Some other issues need to be considered in the light of the debate over the lottery system.
The best predictor of a school's educational achievement is, apparently, the proportion of students getting free school dinners. It should come as no surprise that, within a class society, the most important factor in education is social class.
No education system can magic this fact away until socialism abolishes class society.
That is why socialists have supported an education system that mixes people from all backgrounds, a comprehensive system of schools where children of all backgrounds and "abilities have equal access to a decent properly-funded education.
The only way I can see this being even partially possible is to end any choice of school and draw up of catchment areas that create a cross-section of society in each school.
That would mean not taking just the children from the closest areas (unless you imposed compulsory class- mixed housing).
Such a policy would of course be attacked by parents like those in Brighton and Hove who claim to want ‘schools4communities’ and insist that their twelve-year old little darlings can’t possibly travel a whole twenty minutes to school on public transport, but must be driven in the Chelsea tractor.
But, frankly, I don’t much care about these disingenuous objections.