Page last updated at 03:27 GMT, Friday, 23 October 2009 04:27 UK

A tale of small numbers

Pool balls

Different ways of seeing stats

Politicians like to talk big, but perhaps we - and even they - might have a better idea what they were up to if they counted small, suggests Michael Blastland in his regular column.

The language of politics is billions. Billions up, billions down, billions more, billions cut. Feeling dizzy about the state of the public finances when one telephone number of pounds succeeds another?

Here's a simple alternative, a language politicians seldom use, perhaps because it would be revealing. This language uses small numbers like two, for example. Not a number to excite headline writers. But to see the big picture, you need small numbers.

Here's how they work. Governments can only spend what they tax or borrow. They can only tax a share of what we, the public, already have. So it helps to know what share they want and then how they plan to share that out between all the things they want to do. Note that we're talking shares here, or proportions. Not billions.

British warship
We used to spend four on defence, now we spend two

So two is about the percentage share of what the nation has each year that the government spends on defence. Two is also the percentage share of GDP by which defence has been cut in the last 20 years.

That is, the share of what we have as a nation that we devote to defence has roughly halved, from four to two. The Conservatives took it down most of the way, while Labour seemed content with that and then let it drift a smidgen further.

Two is also roughly the extra percentage share of national income that the government put into health over about five years to provide those record quantities of billions we were often told about.

Using small numbers like these enables us to see how the money we have available is moved around over time. It also shows us how big government is - a bit over 40 (out of 100) depending whether you measure with or without recession - and how much it borrows compared with its income.

If someone says they want more for defence, or more for education, we can say "what share?" or "and what other share does this share come from?" A bit more of the taxpayers' share, a bit more of the share for transport? Tricky, only 1.5 goes to transport as it is.

We could more easily identify trends like those in this chart, and see shifting priorities over the years.

Dfenece statistics graph

Now the sums become easier too. First, you say what the state is going to take - whether it's 40 or maybe 38, or perhaps 42 (these numbers tend not to vary as much as the billions-based commentary might suggest). Then you say how you are going to share it out, whether health is to remain at about eight-ish as now, or grow, or shrink.

You also have to say how you're going to find something like the six that is roughly equivalent to what the government has been spending each year more than its underlying income - whether you plan to take this from the taxpayer or cut it.

And at least now we can also see the scale of the borrowing problem. Six is about three times the defence budget or about three-quarters of the entire health budget. This has little to do with the one-off cost of the recession - it is simply the share of underlying borrowing needed every year if the government raises, say, 36 from tax and spends 42.

Gordon Brown
Gordon Brown wants to raise 16bn by selling assets. That's about a one

When the Institute for Fiscal Studies crunches the political numbers and pronounces on their coherence, the simple method it uses is first to do the calculations with the small numbers and then work out what they might mean in detail.

This doesn't tell us everything, but we'd know much more about what the government or opposition plans to do, roughly how they intend to make the books balance, or not, roughly what their priorities are (instead of telling us that everything is a priority) and how much of our income they will take.

Shadow Chancellor George Osborne could tell us how his billions of savings announced at the Conservative conference compare with the six necessary to achieve balance (they equal about 0.5 by the year 2014). Prime Minister Gordon Brown might tell us how the government reached a position of spending six more than it really raised, even after assuming the recession and all the unemployment it creates has gone.

Our message to politicians could be simple. If you are really interested in informing us, rather than trying to dazzle us, don't only tell us billions, also tell us the small numbers. Tell us the shares. Share with us your priorities. What do you think the shares should be in future?

Do that, and we could then work out what it means to each of us in pounds, and what it means to the long-term prospects for services like health, education and defence.

Though of course they will all say they will achieve everything by some miracle of efficiency. They always do. But have you noticed how these miracles also come in big numbers?

Below is a selection of your comments.

The same principle of dealing with proportions rather than absolute numbers could be extended to legal fines. If someone on a £20k salary is fined one days salary for, say, a first speeding offence, they pay about £54, which is close to the current figure of £60. If a millionaire is fined £60, they would scarcely notice it, whereas if fined 1 day's salary, they would have to pay over £2500, which would be more proportionate.
Wim Clarke, Nottingham

If the economy shrinks, GDP goes down and therefore, the fixed value of each 'share' will also go down. Many costs (such as employee salaries) are fixed. If 1 share used to cover NHS salaries, they might need 1 and a quarter shares to cover the same bill during a period of recession. I suppose you could argue that these costs should be managed internally within each department, but I think we must acknowledge that in practical terms, the government probably does need to make fixed cost (rather than variable share) commitments in at least some situations.
Molly, Cardiff

The headline figures are meaningless but the percentage is all important. For instance the national debt was proportionately larger in the 1960s than it will be after this recession. Most of all could the politicians of all parties start being honest. If we cut government expenditure then we will cut areas of government activity. While this is not necessarily a bad thing I would like to know what is going to be cut. Cutting the sure start schools will simply mean that children from poor and often struggling families will go on to have children in families that struggle. Simplifying the benefit and tax system if done carefully could reduce the number of people employed by the state and improve our experience of the state benefits/tax system. So Please could the politicians be more explicit in their plans and less power hungry.
Steve Gapp, High Wycombe

I'm in favour of anything which makes politicians more accountable to the public through greater transparency.. while we're at it, why not abolish all of the little taxes we're exposed to and come clean.. one tax - it may be 60 - 70 % of wages but at least what we have left over would be ours to keep.
Chris, Liverpool

Politicians and captains of industry know that most people will just "nod through" any decisions involving large numbers. However once the numbers become small enough to grasp then everyone has an opinion. The apocryphal boardroom item for a quote of £99 to paint the bikeshed takes at least half-an-hour of debate to progress.
ChrisJK, UK

Just like in your book, The Tiger That Isn't, it's clear that the way in which information is fed to the public is poor; Few people actually know little about the numbers and percentages being published in newspapers every day, except for the base emotion they feel when they read the headline.
Martin Law, Blantyre, United Kingdom

I agree that the billions quoted by politicians are meaningless numbers when not put into the context. Additionally there are other areas of government that this would be useful for. One example is energy policy. I'd love to see a simple description of the energy load required then the actual input into the national grid of each energy development and renewables project.
Dan Arnold, Edinburgh

I would be interested to see what the rest of the 42 is spent on, after 8 for health, 2 for defence and 1.5 for transport, and how the 36 raised by the government is made up, in terms of income tax, VAT, corporate taxes etc.
R J Tysoe, London, UK

If the politicians won't then can the BBC continue this highly useful and simple language? It could become a bit like the colour coded nutrition wheel on our food!
Gary, Glasgow

Whilst I agree with the gist of this article, I don't think defence is the best example, versus health. Health is a sum that will go up as population increases (as it has and will continue to). Defence on the other hand is a fixed cost for an island our size, therefore as GDP increases, the share of GDP for defence will drop.
Tommy Long, Maidstone, Kent

I think that mastering the numbers 1-100 is the key. In business most work is done in percentages as the relative difference is the main issue (are we getting better). Mastering orders of magnitude (ten, hundred, thousand) is much harder. You can see this in the frequency with which people confuse millions and billions - despite there being a thousand fold difference. What the health defence chart does not show is that defence may have gone up in both in both nominal and real terms over the period.
Chris Tchen, Ellesborough, Bucks

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