Given the fragmented British political landscape, and following five years of coalition government, it should come as no surprise that which party will govern with which other parties, and under what arrangement, has been a major theme of the election campaign.

Based on statements made throughout the campaign, the electoral maths and policy considerations, the below document assesses the key parties’ positions on coalition and what appear to be the most likely outcomes.

Conservatives

David Cameron has publically said his party is competing for a majority and has refused to discuss plans for coalition. There is a possibility the Conservatives win the most votes and seats but are unable to form a Government, while Labour could do so with the support of the SNP.

Many backbench Conservatives have tired of coalition with the Liberal Democrats, though the leadership seems open to a second go-round. Backbenchers would prefer to implement a more right-wing agenda. At times, Cameron has justified his centrism by blaming the Lib Dems for steering policy leftwards. As a result, the 1922 Committee of backbench Conservative MPs has demanded a vote to approve a potential coalition. They have not been granted any formal powers but will hold a silent vote regardless. Cameron would be wise to listen to it; he’s had a hard time controlling his own party whilst working with his coalition partners. If he wants legitimacy within his party and a mandate to govern, this is the only way.

The 1922s could vote for the Conservatives to govern as a minority; however, they’ve indicated they might approve a reasonable coalition deal. A minority would struggle to secure a referendum on EU membership in 2017 – one of the 1922’s key goals. There is backroom talk that Cameron will hold on to power even if he is unable to secure a majority or negotiate a coalition; as the incumbent he has the right. This would essentially force Labour to do a formal deal with the SNP in order to govern, which would be politically toxic. If a second election was called, the Conservatives would look to leverage this into votes and secure a majority, or at least another stable coalition.

A grouping of the Conservatives, DUP and UKIP would almost certainly fall short of a majority. On 8 May, if it is a possibility, the smart money would be on the Conservatives trying to form another Con-Lib coalition. They may not have the option, in which case an unstable minority appears most the likely route to power.

Labour

Conservative scaremongering around the prospect and effects of a Labour-SNP alliance has been effective with the electorate. During Question Time on 30th April, Labour Leader Ed Miliband ruled out, not only a coalition, but also any formal arrangement with the SNP. It’s something he has said a number of times throughout the campaign but seat projections suggest Labour may not have any other option but to deal with the SNP. In that circumstance, expect Miliband to set out an informal arrangement that avoids his party going back on his word. Labour should watch out for traps – the SNP is Labour’s bitter enemy in Scotland and a canny political force, they will pounce on any opportunity that allows them to damage Labour and secure the Scottish vote for the future.

Miliband also appeared to rule out coalition with any party during Question Time. He said: “I am not going to start bartering away my manifesto whatever the outcome of the election, even if I don’t win a majority”. He added that he would not “start trading for Nick Clegg or anyone else’s manifesto”. It wasn’t an answer that the audience necessarily believed but it seemed Miliband was setting out Labour’s options to be majority Government, minority Government and Opposition. Coalition does not feature.

It would be presumptuous to assume the Lib Dems would support a Government that does not offer them any formal powers, so a Lib-Lab coalition may still be on the books. Labour would surely rather have the support of a centrist party that has proven it can work collegiately in coalition than a nationalist party that wants to split the UK. Nonetheless, the maths for a Lib-Lab coalition probably won’t add up, so an informal arrangement with the SNP appears more likely.

Liberal Democrats

The Liberal Democrats have been the most open about their plans for a potential coalition. Indeed, it has been the cornerstone of their campaign. The Liberal Democrats cannot pretend they will be able to govern alone but could hold the balance of power on 8 May, if they retain enough of their seats. As a result, the Lib Dems have crafted a manifesto with policies that could align with Conservative or Labour plans and others that would secure cross-party support.

However, a multi-party coalition will be difficult to form as Nick Clegg has said: “I totally rule out any arrangements with the SNP – in the same way I rule out any arrangements with UKIP – because there is no meeting point for me with one party that basically wants to pull our country to bits and another party that wants us to pull out of the EU”. In addition, many Lib Dems would oppose a coalition including the DUP; their social values are too disparate.

In public and in private, it appears the Lib Dems favour another Con-Lib coalition. Labour are said to be more tribal and harder to work with in coalition, something the Lib Dems have experienced in both Wales and Scotland. However, though Clegg appears likely to hold onto his Sheffield Hallam seat (thanks to tactical voting from Conservatives no less), the party could return more MPs on its left than right. Some of these MPs, like Andrew George, oppose coalition with the Conservatives as a matter of principle. Nonetheless, while Clegg’s right-hand man, Danny Alexander, looks to lose his seat, the Deputy Prime Minister should still be able to count on the likes of Energy Secretary Ed Davey and Scottish Secretary Alistair Carmichael for support.

Clegg could still face a leadership challenge. Former Party President Tim Farron has spent coalition on the sidelines, rallying support from the disillusioned left wing of the party. If the Lib Dems lose over half their seats as predicted, Clegg may be viewed as too toxic a brand, tainted by the tuition fees scandal. A left-wing Lib Dems may warm to Labour, but not the Conservatives. In either case, Farron has signalled a desire to let the Lib Dems rebuild in opposition, their familiar territory, to challenge more strongly in 2020.

Whatever happens, expect the Lib Dems to undertake negotiations with the largest party in the next Parliament. If no Government is possible, they will negotiate with the second largest. It is unlikely they support a potentially unpopular minority without the power granted by being in Government. It is still unclear whether the Parliamentary Party and members would approve another coalition but they appear proud at their party’s achievements in Government – they might like another go.

SNP

The SNP’s Leader, Nicola Sturgeon, has tried – and may have succeeded – to convince the Scottish electorate that voting for her party means they can get Labour policies, but with a nationalist slant. Miliband has tried to refute this view; Labour’s contest with the SNP in Scotland is fierce and often unpleasant. His message has been: if you want a Labour Government, vote Labour.

Nonetheless, the SNP look on course to secure almost all of Scotland’s 59 seats and Miliband may have no option but to deal with them. Miliband’s statements suggest this will have to be on an informal, vote-by-vote basis. Such a relationship could be short-lived, even if it successfully delivers a Queen’s Speech and Budget. The SNP will be looking to inflict permanent damage on Labour. They will ask for increased spending in Scotland, which could alienate English and Welsh Labour. Miliband will be faced with a choice, attempt to win back Scotland, or lose support south of the border. It’s a choice he may not wish to make.

The SNP would be open to an arrangement involving the Green Party and Plaid Cymru. The common ground between the different parties is clear; they are all anti-austerity and left of Labour. This could become a powerful grouping in opposition, and one Miliband will be keen to court, at the risk of fiscal credibility. Sturgeon is a powerful political force; Miliband may like to keep his enemies close. Whatever his preference, on 8 May, the only plausible Government may be a Labour-SNP alliance and choice may be limited.

DUP

The DUP, largely ignored in past elections, could have an important role to play in the next Parliament. Their eight seats could be enough to tip the balance in key votes. The DUP has ruled out coalition with any party but has named the price to earn its support, which include a referendum on EU membership and £13bn a year in additional funding for Northern Ireland. This rules out supporting Labour, who will not hold a referendum on the EU unless there is a transfer of powers from London to Brussels. The Conservatives will rightly see a party they can work with. However, eight MPs will not be enough to cross the line and many Lib Dems do not wish to work with the DUP, who have very different views to their party.

It is most likely that the DUP does not have a place in coalition or even an alliance, but is instead called on for support on key votes. The Conservatives will have an easier time of this, but Labour may be willing to offer increased funding if it enables them to avoid a more toxic relationship with the SNP.

Conclusion

There is no clear path to government for either Labour or the Conservatives. On the basis of electoral mathematics alone, it appears a Labour-SNP alliance is one of the most likely outcomes. The electorate will question the legitimacy of a government formed with a nationalist party. They will question it even more if Labour has fewer seats than the Conservatives. The other most likely outcome would be a fragile Conservative minority. However, if the Conservatives can push on to win over 290 seats, and the Lib Dems retain some of their Scottish holdings, a second Con-Lib coalition is a possibility. The clear uncertainty around the formation of the next Government means a second election is another possibility. It could be a different contest then, with coalition more openly discussed. Parties should, in this instance, be careful of their own rhetoric; it could tie their hands in the near future.