The American author Malcolm Gladwell has an idea about how to improve schooling. I am going to tell you what it is and explain what it means for the new era of public spending control that we have just entered. But before I do so, I am going to tell you about my favourite con trick.

It's really clever, this one. The con artist sends out 10,000 letters selling his services as an investment adviser. He tells the recipients that he is very good at stock picking, but that he doesn't expect them simply to take his word for it. He is going to show his predictive power over the coming four weeks.

In this first letter he predicts the direction in which the price of a particular stock will travel in the next seven days. Now here's the clever bit - he has split the recipients in two. He tells 5,000 of them that the stock will go up, while 5,000 are told it will go down.

Now, let's say the stock goes up. The con artists ditches the 5,000 people he misinformed and concentrates on the 5,000 who thinks he got it right. Again he sends 2,500 letters saying that a particular stock will go up and 2,500 saying that it will go down. He continues until he has 625 recipients hugely, but incorrectly, impressed at his predictive ability. He asks them to give him their life savings to invest. Dastardly but brilliant.

Right, where was I? Oh, yes, public spending and Malcolm Gladwell.

The coverage of last week's Pre-Budget Report concentrated on changes to taxes, but in the long run it is changes to public spending that may prove more important. Labour's realisation that it had no choice but to reduce sharply future spending growth marks the end of an era.

In 1979 the Conservatives were elected with a mandate to get a grip on public spending. They did this by restraining the rate of growth, without substantially changing the way that services were organised. This approach did not prove politically sustainable. In 1997 the Tories were swept out of office and much of the force behind the sweeping came from a strong public mood that services had deteriorated to an unacceptable extent.

So Britain entered a new phase. The Labour Government did not reform services either, but it did start spending. And spending. The growth of spending was faster than the growth of the economy. Logically a time was bound to arrive when this could not continue, unless the public showed an unexpected tolerance of high taxes. The policy was bound to hit the buffers at some point, and last week it did.

The Conservative idea of suppressing spending on essentially unreformed services was not sustainable and neither was Labour's spendthrift alternative. So now we have to try something else - redesigning public services so that they can be maintained at a high standard without spending growing faster then the economy.

Which brings me to Gladwell's new book Outliers. One of his central arguments is that perspiration counts as much as inspiration. He reels off a number of success stories - Bill Gates, high-school ice hockey champs, the Beatles - where 10,000 hours of practice preceded their breakthrough. He hypothesises that this number of hours of practice is essential to success.

He proceeds to assert that successful schooling is down to the amount of time spent at school. The long summer vacation, and relatively short school hours, disadvantages American pupils, in particular poor ones. The reason why Asian pupils do better at maths, he suggests, is simply that they spend more time doing it. He lauds the KIPP Academy in New York City. Despite large classes and a diverse intake, pupils achieve remarkable results. Gladwell's view is that their progress in maths is spectacular because KIPP Academy hours are gruelling - round-the-clock school attendance, very little summer vacation. Maybe we should try this everywhere.

All very stimulating. But also a little confusing. Because at the same time as reading Gladwell, I was also reading the ideas of Matthew Taylor, the former adviser to Tony Blair, and one of the most interesting people in the Labour Party. And Taylor was suggesting pretty much the opposite of Gladwell. Pupils might go to school four days a week, using the other day for more flexible study. He has a success story, too. Apparently the Kunskapsskolan schools in Sweden cut right back on classroom time and achieve great results.

So which is correct? Here's my helpful response. Both of them? Neither of them? Who knows?

Take Gladwell's thesis. It suffers from a problem called survivor bias. It is true that a number of famous successful people have spent 10,000 hours practising. However, it is also true that many people we have never heard of because they weren't successful also practised for 10,000 hours. And that there are successful people who were very good without practising for 10,000 hours before their breakthrough (the Rolling Stones, say). And Gordon Brown isn't very good at being Prime Minister despite preparing for 10,000 hours

In other words, it works exactly like the con trick. In fact, the con trick is the textbook example used to explain survivor bias - the con artist looks like a genius to those unaware of all his failures. Only his successful predictions survive. We hear of KIPP Academy through Gladwell and of the Kunskapsskolan schools through Taylor because they are successful. But what about all the schools that did the same thing but failed? Perhaps they exist, but aren't written about. Perhaps they gave up on their experiment.

It may be that longer school hours work or that shorter school hours work - or that different pupils will benefit from different approaches. We simply don't know. And realising that is the first step to liberation.

In the previous two phases of public sector management - the Tory phase and the Labour phase - we were certain that we could know, that we could find a brilliant example of good practice and spread it everywhere. I remember lauding some American schools to a colleague at No10, and being told that these were progressive schools, so they were bound not to work.

In the next phase we must embrace our lack of knowledge. We must allow for chaotic, greatly diverse public services, never settling on one model of provision. We must allow outside organisations to question the fundamental ideas that shape health provision or welfare provision. We must allow them to innovate and keep the money saved through innovation. That way there is a chance that public services, just like say, electronic goods, will keep improving without costing more.

One things is for sure. We can't carry on as we are, pretending that without reform our money will go farther. That would be a con trick.

daniel.finkelstein@thetimes.co.uk

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