We had an interesting conversation last night with someone who was prepared, quite legitimately, to credit Scottish Labour with a little more good faith over their proposed plan to mitigate Tory tax credit cuts than we were. But we had a lot of trouble coming to an agreement over the arithmetic, and we tend to think that backs up our cynicism.

Labour have presented their supposed funding for the policy in an incredibly dishonest and disingenuous way, and it seems to have confused the media to the point where nobody in the print or broadcast media has challenged what appears to be a huge and (to us at least) incredibly obvious gaping hole in the finances.

Let’s walk through it one more time.

As we noted at the weekend, Kezia Dugdale has said that Labour will use the new welfare powers in the Scotland Bill – which allow the Scottish Government, within certain parameters, to create new benefits. The likely logistical and technical pitfalls of that notion have been dealt with far more expertly by Lallands Peat Worrier than we could manage, so for that aspect we’ll direct you to his analysis.

What we’re concerned with is the money. According to Dugdale herself, the cost of fully compensating the victims of the cuts will be around £440m a year. Plainly, that’s EXTRA money that has to be found on top of the current Scottish budget.

Dugdale says that £250m will come from not implementing the Scottish Government’s plan to phase out Air Passenger Duty. But clearly – really incredibly clearly – that won’t generate an EXTRA £250m, it’ll just avoid LOSING £250m from the budget.

(We suspect the Scottish Government would contend that it wouldn’t be lost at all, and would pay for itself by generating extra airport traffic, tourism income, jobs etc. But we’re not here to make that case – we’re discussing what Labour say they’d do.)

Let’s simplify the figures:

– Say the current budget is £1,000.

– To fund replacing the tax credits – a new additional expense – you need £1,020. (This number isn’t precisely proportionate, just broadly illustrative.)

– The Scottish Government currently plans to spend £10 buying a new hat.

– If Labour cancels the new-hat-buying plan, the budget is still £1000. It hasn’t gone up. You’re still the same £20 short you were to start with. You still have to find extra money from somewhere.

Labour’s plan to do so has two other planks. One is to avoid a planned Tory increase in the thresholds for higher tax rates. But that has the same problem as cancelling the APD cut – it doesn’t generate any MORE money, it just avoids you losing any from your already-inadequate starting position.

The second is an increase in the top rate of income tax, from 45p to 50p. But Dugdale herself admitted to Holyrood Magazine on Friday, with unusually admirable candour, that this could raise nothing at all:

“Up to £100 million. But bluntly, Mandy, it could also raise zero because of the mechanisms by which people can avoid paying tax so it is up to £100 million.”

The IFS estimates that the actual money raised in Scotland would be about £8m (as a population share of the £100m that would be generated were it implemented UK-wide, though if it was in Scotland only it’d very likely be less than £8m as some people would move across the border to avoid the higher rate, and because there are fewer top-rate taxpayers in Scotland to start with).

But even in Dugdale’s impossible-fantasy best-case £100m scenario, it’s still less than a quarter of what’s needed. (In our simplified figures above, at BEST we’d now have about £1,004 in the budget, and realistically more like £1,000 and 36p.)

The figure of £440m also doesn’t take account of what would likely be very high administrative costs, due to the huge cross-border and inter-departmental complexity that would be involved. We’ll very conservatively assume those come out to another £60m, as well as swallowing up whatever pennies Dugdale’s tax rise generates.

(That’s about twice the cost of administering prescription charges, which are far simpler, and it also gives us a nice round number.)

So what that leaves is a £500m black hole in Scottish Labour’s budget if they want to effectively reverse the tax credit cuts. It certainly doesn’t make it impossible, if the political will is there, but it means you have to be honest with people about the fact that you need to find that money somewhere.

There are only two ways for governments to get more cash: they can increase taxes or they can make cuts elsewhere. Labour have already ruled out the former – Dugdale and Ian Murray both said repeatedly on air at the weekend that nobody but the rich would pay any extra tax to fund the policy, and we know that doesn’t produce even remotely enough – so that leaves cuts.

There are remarkably few places to find £500m in the Scottish Government budget.

The graphic above will be familiar to followers of our recent set-to with the BBC’s Andrew Neil. It shows the total amount of money that’s under any sort of control by the Scottish Government, divided into the respective spending areas. If you dig into it, the departmental budgets come out like this:

Health: £12bn per year

Local government: £11bn per year

Education: £3bn per year

Infrastructure (building roads, bridges etc): £3bn per year

Policing/justice: £2.6bn per year

Rural affairs and the environment: £0.6bn per year

Culture and external affairs: £0.3bn per year

We can see that the only two departments that could even begin to afford a £500m cut without spectacular levels of damage are health and local government, and given the massive screaming fit Scottish Labour recently threw over a microscopic one-off drop of about £80m in health spending, slashing six times that much out of it every single year seems like an obvious non-starter.

And given the enormous fuss the party has also made for several years about the council tax freeze, it’d also be politically challenging (to understate the fact by several orders of magnitude) for Scottish Labour to suddenly hack half a billion pounds out of the local government budget, especially as councils are the last remaining bastions of Labour power in Scotland.

As a final option, Dugdale could decide to spread the burden out, perhaps by cutting £100m from each of the top five departments. Again, that’s not impossible, if she’s prepared to swallow the massive hypocrisy of cutting health AND education AND councils AND policing AND infrastructure after spending years in opposition attacking the Scottish Government for not spending enough on them.

But the point is that she’s not. She’s pretending, shamefully, that she can magic hundreds of millions of extra pounds out of nowhere without anyone suffering.

(We also, of course, really ought to be considering the continuing cuts to the budget coming from Westminster, which further reduce the ability to make any savings, and which we haven’t factored in here.)

Dugdale’s dishonesty is compounded several-fold by that of the media, which willingly turns a blind eye to the yawning chasm in her figures even though it’s always happy to scream “BLACK HOLE!” at the SNP at the slightest provocation.

(Not a single newspaper or broadcaster, at the time of writing, has picked her up on the absurdity of saying a non-cut to APD somehow creates extra money, and they can’t all be staffed entirely by innumerate clowns. Although perhaps it just reflects the fact that nobody takes the thought of her actually ever being First Minister seriously.)

But until either Labour or the press treats the Scottish people with some basic respect on matters like this, the Scottish people will be justly and deeply angry with both of them. People will be shouted at intemperately by hotheads on Twitter. Journalists will respond hypocritically, inflaming the sense of injustice and mistrust even further. The tone of public debate will continue to spiral downwards.

Because if you kick a dog a dozen times a day, you shouldn’t complain angrily or act surprised when it turns round and bites you. And if you respond to that by kicking it harder and more frequently, eventually it’s going to jump up and rip your throat out.