“Whoever has will be given more, and they will have an abundance,” reads a particularly depressing verse of the Book of Matthew. “Whoever does not have, even what they have will be taken from them.”

So seems, at least, to be the case in transport policy. London, which by most standards has a pretty extensive public transport system, has been very successful in persuading the government it needs a bigger one. Other cities, which don’t, often haven’t. Is this just because the people who make the spending decisions have to take the tube?

Well, yes, that probably is a factor, if we’re honest. But there’s something else going on too. I suspect there might be maths at work here, too.

To explain, let’s fire up our copy of Microsoft Excel and start modelling this baby. Imagine a country with three significant cities. Because I am a geek, we’ll call them King’s Landing, Winterfell and Lannisport.

To keep things simple, let’s assume that, at the start of our experiment, all of them have economies worth one billion gold pieces; and, all else being equal, their economies grow by 1 per cent a year. So, ten years down the line, you get this:

Equality reigns. It’s all very predictable.

But in year 10, Ken Targaryen, the mayor of King’s Landing, somehow manages to find the money to build a metro line. (Doesn’t matter how, he just does.) Public transport investment makes a city more prosperous – people can get to a wider range of jobs, that sort of thing – and also attracts more people to move to the city. So let’s say that it boosts the city’s total growth rate by, say, 0.5 per cent.

Thanks to its wise investment strategy/stroke of good luck, King’s Landing is now growing faster than the other cities. So, in year 20, the economic map looks like this:

King’s Landing is now richer than the other cities – not by much, but it is.

So. The Westerosi national government (which is based in King’s Landing, but that’s just a coincidence) is now deciding where to make its next public transport investment. This, too, will improve the potential growth rate of any city by 0.5 per cent.

Now the fair thing to do would obviously be to send it to one of the provincial cities – let’s say Winterfell – so that it has half a chance to catch up with King’s Landing. If it does that, then two of the three cities would be growing at 1.5 per cent a year, and the third by just 1 per cent. A decade later the chart would look like this:

But the Westerosi Treasury is charged with making sure it gets maximum bang for its buck with every investment it makes. So, it decides to check what would happen if it instead invested the money in adding a line to the existing King’s Landing transport network.

If it did that, the King’s Landing economy would be growing at 2 per cent a year; the other two would be stuck stubbornly on just 1 per cent. Here’s where we are ten years later:

Well, would you look at that? Turns out that building another line in King’s Landing is better for the national growth rate than building an entirely new system in Winterfell. Only by 6m gold pieces – that barely buys you anything, these days – but it counts, nonetheless.

And so the Treasury, being the committed guardians of the public finances it is, goes with option B.

You’re getting the point now, I’m sure, but let’s roll this forward 50 years to hammer things home. Every ten years, the Westerosi Treasury announces that one lucky city will be getting a new transport line. Every ten years, it runs the numbers and finds it’ll get the best result from investing in King’s Landing yet again. Here’s year 80:

King’s Landing is now a booming metropolis with seven metro lines and an economy worth 5,808 million gold pieces. Its GDP grows by 4.5 per cent every year.

The struggling cities of Winterfell and Lannisport, though, are still sluggishly trundling along at growth of just 1 per cent, and their economies are worth barely a third of that of the capital. King’s Landing’s new mayor, Boris Baratheon, is starting to ask irritable questions about whether it’s fair that his hard-working citizens should be expected to support lazy provincials through their taxes.

In year 80, Winterfell asks the Treasury for money for public transport once again, but the numbers just don’t stack up. If they build line one of the Winterfell Metro, it’ll add 352m gold pieces to the city’s GDP over the next ten years. But if they build the much needed King’s Landing Crossrail, it’ll add 5.4bn gold pieces to the capital’s GDP. The latter will cost a bit more – quite a lot more, actually – but even so, with benefits like that, it’s a no brainer, really, isn’t it?

One last graph to sum the situation up. Here’s the GDP of King’s Landing, with its ever growing public transport network, plotted against a provincial system without one.

Yep.

Now this is, very obviously, a massive over simplification (it’s a model, that’s what they’re for). For one thing, we’ve conflated population growth and productivity. For another, not all transport investments will have the same effect on GDP growth: perhaps the boost a city gets from moving to zero to one metro lines would be bigger than the boost it gets when it goes from seven to eight. And it’s far from clear that you can keep adding half a point to growth rates just by building new metro lines.

But the point, nonetheless, is clear. If transport investment is assumed to add to a city’s potential growth rate; and if the people deciding where to make transport investments are focused on getting the maximum impact from that investment; then it’s always going to seem more sensible to invest in the place that’s bigger and faster growing. It’s simply a property of the maths: it’s better to increase the growth rate of the big thing than the small thing.

This is, to my mind, the single strongest argument for some kind of devolution. The national Treasury may never feel it’s a good investment to build a metro line in a struggling city; that city’s residents and government almost certainly would.

Otherwise you’ll get to the end of the century and find that Winterfell and Lannisport are still stuck in the economic doldrums, while the economy of King’s Landing is so over heated that Bravosi oligarchs have started buying up patches of the place and nobody can afford to buy a house. And who wants that?