The conventions governing a hung parliament have been published for the first time in a cabinet manual drawn up by Gus O'Donnell, the Cabinet Secretary. I helped with the production of the manual, the terms of which have been attacked by David Cameron as being biased against the Conservatives and giving the incumbent Prime Minister an unfair advantage.
But the conventions are not intended to be biased against the Conservatives, or indeed any party. They do nothing more than codify current arrangements. It is open to the Conservatives to propose reform if and when they obtain office. They might, for example, propose that Westminster copy the Scottish Parliament, where different rules apply. For the moment, however, the manual remains an accurate guide to what has been happening.
The conventions reflect the fundamental principle of parliamentary government: that parliament decides who should govern. A prime minister in office is not defeated until the Commons votes him out. Until 1868, it was common practice for incumbents to test the opinion of parliament after a general election. That year, Disraeli became the first to break from this tradition - he thought it pointless to meet parliament when his opponents enjoyed an overall majority.
With the development of a two-party system, it became customary for incumbents to resign if the election resulted in an overall majority for the opposition. But, in 1885-86, 1892 and 1923-24, with hung parliaments, prime ministers - Conservative in each case - waited until parliament had met and then produced a Queen's Speech that was, in effect, a vote of confidence. It is for parliament, not the bankers or the Daily Mail, to decide who should govern.
If Gordon Brown were to present a Queen's Speech to parliament, its centrepiece would presumably be a bill providing for a referendum on proportional representation. It would then be for the Liberal Democrats and nationalists to decide whether to vote for it. If they did, it would probably pass. But if it failed, it would be many years before the issue presented itself again. The last time a government produced a bill to reform the electoral system was in 1931, when Labour proposed the Alternative Vote. A bill passed the Commons, but suffered wrecking amendments in the Lords, and was swept away in the financial crisis of the same year.
Before that, in 1917, the first Speaker's conference had unanimously recommended the Single Transferable Vote in urban constituencies (and, by a majority, the Alternative Vote in the rest). But Lloyd George, Liberal prime minister in a coalition government, rejected the proposal. In the first vote on proportional representation, 77 Liberals voted for it and 53 against. PR was lost by just eight votes. Since then, however, proportional representation has become part of Britain's political culture, being used for elections to the devolved bodies in Scotland, Wales, Northern Ireland and London, without any noticeable ill-effects.
Whatever new government is formed, the current parliament is unlikely to last for long. A Conservative-Liberal Democrat arrangement could, it is true, provide a numerically comfortable majority. But the differences between the two parties are, as Cameron has admitted, so great on matters such as Europe, immigration and defence, as well as on the need for immediate cuts in public expenditure, that it might prove no more than a very rickety coalition of convenience. Liberal-Conservative co-operation in coalitions, moreover, does not have a very happy history. The Liberal Unionists of 1886 and Liberal Nationals of 1931 were swallowed whole by the Conservatives, while the independent Liberals left the Conservative-dominated national government after just one year in 1932, in protest at an imperial tariff.
The British history of minority governments is no happier. The first two Labour minority administrations were bereft of legislative achievement. The 1924 and March 1974 governments lasted less than a year. The 1929 government and that of Callaghan lasted longer, buttressed in each case by agreement with the Liberals, but both eventually collapsed in ignominy.
A second general election is therefore likely in the foreseeable future. In that election, the Liberal Democrats might well be squeezed as voters are urged to polarise between the two "old" parties. That is what happened after the hung parliaments of 1924 and 1974, and after the short parliament of 1950-51. But a happier scenario for the left is possible.
Coalitions and pacts work effectively only when, as in other European countries, there is agreement on a common programme, not when they are the product of a sudden emergency. A Labour-Lib Dem arrangement would, therefore, have to go further than a referendum on the electoral system. The two parties would need to agree on a common programme buttressed by an electoral pact. That would involve Labour standing down in Lib Dem seats where the main challenger was a Conservative, and in Conservative-Lib Dem marginals where Labour had no chance. The Lib Dems would, in return, have to agree to stand down in Labour-Conservative marginals where they stood no chance. If that happened, the inconclusive and muddy outcome of the general election could inaugurate a new "progressive alliance".
The 20th century was the Conservative century because the left was divided. Unlikely though it may seem, the general election of 2010 might just herald the dawn of a progressive century, if the parties of the left prove to be serious about altering the electoral system.
Vernon Bogdanor is professor of government at Oxford University. His books include "The New British Constitution" (Hart, £17.95)