Towards the end of last year the pollster Peter Kellner from YouGov set out in The Times four possible results of the May 2015 election and what they would mean. Looking at these, all of them realistic, shows just how complex the arithmetic, the politicking and the negotiations will be for our country to have a workable government straight after the first election. Kellner doesn’t think there is a chance of any party actually winning an outright majority, so we are looking how parties might combine depending on the possible outcomes.

Before I run through the four possibilities, it is worth reminding you that to win a majority of seats a party would need 326 seats, although with Sinn Fein not taking their seats (this effectively abstaining on every vote) and the Speaker of the house not voting either a majority would actually be 323 seats. But you should remember that just achieving that number does not a functioning government make. It would mean that every single member of the governing party votes with the government on every vote for them to get their programme through. That doesn’t happen, even with a ‘three-line whip’ because of the independence of some back benchers, especially those who know there is little chance of a ministerial job. So bear in mind that in reality a government would want about 350 seats in total, whether in coalition or not, as the opposition parties would then only have 300.

Also bear in mind that a ‘Government’ does not have to be a coalition, it can be a ‘confidence and supply’ arrangement, which means that a party or parties agree to support the governing party on all votes of confidence and finance bills (passing budgets), in return for a few concessions.

Finally, in the hypothetical situation below ‘Others’ are the Northern Irish parties, who have 18 seats (Likely to be DUP 8, Sinn Fein 5, SDLP 3, Alliance 1 and Independent 1), Plaid Cymru with 3 seats and the Greens with 1 seats.

Anyway, here are the four outcomes Kellner discussed, and their significance and possible consequences:

Outcome 1 – Labour near majority Conservatives 259 Labour 312 Lib Dem 37 SNP 10 UKIP 10 Others 22

This situation, which can be achieved with about 33% of the vote, which is where Labour is at the moment, would put them in pole position to form a Government. Although our constitution states David Cameron as incumbent Prime Minster gets the first opportunity to form a Government I would imagine he would almost immediately defer to Ed Miliband to do so. Labour would have some choices here, as they are only 10seats from a majority. They could try and form a minority government with, say, the SDLP from Northern Ireland supporting them, although this may not last for long. Or they could do a deal with the Liberal Democrats, which would give them a majority of 48. I would have out that first, but I suspect the Lib Dems may be reticent to go into Government with a party who is so dominant as they would have even less influence than they do with the Conservatives’ current 304 seats. Then there is the SNP. Granting more powers to Scotland would probably see a confidence and supply agreement at least. If the SNP won as few as 10 seats they would certainly be licking their wounds and easier to deal with as they would be with 30 or more seats.

Outcome 2 – Conservatives ahead but well short of majority Conservatives 300 Labour 267 Lib Dem 27 SNP 30 UKIP 4 Others 22

This situation, which involves the Conservatives having the most seats but actually having lost seats since 2010, would see the Conservatives in a difficult but not impossible position. Should the UCUNF (a combination in Northern Ireland between the Conservatives and the UUP) win any seats they would certainly support the Conservatives in a minority government. Possibly the DUP too and maybe UKIP. The trouble is that they wouldn’t have a workable majority with just the Lib Dems and would often find themselves outvoted on policy by a combination of Labour, SNP and Lib Dems. They may be able to get a vote by vote agreement with the SNP but the SNP has said there will be no formal deal with the Conservatives. Meanwhile, the EU referendum, which would need to be legislated for, would be defeated in Parliament unless the Lib Dems join with the Conservatives on it. It is worth pointing out here that having the referendum used to be in the Lib Dem manifesto. But knowing how politically flexible the Lib Dems can be I wouldn’t predict what they would do. Whatever arrangement emerges is unlikely to remain for 5 years so another election may be needed.

Outcome 3 – Liberal Democrats get to choose the government Conservatives 290 Labour 290 Lib Dems 40 SNP 7 UKIP 1 Others 22

Lib Dems would be expected to form a coalition as if not they would be seen as irresponsible. Cameron could be unseated by his party as he didn’t win. Whatever happens lib Dems would be expected to choose.

Outcome 4 – Multi-party government Conservatives 280 Labour 280 Lib Dems 30 SNP 30 UKIP 8 Others 22

Can’t form government between lib Dems and anyone. Conservatives would need lib Dems and SNP and his own back benchers. To get all three would be unlikely. Most likely would be a labour led government with lib Dems and SNP with Sdlp too.