Britain officially has a hung Parliament – the first since 1974 – with the Conservatives the largest party.
Because there are 650 seats in the next Parliament, the winning post for a single party to have an overall majority in the House of Commons is 326 seats.
None of the parties achieved this, so we have a hung parliament for only the ninth time since 1832.
In most of the previous cases, another General Election was been called shortly afterwards.
A party is not required to have an overall majority in the Commons in order to form a government.
The largest party (although it does not have to be the largest) could form what is known as a minority government.
Of course, this makes it vulnerable to the remaining parties combining and defeating it on votes about legislation.
But there are many reasons why this might not happen.
The other parties may disagree with one another or they may be wary of defeating the government because this may trigger another General Election which will cost them resources and even seats.
There are many examples of minority governments around the world that work perfectly well, such as New Zealand.
There are also many local authorities in this country where minority-run councils still manage to run effective local services.
Alternatively, in a hung parliament two or more parties may have an informal agreement whereby, in exchange for concessions over policy, one of the parties to the agreement forms the government knowing that the other parties will support it in any votes in the House of Commons. In essence this was the so-called ‘Lib-Lab’ pact of the mid-1970s.
When coalitions do break up that does not necessarily lead to another General Election. One of the parties involved could opt to carry on as a minority government. It might seek out alternative coalition partners, assuming that the arithmetic allows other majority coalitions (a combination of parties that have an overall majority) to form.
Anticipating that a hung parliament could result after the 2010 General Election, a set of guidelines was written that outline the constitutional position. As the incumbent Prime Minister, Gordon Brown is not required to resign immediately his party loses its overall majority.
A pact is less formal than a coalition government. Normally, coalition governments include politicians from all the parties involved in the coalition as ministers and members of the Cabinet. The negotiations leading to coalition formation are normally about which ministerial and Cabinet posts each party is to be awarded.
Many countries, particularly those that use some form of proportional representation to elect their parliament, are governed by such coalitions. Sometimes, coalitions break up because the partners disagree over vital policy issues but they are actually more stable than most people probably imagine.
As the incumbent Prime Minister, Gordon Brown is not required to resign immediately his party loses its overall majority.
In February 1974, then-Prime Minister Edward Heath spent some time discussing a possible agreement with Jeremy Thorpe’s Liberal Party having lost his majority.
When no support came Heath resigned, leading the way for Harold Wilson to form a minority government. Another election followed in October the same year.
Mr Brown might try to negotiate with other parties, depending on the electoral arithmetic.
It is most likely that discussions would take place with the Liberal Democrats. This might lead to a pact or even a coalition although the latter is extremely rare outside of wartime conditions.
It might also lead to no agreement at all in which case Mr Brown has two options: continue to govern alone as a minority government or offer his resignation to the Queen and suggest to her that David Cameron be asked to form a new government.
If the former option is taken the first real challenge to his government comes with the Queen’s Speech, the statement of the government’s legislative plans for the new Parliament. If the government was defeated on this measure then Mr Brown would be expected to resign and the Queen would be advised on which party leader to invite to form a new government.
The second option will have already been discussed extensively between the political parties before it happens. If David Cameron’s name is offered to the Queen then he will already have indicated that either he is prepared to govern as a minority or has identified another party or parties to join him in either a pact or a coalition.