THERESA MAY and Jeremy Corbyn do not have much in common. Yet both are offering education policies focused on improving the chances of children from poor families. Mr Corbyn’s Labour Party manifesto includes a promise to abolish tuition fees, levied by most universities at £9,000 ($11,600) a year. Mrs May plans to introduce new grammar schools, which are allowed to select pupils at 11 on the basis of scholarly talent.

Both policies will win votes: polls suggest that people quite like grammar schools and greatly dislike tuition fees. That is partly because both ideas hark back to a post-war golden age of social mobility, in which bright, poor children could take the 11-plus entrance exam to win entry to a good school, before proceeding to a free university and, later, a career in business, government or science.

Yet, in truth, the post-war years of upward mobility had more to do with the changing structure of the labour market than educational institutions. And the evidence suggests that both policies will probably fail to improve social mobility.

Take fees first. The Labour manifesto argues that there “is a real fear that students are being priced out of university education”, but provides flimsy evidence to support the claim. Although, as it notes, the number of students has fallen this year, that reflects a fall in the 18-year-old population, Brexit’s deterrence of foreign applicants and the abolition of bursaries for those on nursing and midwifery courses. The reality is that the gap in higher education attendance between rich and poor students has narrowed since the government tripled the amount that universities were allowed to charge in 2012.

Shifting funding from the state to students enabled the government to remove limits on the numbers universities could admit. The resulting increase particularly benefited poor students. In Scotland, where tuition is free and a cap on student numbers remains, the growth in university attendance in deprived areas has been slower. In England loans are available to pay for tuition and are paid back only once a graduate earns more than £21,000 a year. Since outstanding debts are forgotten after 30 years, almost three-quarters of graduates will probably never fully repay their loan. Thus the abolition of tuition fees would mostly benefit high earners. The Institute for Fiscal Studies, a think-tank, estimates the policy would cost £8bn a year.

Likewise, children from well-off families are the main beneficiaries of Britain’s 163 existing grammar schools. According to research published last year by the Education Policy Institute, another think-tank, children at grammars score one-third of a grade higher in each of their GCSE exams, which are taken at 16, than do those at comprehensive schools. Yet few poor children pass the entrance tests: just 2.5% of children at existing grammars receive free school meals (a proxy for poverty), compared with 8.9% at nearby state schools. And those at comprehensive schools near grammars do worse than their peers elsewhere, partly because grammars attract the best teachers.

There are ways to increase the number of poor pupils at grammar schools: from creating entrance tests that are harder to prepare for to mandating a certain number of places for children on free school meals. But those children who failed to make the cut would still do worse than they would under a comprehensive system. Studies have demonstrated that selection at 11 does not improve overall results: it merely changes the distribution of good grades.

Both Mrs May and Mr Corbyn say that a desire to improve social mobility lies at the heart of their education policies. In fact, they risk doing just the opposite.