UNIVERSITY tuition fees separate politicians’ heads from their hearts. A broken pledge by Nick Clegg, the deputy prime minister, not to raise them is widely credited with costing the Liberal Democrats legions of student voters. Both the Labour and Conservative parties have, in the past, reversed similar pledges. But as The Economist went to press, Ed Miliband, leader of the opposition Labour Party, was set to promise to reduce the cap on annual fees from £9,000 ($14,000) to £6,000 if he becomes prime minister. This proposed cut is less good than it sounds.

The system that has emerged from more than a decade of rows over fees is complex but progressive—that is, it redistributes from rich to poor. Graduates in England can borrow from the government to pay for fees and living costs, but must only repay 9% of their earnings over £21,000 (much as if they were paying an additional income tax). In 2012—amid noisy student protests—the government raised the cap on fees from £3,300 to £9,000. It also boosted the repayment threshold—from £15,000—bringing down graduates’ monthly bills. The change was costly for students on average, but also made the system much more redistributive. Debts are written off after 30 years, so whereas poor graduates benefit from lower monthly payments, they do not end up paying the higher fee. As a result, the true cost of university depends more on lifetime earnings than on the fee (which explains why even some obscure universities set prices high). Lower fees would help only the successful; low earners would simply have less debt written off. By one estimate, Mr Miliband’s policy will benefit only those with a starting salary of at least £35,000 followed by lots of pay rises.

Savings from the new system have not been as large as once hoped, as forecasts for debt write-offs have risen. Costs to government were initially expected to total 32p per £1 lent. That was revised up to 45p in 2014. Repayments hinge on assumptions about wages and behaviour several decades in the future. On the current best guess, the new system looks only 5% cheaper than the old one (though universities are 25% better funded).

At the time fees were raised, opponents said they would deter disadvantaged students from applying. That does not seem to have happened: applications from poor students hit a record high this year. However, it remains the case that many more wealthy students attend elite institutions than do poor ones. Just 3% of children from poor backgrounds in England go on to high-status universities—less than in South Korea, Canada and Sweden. Mr Miliband wants to look like he is helping to plug that gap. He also wants the votes of those in university towns, many of whom are disillusioned with Mr Clegg’s volte-face.

The proposal would leave universities with less funding unless they were compensated with an increase in their direct grants. This might not happen: unlike debt write-offs, increased grants boost the deficit. That means Labour must find a way to pay for the policy, even though the government’s cashflow would be largely unchanged (under either system, it pays the full cost of the course up front). Fearing for their budgets, university chiefs have criticised the proposal. Mr Miliband is expected to find the cash by reducing tax relief on saving for retirement.

The only genuine cost to the taxpayer under the plan would be lower repayments from well-off high earners. Lower headline fees would certainly warm some hearts in the short run. But the head says the policy is a bad idea.