The most important thing about the debate over Labour’s tuition fee pledge is that most of the arguments, on both sides, don’t add up.

I want to first address the arguments against the pledge that don’t work.

The first, and most frequently deployed, is about people who don’t go to university subsidising those who do. The difficulty here is that they are already under the current system. After 30 years, the debt is written off by the Treasury, a bill paid out of, you guessed it, general taxation.

(Though because our tax system is already fairly progressive, this bill is again, predominantly paid by higher-earning graduates as well.)

This is more acute if people do work that is socially important but low-paying. A social worker, even one who makes the highest pay grade, is not going to pay off their tuition fees. A teacher who stays in the classroom is not going to pay off their tuition fees. The bulk of people who work as artists or designers are not going to pay off their tuition fees.

So you can’t really defend tuition fees using that argument. That Labour’s plan to pay for abolition – of which, more below – is levied on the highest earners makes the argument even more redundant.

The second argument is that a tuition fee cut is regressive – that is, it hands a great deal of money to above average-earners at the expense of lower earners. It is true that the policy was the single most expensive item in Labour’s manifesto, at £11.2bn a year. But as I’ve written before, what people miss about tuition fees is that they are a form of taxation: they are levied on graduates, not students, through PAYE or through your tax return. They don’t behave like any other type of fee or loan you might take out and should be seen as a tax.

That matters a great deal because taxation has to be seen in the round, not simply in isolation. The question over whether any tax cut is regressive is only partially about who the cut benefits.

Taken in isolation, decisions on tax made since 2010 have been highly progressive, increasing the share of public spending borne by the richest. But taken in concert with what is done with that revenue, changes to tax-and-spend have been highly regressive. The gains to the lowest earners from increases in the threshold – the amount you have to earn before levying taxation – have been more than wiped out by cuts in working-age benefits and the knock-on effects of cuts in services.

Labour’s tuition fee cut is paid for by increasing taxes on capital gains – that is profit made selling an investment – and people earning more than £80,000. So it is basically, for the most part, a tax cut for people earning £21,000 to £45,000 paid for by people earning more than £80,000. The overall package distributes from the highest earners to people earning above average – so it is downward redistribution, albeit not to the very poorest.

You can argue of course that this is not a particularly good use of £11.2bn. But the difficulty here is that for this argument to work, you have to believe that Labour would have been able to go into the 2017 election without promising to abolish fees and instead planning to spend the £11bn on, say, wraparound childcare or housebuilding, and would still have received the boost in 18-24 turnout that helped the party gain Warwick and Leamington, Canterbury, Cardiff North and Bristol North West, among other seats. This doesn’t seem particularly likely.

That doesn’t change the fact that while Labour is getting a lot of bang for its buck electorally speaking, it is not getting a lot of value policy-wise for its £11.2bn. Why not? Because the cost per graduate is actually quite small.

The cost for Plan 1 graduates – that is, graduates who went to university on the £3,000 fee – starts at £2 a month for people earning £17,776 or more a year, which gradually increases as you earn more. Earners at £80,000, when Labour's planned tax hike would kick in, pay £469 a month.

For Plan 2 graduates, the cost of repayment starts at £4 a month when you start earning more than £21,500 a year, and again, increases as you earn more. Earners at £80,000 pay £443.

These are not life-altering sums. If you are seeking to meaningfully alter the take-home pay of a graduate, reducing income tax by a penny – or value added tax, or for that matter duty on petrol – has a far more significant effect than cutting fees. Just ask people earning above £80,000, who would lose significantly more than they'd gain under Labour's plans.

(This is probably why tuition fees mostly exercise the parents of people paying them and students who have yet to pay them, rather than tax-paying graduates. It’s striking that Labour’s turnout boost came among 18-24s and they flipped parents from Tory to Labour. Actually, if you are a taxpaying graduate, Labour policies on housing and the taxable threshold do have a meaningful effect on your quality of life. Tuition fees, not so much.)

This is even more stark when you remember the cost of tuition fee abolition to the Exchequer, which comes in at a heady £11.2bn a year. There are lots of things you can do that actually would improve the pay packets of graduates – not least build a lot more housing – with £11.2bn, but not much that any individual graduate can do with £2 a month.

But regardless, it comes back to the earlier question: could Labour have got the results it did while pledging the tax rises that paid for that £11.2bn a year tuition fee cut but spending them elsewhere? I don’t buy it myself. Abolishing tuition fees is to Labour as redistribution to the affluent elderly is to the Conservatives – counterproductive as far as their policy aims go, but essential to their election-winning coalition.