Allow me to take you on a journey. Journeys are all the rage. Tony Blair has been on one, from popularity to un-, although that rather simplifies the story that will be told in his memoir in September. Yesterday, David Cameron went on one. In a speech in Putney, he claimed that the Conservatives were now a different party: "I took it on a journey of change."
This column is going on a rather shorter journey. I began it thinking that the politics of a hung parliament, which is where almost all the opinion polls suggest we are headed, were complicated. I was ready to cite 1924 and 1974. I wasn't going to mention 1929, but my esteemed colleague Mr Alan Watkins, returning to the subject despite himself, fills that gap on page 47.
I was going to mention Christopher Geidt, former Army intelligence, diplomat, UN adviser in the Balkans, who is the Queen's Private Secretary. He and Gus O'Donnell, the Cabinet Secretary, would handle the discussions between the parties. By the time I reached the end of the column, however, I realised that, actually, a hung parliament is very simple. Nick Clegg has already told us what will happen. So I went back to the beginning and started again.
The key principle, which the Liberal Democrat leader has set out for at least a year now, was repeated in an interview in The Independent 10 days ago: "If a party with no majority has the strongest mandate, we accept the principle that that party has the right to govern either on its own or to reach out to others."
The only wrinkle is how to define "mandate", given that it is possible for Labour to win more seats while the Tories win more votes, as happened in February 1974. (The opposite is most unlikely.) Clegg refuses to be drawn on that: "If you say 'seats' you get a headline saying you are in the Labour corner. If you say 'votes' you are in the Tory corner."
In practice, however, it is seats that matter. If Labour is the largest party in the House of Commons, then it is almost inevitable that Gordon Brown will stay as Prime Minister. For two main reasons.
One is that, unlike two years ago, the last time that Westminster was awash with hung parliament speculation, an inconclusive election result would now look like some kind of moral victory for Brown.
That confuses what might be known as the Jeremy Thorpe Question. In February 1974, when Ted Heath spoke to the Liberal leader in an attempt to stay on in No 10, Thorpe told him that, although it may not be clear who had won, it was obvious who had lost. The loser was Heath, who had gone to the country asking, "Who governs?" If there is a hung parliament on 7 May, on the other hand, and especially if Labour were the largest party, it would look, paradoxically, as if Cameron had lost.
Not only that, but the kaleidoscope of policy has been shaken by the recession. Where two years ago Cameron the "liberal Conservative" seemed to be Nick Clegg's kind of guy, they are now at odds over the need for public spending cuts. Clegg tried to show a bit of Thatcherite ankle before his spring conference last weekend, praising the Great She-Elephant's victory over the trade unions as "immensely significant" and saying that the public finances should be repaired by spending cuts rather than tax rises.
But his party twitched ominously and he publicly recanted, reciting the hate-Thatcher mantra. Meanwhile on spending cuts he offers only Augustinian austerity – he promises fiscal virtue, but not yet. He and Vince Cable agree with Labour that spending cuts should not start too soon. (You might think that last week's discovery of an extra £10bn down the back of the Office for National Statistics sofa might change the terms of this debate, but it won't.)
So, if Labour is the largest party, Brown could offer Clegg a deal. Already, Labour offers the Lib Dems the Alternative Vote – a limited electoral reform that would give the Lib Dems significantly more seats. Because it will be in Labour's manifesto, Brown should be able to deliver his MPs. Then he could offer Clegg a two-year agreed recovery programme, given that the parties are close on economic policy. Does anyone doubt that, if necessary to keep him in office, Brown would also offer Vince Cable the post of Chancellor? Labour MPs wouldn't like it, but as the price of power? The Lib Dems would be deeply suspicious, but as one Lib Dem source told me: "There is a limit to what Nick Clegg can say No to."
Clegg has discussed with his colleagues the option of making Lib Dem support conditional on Labour changing its leader. But Brown doesn't want to go. Last week, he told Woman's Hour that he would "keep going" if he did not have a majority after the election. It has proved hard enough for Labour MPs to decide for themselves to get rid of Brown; making the change at the behest of a rival party would be even harder.
Because of Clegg's acceptance of the doctrine of the mandate, the mechanics of a hung parliament are, therefore, surprisingly simple. If Labour is the largest party, Brown will stay as Prime Minister; if the Tories have more MPs, Cameron will form a minority government. If YouGov is right, and the Tory share of the vote on 6 May is five percentage points more than Labour's, or less, Labour will be the largest party. If the other polling companies are right, and the Tory lead is greater, the Tories will have a definite "mandate", measured by both votes and seats.
Clegg has already conceded Cameron's "right to govern" in that case. The implication is that Lib Dem MPs would abstain on the Queen's Speech and, within 50 days of the election, George Osborne's emergency Budget. If the Tories are the largest party, Clegg has little bargaining power; he has already sold the pass: Cameron will be prime minister.
John Rentoul's blog is at: independent.co.uk/jrentoul