It comes down to simple mathematics - but will lead to considerable heartache for the unlucky families.

East Renfrewshire Council is considering proposals for Scotland's first-ever lottery on school places at one of its primaries.

The reasons for the move, at Mearns Primary in the Glasgow suburb of Newton Mearns, are two-fold.

East Renfrewshire schools such as Mearns are some of the most successful in Scotland and many families move into the area to take advantage of the high quality of education on offer.

In addition, every year hundreds of parents in neighbouring authorities such as Glasgow also try to get into the council's schools by using placing requests.

The result is that, despite depopulation in some areas of Scotland, numbers in East Renfrewshire continue to rise. Schools are oversubscribed.

Into this scenario comes the Scottish Government's demand that local authorities make "year-on-year" progress towards reducing class sizes to 18 in the first three years of primary.

Many authorities, particularly in rural areas, will be relying on falling population over the next decade to achieve this, but East Renfrewshire has no such luxury - which brings officials back to the mathematics.

Last year's P1 intake to Mearns Primary was 133, split into four classes of 33, but this year the council has decided to reduce the intake to 115 to provide three classes of 29 and one of 28 as part of the move towards the SNP targets. That means 18 fewer places this August.

The results are obvious. Although families living in the catchment area will be allocated a place as normal, some parents whose children would have got in last year through a placing request will now be turned away.

The school has already received 16 such requests, half from families with children already at Mearns Primary. These have been refused.

However, because schools routinely keep back a handful of places every year until the last minute to cater for families moving into the area there are a few spare places - and parents who have older children at the school and who appeal against refusal are likely to be entered into a ballot to decide who gets in.

Admittedly, the numbers involved are small, but the precedent is significant as East Renfrewshire Council claims pressure on its schools is likely to trigger more such lottery scenarios in future.

"We are under extreme pressure from rising school rolls because of the quality of education we offer and the attractiveness of our schools," said an authority spokesman. "The problem has been made more acute by the class sizes commitments we have to meet, which means the P1 intake will be reduced.

"It has come to the stage where we have to say that we are a special case because we have no spare capacity and, because our schools are full, we have no land to sell off to rebuild our school estate. We need to be funded for the growing numbers in our schools. If that is not the case then I think a ballot system could well be replicated elsewhere."

The authority is well aware the policy will prove to be highly controversial amongst parents, with well-documented opposition where similar schemes were implemented elsewhere.

The principle behind the introduction of lotteries is straightforward enough. The pursuit of the best schools by the middle classes has forced up property prices in areas surrounding them, preventing access for less well-off families. Introducing a lottery is one way of creating a level playing field, supporters argue. Earlier this year, Brighton and Hove became the first council to opt for a ballot element in its school admissions system, which prompted a furious reaction from some parents.

In that case, the council said it wanted to shake up the admissions system to make sure more children had access to a local school. As such, it introduced fixed catchment areas, effectively stopping children going to popular schools outside their own catchment area.

Crucially, where there are two schools serving an area, the allocation of places between them will be decided by a lottery.

The result of the policy was that hundreds of parents attended public meetings, almost 4000 people signed a petition, protest websites carried the latest developments and tens of thousands of leaflets were distributed.

Shortly after the Labour-controlled council revealed its intentions it was announced that Hertfordshire County Council, run by the Conservatives, had decided to introduce a random electronic ballot for admission to its single-sex schools, which traditionally have far more applicants than places.

The authority also said it wanted a fairer system by ruling out the advantage parents who live near to the school of their choice have.

Given the small numbers affected by the Mearns Primary case, it is unlikely to provoke a similar outcry, although one family member affected has already expressed doubt.

However, the authority has had to make tough decisions in the past on school entry - barring entry to one school to parents from new housing estates in a neighbouring authority area and introducing catchment areas for nursery schools - and should the lottery system be rolled out for entry to other schools there will undoubtedly be a public outcry.

Judith Gillespie, policy development officer with the Scottish Parent Teacher Council, believes that, rather than representing a fairer system, a lottery is unfair as it ignores objective reasoning. "Normally, placing requests work objectively and there are clear criteria which everyone understands such as how far away you live from the school in question. This brings East Renfrewshire closer to the randomness elsewhere," she said.

"By cutting class sizes in this way, East Renfrewshire appears to be jumping the gun, but what we are seeing is clear proof that the class-size policy can have a very negative impact."

While the name-out-of-a-hat approach might seem arbitrary for something so important, it is already used in other countries, including parts of the US, Sweden and New Zealand.

UK Government ministers have also backed authorities who choose the route. Jim Knight, Schools Minister, said it was "absolutely right that schools and town halls are responsible for choosing their own fair and transparent admission arrangements".

He said a lottery was just one method that could be used under the government's mandatory school admissions code. The Social Market Foundation recently called for the UK Government to introduce a lottery-style draw for places at over-subscribed secondary schools throughout England.

The think-tank said parents should be able to list up to six schools, in order of choice, anywhere in England, with ballots drawn for those which were over-subscribed until each pupil was allocated a place. The foundation said this would make the school entry system "equal for all", and "improve standards and social mixing". A spokesman said: "The present admissions system guarantees schools an intake regardless of how badly they perform. It is also more likely to benefit the rich than the poor. This is fundamentally unfair."