Imagine a world in which every school was great, apart from those that were magnificent. It would hardly matter if children did not get a place in their preferred, magnificent, school. They would just have to make do with the school that was merely great.

But, this morning, here in the real world, almost 100,000 parents will receive, by letter, e-mail or text, the news that they have not got the school they wanted. Everyone will proclaim that new Labour’s obsession with choice is pointless and what matters is a good local school. They are wrong.

Of course it is hugely disappointing when a child fails to get a place in the school of their choice. So many mum hours and so much school-gate wisdom wasted. But we need to calm down and stop having the wrong argument. It’s not actually the number of successful first choices that counts; it’s the low quality of the second choices that matters.

We need to remember that some parents play the system like a game. An Institute of Education study last month reported that 7 per cent of parents who did receive their first choice would, ideally, have preferred to send their children somewhere else. But rather than risk a rotten school by pursuing a place in the best, they opted for a middling school they were confident of getting into.

We need to remember, too, that a quarter of all parents choose the local school because they can walk there. They get their first choice but some of them discover later that it’s not very good.

Then there is the small minority of parents who are satisfied with the education their children are getting but probably shouldn’t be. In other words, not all first choices are good.

The trouble is that very few second choices are. The annual recrimination about parental choice teaches us that there are still not enough good schools. That is, in part, because local bureaucracies refuse, for perfectly good financial reasons, to fund surplus places. Hence the supply barely alters from year to year.

There is little or no chance of this changing under the current management. Labour has a better record on education than it is given credit for but Ed Balls’s time at what is no longer the Department of Education has been dominated by child protection issues. In the process, Labour has, foolishly, abandoned school reform to the Conservatives.

If Michael Gove succeeds Mr Balls he has pledged to allow parents to set up their own schools with state funding to the value of about £5,000 a child. Existing schools too will be able to expand if they wish. It would help if the Tories called for school admissions to be announced in October rather than in March. That would allow the governing body to reconfigure their space to offer more places if they were able to do s —, as plenty are.

However, this is not a reform that comes free of charge. If the state stumps up the capital, then the more succesful it is at encouraging new schools, the more it costs. The really bold decision, from which the Tories are shying away just as Labour always has, would be to invite educational companies to make a profit in return for them providing the start-up capital. This will have to happen soon enough because, even if there are enough voluntary sector providers out there, which is doubtful, there is no money.

Ten more years of reform would certainly mean that the second best schools would be a lot better than they are. But even that wouldn’t solve the problem entirely. There is no admissions system within the wit of man that will avoid the best schools being over-subscribed. Even in the utopia of universal greatness it will still be rational for parents to choose the best school they can.

Therefore, it is crucial to find a fair way of distinguishing between applicants. At the moment, the closer you live to the school, the better your chance of getting in. Formal catchment areas for the best schools have now shrunk to a tiny radius. The market then works its efficient magic. A 10 per cent improvement in Key Stage 2 results in primary schools brings with it a 7 per cent increase in house prices. The middle class choose whether to pay termly fees or a monthly mortgage supplement. Meanwhile, admissions officers can be spotted walking the streets with a tape measure, as if school admissions were like working out who has won a game of bowls.

There is a time-honoured way of distinguishing between people who all want the same thing. It allocates equal weight to every child, regardless of the wealth of their parents. It is indisputably even-handed. It is a lottery. This is how it works.

Catchment areas are abolished and all parents exercise their choice. If their preferred school is not over-subscribed they get it. But if it is, every child’s name should go into a hat. The first names out get the places and there is a right to appeal only on the grounds that the lottery had been administered wrongly.

There is one decisive political objection to the lottery scheme: it means that, all of a sudden, access to a good school cannot be purchased via the housing market. In politics, the complaints of those who lose will always drown out the muted thanks of those who gain. It will be hard to do but it is only when we have enough good schools and a fair way of selecting children that parental choice will become really meaningful.