A bit of further background before going through actual figures - the SNP had six seats in the last parliament, but opinion polls at the moment show them as likely to get over 50 of the 59 Scottish seats in the next parliament, which will make it the largest party in parliament other than Conservative and Labour. The SNP has stated that it will vote against any attempt by the Conservatives to form a government but is willing, given certain conditions, to support a Labour government from the opposition benches. At the moment, neither Labour nor Conservative looks at all likely to get an overall majority of the 650 seats in parliament - any government will therefore need at least tacit support from the SNP, the Liberal Democrats (the Conservatives' partner in the coalition government of the last five years) or one or more of the six to eight other parties likely to get seats in the new parliament.
I have taken most of the figures below, earlier this evening, from may2015.com. In each of my scenarios, I have left may2015's Scottish percentages, and thus the predictions for Scottish seats, unchanged - the SNP is therefore always assumed to get 55 seats. When I vary the projected percentages for the Conservatives, Labour and Liberal Democrats below, these only affect seats in England and Wales. Of the minor parties likely to get seats in England and Wales, may2015.com predicts that Plaid Cymru (Welsh nationalists) will get 3 seats (all in Wales); UKIP will also get 3 seats (all in England); and the Greens and Respect will get one seat each (both in England) in all the tested scenarios. For the 18 Northern Ireland seats, which may2015.com does not predict, I am assuming (subject to correction by nwhyte) that the DUP will take 8 seats, Sinn Fein (who never take their seats in parliament) 5 seats, and the other 5 seats will go to smaller parties and independents.
May2015 currently shows the Conservatives with 33.6% of the vote, Labour with 33.7%, and the Liberal Democrats with 8.3%. This results in 273 seats for Labour, 270 seats for the Conservatives and 26 seats for the Liberal Democrats.
After the election, if the Liberal Democrats decide to continue their coalition with the Conservatives, the two parties together would have 296 seats - 30 short of a majority, or 27 short if, as is almost certain, Sinn Fein don't take their seats. The DUP would probably also be willing to make a deal with the Conservatives and Liberal Democrats, bringing the number of seats up to 304, and UKIP might also, giving a total of 307, still 16 short of the majority.
And there things stick. Labour would certainly vote against the Conservatives forming a government and so would the SNP. And so, almost certainly, would all the other British small parties and at least four of the other five Northern Ireland MPs, giving a total of 337 or 338 - the proposed new Conservative-led government would be defeated by about 30 votes.
So Labour would then presumably attempt to form a government - does this mean that it is totally dependent on the SNP to do so? Well, no - the Liberal Democrats have been clear that they would be willing to do a deal with Labour, if Labour is the largest party, and the DUP seems willing to do a deal with any prospective government that will meet its relatively cheap shopping list. Even without any of the other parties (including the Scottish Nationalists), this would provide a proposed Labour government with 307 votes - and the SNP would actually have to vote with the Conservatives against this proposed government (not just abstain) to defeat it. After that, unless the SNP was willing to support the Conservatives after all, there would be another general election - in which the SNP would be risking the loss of far more seats that it would be mathematically possible for them to gain.
In this scenario, the SNP has some power, but only to the extent that they are willing to risk an early general election, other parties are not willing to do deals with Labour or they offer a better deal for to a Labour government than other parties do.
So now, let us suppose that there is a swing towards the Conservatives. It turns out that they would need a swing to them of well over 2% to form a government. So now let us try this one out - the Conservatives' campaign achieves a swing of 2.3% (bringing them to 35.9%), of which 2.1% comes from Labour (now on 31.6%) and 0.2% from the Liberal Democrats (now on 8.1%).
That is still, though, probably not quite enough for the Conservatives - they now get 288 seats and the Liberal Democrats 23 seats, 311 in all. Adding in the DUP and UKIP brings the total to 322 - and their opposition still has 322 or 323 votes.
Mind you, Labour is also in difficulties - with only 258 seats, they need not only the SNP's 55 votes but all those of all the other minor parties. And even if the Liberal Democrats and DUP, in order to avoid an early general election, tried to do a deal with Labour, such a government would still be reliant on the SNP actively voting for it. This would effectively be the Conservatives' nightmare scenario - but occuring because of the swing to the Conservatives. But the prospective difficulties for Labour of keeping such a government going for more than a few weeks would probably be enough for Labour to decide not to try forming a government but opt to vote against any further Conservative attempts to form a government and go for an early general election instead.
Finally, let us suppose that there is an opposite swing, of 2.3% against the Conservatives (now on 31.3%) and with Labour now on 35.8% and the Liberal Democrats on 8.5%. Labour now has 305 seats and the Liberal Democrats 26 seats, a total of 331 - and an effective majority of about 18. Or Labour could go instead for a minority government, doing one-off deals with the Liberal Democrats and the SNP as needed - the one thing Labour would have to be careful of is not alienating them both at the same time. The SNP would still have some power - but only on any issues where Labour could not do deals with the Liberal Democrats. All in all, less potential for chaos or backroom control than the Conservatives could achieve on any of the three scenarios.
Of course, just because this is the situation nationally does not automatically mean that voting Labour is the best thing to do in every single British constituency - but that (if I have the time) is best discussed in another post