I have tried, but I cannot make the Barnsley by-election mean anything. It was a "bad result for the Liberal Democrats", as Nick Clegg put it, but we knew that they were in trouble before Thursday. For everyone else, it was a Mirror of Erised election, in that you saw in it whatever you wanted to see.

For the shiny-faced New Generation of Ed Milibandites, it was evidence that two new spin-doctors and a bit of steadiness at Prime Minister's Questions was enough to expose the Tory-led coalition for the deeply unpopular craze of right-wing horridness that it really is.

For the hard-faced Conservative traditionalists, whose main complaint is that this is precisely what the Coalition ought to be but is not, it was evidence that Sunshine Cameron is being dangerously outflanked by the true Tories of the UK Independence Party.

(For Jim Murphy, Labour's defence spokesman, it was vindication of his advice that the party should choose more candidates who have served in the armed forces.)

Yes, it was a striking result. Labour is not used to increasing its share of the vote in by-elections, mainly because it has been in government for so long. It was the first time that Ukip had come second in any parliamentary election. And sixth place, down from second, was embarrassing for the Lib Dem, coming behind the Tory, the BNP and a local independent, Tony Devoy, a former miner whose main pledge was to donate half his MP's salary to charity if he won.

However, once you twiddle all the dials on the vote-interpreter to account for known variables, the machine tells us what we already know. First, it was a by-election, and by-elections tend to be poorly attended street parties of anti-government sentiment. Second, a good candidate (or the absence of a weak candidate) can maximise this anti-government effect. Third, a sense of nationhood, to put it delicately, matters to a lot of voters. Fourth, the coalition parties performed as poorly as each other when you take into account the collapse in Lib Dem support last year.

This last point may need some explanation. The formation of the coalition last May roughly halved the Lib Dem base line by driving away the Labour-leaning half of Lib Dem voters. Thus, while the Tory share of the vote in Barnsley halved compared with the general election, the Lib Dem share shrank by three-quarters.

But a grim result for both governing parties doesn't mean what the coalition's opponents say it means. Mid-term by-election wins are a poor predictor of general election victories. Labour's current lead in national opinion polls, of about five percentage points, is not much better. Nor even, I would suggest, is a more significant polling number, which is David Cameron's 12-point lead over Ed Miliband when people are asked who would make a better prime minister. But that last figure describes the underlying structure of British politics: it's just that we've got four years of spending cuts and unknowable economics to pile on top of it.

Nor should we waste time on the argument that Ukip's success is a warning to Cameron that he should return to the policies that lost elections for William Hague and Michael Howard. Ukip is not the provisional wing of the 1988 Conservative Party: its vote is almost as much a disaffected Labour vote as it is a disaffected Tory vote. The only poll in Barnsley, by a new company called Survation, suggested that the largest chunk of the Ukip candidate's support came from people who had voted Labour in the general election.

No, the success of Ukip and the BNP in Barnsley reflected a largely working-class disillusionment with the political establishment, which is seen as soft on immigration and weak in standing up for British interests in Europe. And we knew that, too.

Which is not to say that the Lib Dems are in good shape. Nick Clegg's strategy of proving he can be trusted with the tough decisions of government by being just as enthusiastic as the Tories about cutting public spending was never going to give his party a separate identity. The big political event of this month, the Budget, is essentially a Tory-Labour fixture, or even just the Osborne and Balls show. Ed Balls limbered up last week by launching a campaign against his policy in government, which was to raise the tax on petrol from April, while Osborne countered by suggesting that next month's cuts – most of which were planned by Alistair Darling – are "Labour's cuts".

So it was interesting that Clegg gave a speech last week on multiculturalism in which he set out the difference between him and the Prime Minister. The week before it was voting reform. This is intended to get away from what one insider described as "the danger of homogenised language". Where Cameron suggested, I thought, that "state multiculturalism" in some way helped to radicalise the 7/7 bombers, Clegg was robust - even "muscular" - in rejecting any role for government policy, however misdirected, in causing terrorism. Clegg's speeches have often been poor, but this was a good one.

Other Lib Dem cabinet ministers have been giving what they regard as important speeches. Vince Cable, at the Mansion House last week, trumpeted his success in getting the Bill through the Commons for part-privatising the Post Office. Chris Huhne came close to saying that $100-a-barrel oil was a jolly good thing because it made a low carbon economy less expensive by comparison.

Even if anyone had noticed, none of that really hangs together as a distinctive Lib Dem contribution to the coalition, still less as the outline of a vote-winning Lib Dem programme at the next election.

The main lesson to be learned from the Barnsley by-election was provided by Nick Clegg, who warned people not to "write off the Liberal Democrats". Ah, now, writing off the Liberal Democrats. No one had actually said that. But now that he has put it in people's minds...

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