Linda is outspoken and very bright. In college she majored in philosophy. She was concerned about social justice and went on anti-nuclear demos. Recently she turned 30. What do you think she is up to now?

When Daniel Kahneman and Amos Tversky put this question to a group of survey respondents, I don't suppose they intended to illuminate the stupidity of much of the British debate over public spending. But I think that they did.

In his new book on randomness, The Drunkard's Walk, Leonard Mlodinow recounts the results of Kahneman and Tversky's experiment - one of the great classic studies of decision-making. Respondents were given a series of possible occupations for Linda and asked to rank their probability. Is she, for instance, now active in the feminist movement? Does she work in a bookshop and take yoga classes? Is she a bank teller? A teacher? An insurance salesperson? A bank teller who is active in the feminist movement?

Unsurprisingly, given what they were told about Linda, it was thought most likely that she would be active in the feminist movement and least likely that she would be an insurance salesperson. There was, however, an interesting kink in the results. People ranked the likelihood of Linda being a bank teller active in the feminist movement higher than the probability that she is merely a bank teller.

This makes sense, doesn't it? After all, how likely is it that someone as socially concerned as Linda would give it all up and become simply a bank teller? But, as Mlodinow explains, however plausible their conclusion appears, the respondents had violated what he calls the first law of probability - “the probability that two events will both occur can never be greater than the probability that each will occur individually”.

In other words, the probability that Linda is now not only a bank teller but also a feminist cannot be greater than the chance that she is a bank teller.

If this appears obvious, consider this - this exact error has cropped up again and again in politics in the past two decades without anyone pointing it out. In fact, it has become central to our debate on public spending.

The other day Yvette Cooper, the Treasury Minister, accused the Tories of advancing proposals for increased public spending that were “unfunded”. Her implication is that spending promises should not be believed unless they are accompanied by promises of matching savings or tax increases. Ms Cooper's statement is bog standard, and hardly raised an eyebrow. It is always accepted that a party is more likely to carry out its promises if it can show exactly where the money is coming from.

Yet to believe this is to believe something that violates Mlodinow's first law of probability as surely as the respondents did when asked about Linda. For that law is quite clear - it is more likely that a political party will, for example, increase the number of police officers, than that it will increase the number of police officers by cutting spending on bureaucracy. As Kahneman and Tversky put it: “A good story is often less probable than a less satisfactory explanation.”

This is not merely an abstract point. In practice, over the past 20 years political parties have repeatedly made promises that are perfectly reasonable, and then offered to pay for them with detailed proposals for savings they were unlikely to make.

I participated in such an exercise. In 2001, when I was Tory policy director, we made some fairly modest proposals for tax cuts that would not have been difficult to achieve. But we also offered some proposals for saving that would not have raised enough money to cover our promises. Linking our tax cutting with specific saving made the proposals easier to defend because it seemed to make the whole thing more plausible. In fact, we had made it less, not more, likely that we would deliver the full promise we made.

But it was not only Mlodinow's first law of probability that was involved in the error. It was also Finkelstein's first law of opposition policymaking.

Oppositions do not have the capacity to decide on anything more than broad principles, and should not try. As director of opposition policy, I probably had fewer people working for me than the Government employed on its policy (it had one) to ensure that the selection of carpets in government offices helped to promote the arts. We got things wrong because we didn't have the capacity to get them right.

Why am I writing about all this now? Because on Monday George Osborne, the Shadow Chancellor, let it be known that he is reviewing the Tory stance on public spending. And this provides the possibility for an escape from the barren debates of the past two decades.

Last year, anticipating an early election, Mr Osborne promised that if the Tories won, he would adhere to Labour's spending plans until they expired in 2011. Politically, he didn't have much choice. To do anything else would have been to risk running exactly the same campaign as the last two. And with the same result.

Now the need to match Labour has gone. The Government lacks the credibility to set the terms of the debate. And its recent decisions to borrow to get itself out of a hole means that it can no longer argue credibly that it is wrong to make unfunded offers to the voters. Mr Osborne, it seems, is ready to say this. And this is a big opportunity.

Now there are, of course, many things that the Shadow Chancellor can't do. He can't, as some on the Right ludicrously suggest, promise now that he will spend less than Labour, because he does not yet know what Labour's plans are. And he cannot promise tax cuts because that would be irresponsible given the state of the public finances.

Yet what he can do is greater than what he can't do. He is able to do something not just for himself but for the rest of us. He can liberate us from elections dominated by bogus arguments about fictitious figures.

He can announce that the charade of the past 20 years is over. He can say that he no longer intends to use the figures of the outgoing Government as his baseline. He can say that he refuses to offer bogus “matching savings” for every minor promise. He can say that an opposition party is in a position to tell voters that it is by instinct fiscally conservative and desirous of low taxes, but that it is not in a position to decide the size of the budget for, say, juvenile courts in the year 2013.

Mr Osborne should not just say that he won't match Labour. He should issue a declaration of independence from the whole sorry mess that is the public spending debate. Such a declaration might help him to win. It would certainly help him to govern. And for the rest of us it would be a blessed relief.

daniel.finkelstein@thetimes.co.uk

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