers two possible seat counts, one, the "nowcast", based on raw data from all its polling and nothing else. The other, the "forecast", factors in analysis and predictions from the YouGov chairman Peter Kellner.

* Plaid Cymru and Northern Irish parties.

How are the parties trying to win our vote?

Here is The Week's guides to the main parties' manifestos:

• Conservative manifesto: PM to revive right-to-buy scheme
• Lib Dem manifesto lays out non-negotiable schools pledge
• Green Party manifesto calls for 'peaceful revolution'
• Labour manifesto highlights: from the economy to football fans
• Ukip manifesto: from tax revolution to national holidays
• Green manifesto calls for 'peaceful revolution'
• SNP manifesto sets out policies for Scotland - and England

What happens if there's another hung parliament?

If no single party commands a majority, David Cameron will remain in office while negotiations take place between the parties, and as the incumbent he will be first in line to form a government, either through formal coalition or a looser alliance of parties. If he cannot, the party with the next largest number of seats, ie Labour, will make the next attempt to form a government.

Is it curtains for the current coalition?

Most projections put the Conservatives well short of the 326 seats they would need to form a majority government, and the Lib Dems may not be left with enough MPs to make up the shortfall. Peter Kellner, the chairman of YouGov, had predicted that both the Tories and Lib Dems would do better than expected, and could end up with a narrow working majority between them. Now he has revised down his expected seat count for the Conservatives, but revised up his estimate for the Lib Dems. The result is delicately balanced. "As things stand," Kellner writes, "the future government of Britain could depend on whether the Conservatives and Liberal Democrats continue working together in the new Parliament. Unless the Tories win well over 290 seats, they will have to rely on Lib Dem support. Without it, Labour could end up in power, or at least in government, with fewer seats than the Tories."

Will the Lib Dems want to keep the existing coalition alive, even if they can?

The Lib Dem leadership has been careful to avoid ruling deals with either of the main parties in or out, and their manifesto was careful to leave room for negotiation with both the Conservatives and Labour. Many in the party would feel happier leaning leftwards towards Labour, and if Clegg loses his seat, many analysts believe that his replacement as party leader would be much less enthusiastic about a second term in office as the Tories' junior partners. In recent days, the Lib Dems seem to have been attempting to put yet more distance between themselves the their coalition partners. However, Clegg's chances of retaining his seat appear to have improved, thanks to the willingness of Tory voters in Sheffield to vote tactically to save the Lib Dem leader.

What are the chances of Ukip gaining a lot of seats?

Relatively slim. Recent polls have showed them slipping from a high-water mark of 23 per cent to somewhere in the low teens - but even that would be a stunning increase from the 3 per cent share of the national vote they got at the 2010 general election. However, Britain's first-past-the-post system does not favour minority parties, especially when their support is spread evenly around the country. Indeed, Electoral Calculus suggests that Ukip will win just two seats if its share of the vote remains around 13 per cent, and few commentators expect them to end up with more than three.

Could Ukip affect who wins the 2015 general election?

What really counts on 7 May is not how many seats Ukip wins, but how many votes they take from the Conservatives and Labour in marginal seats. Among switchers to Ukip, says Peter Kellner of YouGov, ex-Tory voters outnumber ex-Labour ones by a margin of three to one. In short, David Cameron could be denied his return to Downing Street by these Tory switchers. Ukip insist they are a threat to Labour too, and trumpet the fact that they came within 617 votes of taking the Heywood and Middleton by-election last year. Polling by Lord Ashcroft early in the campaign also found that "rising support for Ukip has eroded the swing to Labour" in Tory-Labour marginals. But while Ukip's line on EU immigration and the Westminster "disconnect" is clearly popular with some traditional Labour supporters, opinion polling points to Farage's troops being a far greater danger to the Tories than to Labour in terms of seats. It follows that any decline in Ukip's support is likely to benefit the Tories disproportionately.

Can the Tories win an overall majority?

That seems unlikely. Amid all the uncertainties surrounding this election, there is one safe bet – that no party will gain a majority, for which they would need 326 seats (or 323, assuming that Sinn Fein wins five seats and leave them vacant). The Tories didn't manage it last time and that was before the rise of Ukip. Recent opinion polls suggest that the Tories will win somewhere in the region of 280 to 290 seats.

What about a Tory coalition with Ukip?

Many right-wing eurosceptic Tories would love to go into coalition with Ukip, but David Cameron has ruled this out. Nigel Farage is also thought to be against the idea: the Ukip leader has made it clear that he sees Cameron as a metropolitan modernist who is personally responsible for driving away traditional Tory voters (into the arms of Ukip) and insulting them as they go. There is a widely held theory that Farage wants to see the Tories lose office and a weak Miliband government rule for one term while the Right fractures and regroups under a new leadership.

However, there is one possible scenario that could see the Tories and Ukip govern together: if the Tories can come out of the election as the largest party, might Cameron step aside for a new leader – possibly Theresa May, possibly Boris Johnson, who has been making Ukip-friendly noises in recent months – who would do a deal with Farage to govern in coalition? At this point, it still seems like a long shot.

Can Labour form the next government?

Despite Ed Miliband's poor personal rating, Labour seemed – for most of this parliament – to have a reasonable chance of winning power and ruling on their own. Over the past six months, however, the Labour poll average slipped from 37 per cent to about 33 or 34 per cent, even as Miliband's personal rating increased.

Labour might still have hoped to squeak a majority if it wasn't for Scotland. Polls pointing to a SNP landslide and the destruction of Labour's long-time dominance north of the border have become routine. Last week it was even suggested that the SNP might win every seat in Scotland. Unless Labour can roll back that surge, and that seems impossible, Miliband's best hope seems to be to come out of the general election leading the biggest party.

Could Miliband do a deal with the Liberal Democrats?

Assuming the Lib Dems were prepared to enter an agreement with Labour – perhaps with the more Labour-friendly Vince Cable replacing Nick Clegg as party leader – the Lib Dems would need to do a lot better than their projected 25 seats or so to make up the numbers.

If Labour do better against the SNP than expected and come out with 295 seats, the Lib Dems would also need to hang onto 31 of their current 56 to allow the two parties together to hit the 326 mark. Some analysts believe the Lib Dems can achieve that, but it would be a stretch for both parties.

What about a Labour-SNP deal?

Although Labour has repeatedly ruled it out, a coalition between Labour and the SNP could well produce a Commons majority - adding together Labour's 275 or so seats and 50 or so from the SNP. Both Salmond and his successor as leader of the SNP, Nicola Sturgeon, have said that they would be prepared to work with Labour in government (and vowed not to support a Conservative-led government), and in the Challengers Debate, Sturgeon repeatedly said that she would support a Labour government, as long as it was sufficiently different from the Tories. Miliband, however, has rejected the idea of a Labour-SNP coalition out of hand, and in recent days has been increasingly vociferous in ruling out any kind of "deal" or "arrangement".

Still, many believe that the SNP will influence the outcome of the election. "Let's get something clear," says The Times's Red Box election blog. "If we get a minority government of either shade it will talk to the SNP. In the House of Commons all parties talk to each other. Labour will talk to everyone else; so will the Conservatives."

It would be politically impossible for the Scots nationalists to prop up the Tories, so they would almost certainly abstain or back a Labour government in a confidence vote, and would be prepared to support Miliband on most of his policies. Where Labour and the SNP differ – on Trident and deficit-reduction – the Conservatives would almost certainly provide sufficient support to pass the necessary legislation.

What about a Labour deal with all the left-leaning parties except the SNP?

If Ed Miliband is serious about snubbing the SNP, and he has given himself very little wiggle-room, he may try to put together a government that involves the Lib Dems and a range of small parties. The Greens (likely to have one seat) and Plaid Cymru (three seats) have both said that they would be prepared to vote with Labour on a case-by-case basis, and in Northern Ireland the SDLP (three seats) would be natural allies. The DUP (nine seats), which would usually lean to the right, has also kept open the option of doing a deal with Labour. Elections Etc says that only if this grouping failed to provide a majority would Labour "look to the SNP to sustain them in government". If the Lib Dems could get 25 seats and the smaller parties achieved their expected 16, Labour would need 285 seats (or 282 Sinn Fein leave their five seats vacant). On present projections Labour would fall short, but not by much – and since the SNP has vowed not to put the Conservatives in power, a rainbow coalition of the left would have some room for manoeuvre.

Will the new government have legitimacy?

"With all the polls pointing to a hung parliament," says The Times, "the question of legitimacy is now at the front of the minds of senior politicians." This is not really a constitutional matter: if a government can command a majority of votes in the Commons then it stands, and that is the end of the matter. The question posed during the campaign has more to do with whether the electorate feels that its voice has been heard.

Last autumn, when Labour was on course to win most seats, its supporters were suggesting that Cameron may try to "cling on" in government even if his party were not the largest. As the incumbent, that would have been his constitutional prerogative, and he could have put together another coalition with the Lib Dems – but his opponents said that this approach would have lacked legitimacy. Now the tables are turned, and Cameron may well end up leading the largest party but unable to put together a majority. Labour, with tacit or explicit backing from the SNP, may then find the parliamentary arithmetic works in its favour – but the Conservatives and their supporters have spent the past fortnight claiming that this arrangement too would lack legitimacy.

That message seems to chime with voters. "There is strong opposition in England and Wales to the SNP enjoying huge influence in a hung parliament," The Independent says. "Seven out of 10 people believe the Scottish National Party should not be able to veto any UK government policies if they do not affect Scotland." Even so, says The Times, while "the question of legitimacy continues to dominate … it will be mathematics that really matters as party leaders see how close they can get to the magic 323 figure that would allow them to govern".

What about minority government – could it happen and how does it work?

In 2010 David Cameron opted to negotiate a full-blown coalition with the Lib Dems rather than a less formal "confidence and supply" (C&S) arrangement. As The Guardian explained at the time, under a C&S deal the smaller party – or parties – agrees to support the larger party on its Budget and in any vote of no confidence, should one be tabled. Otherwise, every government policy would have to be assessed to check that it would be supported by the smaller party or parties.

Both Cameron and Miliband could consider this option if they find themselves leading the largest party but are unable to pass the 326-seat mark. Cameron could suggest a C&S deal to the Lib Dems in place of a second formal coalition. Miliband could make a similar approach to the Lib Dems or the SNP.

The last time we saw this scenario was when the February 1974 general election produced a hung parliament. The defeated Tory Prime Minister Edward Heath got the first chance to form a government but his negotiations with the Liberals failed. Labour leader Harold Wilson decided to rule as a minority government. Wilson's plan was to gain a quick poll boost by introducing popular policies and then seek an overall majority at a second general election, which he duly called in October, winning a small majority.

There's just one problem. The Fixed Term Parliament Act of 2011 would deny either Cameron or Miliband the right to call the second election. Five full years of minority government could prove intolerable for the parties concerned, not to mention the electorate.

What's the impact of the Fixed Term Parliament Act?

Fixed, five-year terms mean that a prime minister can't simply call an election, and nor does losing a vote of confidence immediately trigger one. Instead, Parliament's website explains, an early election can only be held "if a motion of no confidence is passed and no alternative government is confirmed by the Commons within 14 days", or "if a motion for an early general election is agreed ... by at least two-thirds of the whole House". So if, for example, a minority Conservative government failed to pass its Queen's Speech and then lost a confidence vote, Labour would have two weeks in which to put together a coalition or pact, and could form a new government without going to the polls again.

So, what's the most likely outcome?

As things stand, a hung parliament is by far the likeliest outcome. The Conservatives are more likely to end up with more votes and more seats, but Labour is more likely to have the support in the Commons to put together a government. The Tories would need to enjoy a massive surge in support on Thursday to win a majority, but a relatively small swing would put them into government. The polls suggest that this has not yet happened, but some analysts still believe it will.