A Lib-Lab coalition may be what Liberal Democrats want at the next election, as we report today, but it is not an outcome they can bring about. Brutally put, the Lib Dems are the leftovers of British politics.

Their success in getting into government last time was a fluke of numbers. One number, in fact. The only number that matters to them is the difference between the Conservative and Labour shares of the vote. Anything between a one-point Labour lead and a seven-point Tory lead is likely to mean a hung Parliament, in which the Lib Dems have power.

Whether that will be the result again depends on stuff happening. The opinion polls are not in that zone at the moment. For the past 18 months, they have been in the part of the chart marked “Labour majority”. Everyone expects the Labour lead to shrink as the election nears, which might be a good reason for thinking it will grow. But only if Labour’s lead all but disappears will the Lib Dems be back in business.

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Let us assume, therefore, that they are not wasting their time in Glasgow this week. Then, however, there are two hung Parliament scenarios, depending on whether Labour or the Conservatives are the largest party. If it is the Tories, nothing much would change. Nick Clegg would carry on as Deputy Prime Minister, and some of the policies agreed in Glasgow would become negotiating positions for the next phase of the coalition.

As The Independent on Sunday reported last week, Clegg’s plan for free childcare for one- and two-year-olds could become a Lib Dem gain in another Tory-led government. Similarly, this week’s conference motion demanding the rolling back of the alleged extension of “secret courts” might be used to score a civil liberties point – although that would draw attention to how Lib Dem ministers let the Justice and Security Act 2013 pass in the first place.

Other Lib Dem policies are more obviously aimed at the second scenario, in which Labour is the largest party. The mansion tax, for example, which David Cameron rejected, to Clegg’s private surprise and satisfaction: “I’ll have that for 2015,” he said. “It’s very popular. Thank you very much.”

If Labour were the largest party, though, that would be the end of Clegg’s leadership. In a reversal of the balance of power in the 2010 coalition talks, in which the Lib Dems insisted that Labour dump its leader if it wanted to talk terms, Labour would tell the Lib Dems in 2015 that Clegg’s departure would be a condition of co-operation. Not only do Labour people regard Clegg as a crypto-Tory, his survival in office would look as if a permanent political elite had defied the verdict of the people.

That is the subtext of what is happening in Glasgow: the Vince Cable versus Tim Farron leadership contest. Farron, MP for Westmorland and Lonsdale and president of the party, last week praised Ed Miliband with all the subtlety of a mallet with “mallet” written on its head. Cable has gone for the more subtle approach of trying to be an effective Cabinet minister who was once a special adviser to John Smith. Notably, he has been responsible for two of the Government’s most unpopular policies – tuition fees and Royal Mail privatisation – and yet still comes across as the nation’s favourite wise uncle.

It helps, I suppose, that a good intellectual case can be made for both the trebling of student fees and the sale of the postal service. Figures to be published soon by the Business Department will show that, for the second year running, the proportion of students from poor households going to university has increased – contrary to the predictions of doom, disaster and discouraged working-class polymaths. And it is striking that 54 per cent of Lib Dem members now support higher tuition fees in the Lib Dem Voice poll that we report today. Most economists, meanwhile, would agree that the scale of investment needed by the Royal Mail would be best secured in the private sector. But these are emotive subjects, and it is only Cable’s social-democratic ballast that keeps him upright.

It will have done Cable no harm that the Prime Minister called him a “perpetual Jeremiah” last week. Or that he has annoyed David Cameron by arguing for the benefits of immigration. Cable will be 72 on the Saturday after polling day in 2015, but he could turn age to his advantage against Farron’s inexperience.

Cable’s satisfaction rating with party members of 77 per cent compares with Farron’s 68 per cent. This means that, if Labour is the largest party in a hung parliament, Cable could be Ed Miliband’s deputy prime minister. I remember speculating before the last election that Cable might be Chancellor in a Lib-Lab coalition, so I won’t make that mistake again. Equally, though, the Lib Dems won’t repeat Clegg’s mistake of taking a grand title without a department to go with it. If Cable does lead the party into a Lib-Lab coalition, he might be deputy prime minister and home secretary.

But that will happen only if the gap between Labour and the Tories, which the Lib Dems cannot control, falls in the magic range.

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