A statistical trick which reveals whether MPs are lying about expenses

Benford's law has many uses. Can it trip up MPs?

Are politicians routinely making up expenses? A simple statistical test suggests not.

Benford's law is a statistical artefact found in numerical data spanning several orders of magnitude. Ben Goldacre explains:

Imagine you have data on, say, the population of every world nation. Now, take only the "leading digit" from each number: the first number in the number, if you like. For the UK population, which was 61,838,154 in 2009, that leading digit would be "six". Andorra's was 85,168, so that's "eight". And so on.

If you take all those leading digits, from all the countries, then overall, you might naively expect to see the same number of ones, fours, nines, and so on. But in fact, for naturally occurring data, you get more ones than twos, more twos than threes, and so on, all the way down to nine. This is Benford's law: the distribution of leading digits follows a logarithmic distribution, so you get a "one" most commonly, appearing as first digit around 30% of the time, and a nine as first digit only 5% of the time.

This pattern should repeat for almost any data which matches the key condition of spanning a large range of sizes. Take the example above, world populations, which goes from 800 in the Vatican City to 1.35 billion in China. But one category of data which rarely obeys the law is that where the numbers are made-up. When people are trying to "randomly" write down numbers, they rarely do it very well, more frequently following the intuition that random data ought to have just as much chance of starting with any given digit.

The value of MP's expenses certainly spans several orders of magnitude. Excluding repaid claims, expenses in the latest tranche, released last week, span from a value of 10p (reconciliation for a travelcard between Euston and Coventry) to £9900 (for staffing costs in Woking constituency office).

So does the data follow Benford's law? It largely does:

 

The largest variation is a 3 percentage point difference between the expected number of leading 2s and the actual number, with most other digits being present in slightly larger quantities than expected.

Scanning through the data, it's easy to see why this is. There are a large number of claims which are made repeatedly. For instance, 18 different MPs claimed £139.26 for the same twin pack of HP toner cartridges; while nearly every claim for petrol costs came in between £10 and £19.99, boosting the 1s' count again. Conversely, there simply weren't that many must-have services which began with a 2 (although a lot of things MPs need do, apparently, cost £20 on the dot, from venue hire to cleaning bills and car parking).

None of which means there may not still be fraud in the expenses. It simply means that the actual values being claimed for have been drawn from real life. MPs are not, on the whole, making up numbers on the spot as the fill in expense forms; whether what they are claiming for ought to be paid out of the public pocket, statistics are less likely to help with.

(As an aside, it's actually surprising that the figures match Benford's law quite so well; while MP's may not be choosing the numbers they submit, the people who set the prices clearly are. That's probably the reason for the slight uptick in the 9s, for instance; a lot of things which may cost £10 instead are charged as £9.99. It seems that there are either enough counter-examples that it gets balanced out, or lots of claims for things like mileage, which have no set price)

Two data CDs, much like the ones which sparked the original expenses scandal. Photograph: Getty Images

Alex Hern is a technology reporter for the Guardian. He was formerly staff writer at the New Statesman. You should follow Alex on Twitter.

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I can’t follow Marie Kondo's advice – even an empty Wotsits packet “sparks joy” in me

I thought I’d give her loopy, OCD theories a go, but when I held up an empty Wotsits bag I was suffused with so many happy memories of the time we’d spent together that I couldn’t bear to throw it away.

I have been brooding lately on the Japanese tidying freak Marie Kondo. (I forgot her name so I typed “Japanese tidying freak” into Google, and it was a great help.) The “Japanese” bit is excusable in this context, and explains a bit, as I gather Japan is more on the case with the whole “being tidy” thing than Britain, but still.

Apart from telling us that we need to take an enormous amount of care, to the point where we perform origami when we fold our underpants, which is pretty much where she lost me, she advises us to throw away anything that does not, when you hold it, “spark joy”. Perhaps I have too much joy in my life. I thought I’d give her loopy, OCD theories a go, but when I held up an empty Wotsits bag I was suffused with so many happy memories of the time we’d spent together that I couldn’t bear to throw it away.

After a while I gave up on this because I was getting a bit too happy with all the memories, so then I thought to myself, about her: “This is someone who isn’t getting laid enough,” and then I decided that was a crude and ungallant thought, and besides, who am I to wag the finger? At least if she invites someone to her bedroom no one is going to run screaming from it, as they would if I invited anyone to my boudoir. (Etym: from the French “bouder”, to sulk. How very apt in my case.) Marie Kondo – should bizarre circumstance ever conspire to bring her to the threshold – would run screaming from the Hovel before she’d even alighted the stairs from the front door.

I contemplate my bedroom. As I write, the cleaning lady is in it. To say that I have to spend half an hour cleaning out empty Wotsits packets, and indeed wotnot, before I let her in there should give you some idea of how shameful it has got. And even then I have to pay her to do so.

A girlfriend who used to be referred to often in these pages, though I think the term should be a rather less flippant one than “girlfriend”, managed to get round my natural messiness problem by inventing a game called “keep or chuck”.

She even made up a theme song for it, to the tune from the old Spiderman TV show. She would show me some object, which was not really rubbish, but usually a book (it may not surprise you to learn that it is the piles of books that cause most of the clutter here), and say, “Keep or chuck?” in the manner of a high-speed game show host. At one point I vacillated and so she then pointed at herself and said, “Keep or chuck?” I got the message.

These days the chances of a woman getting into the bedroom are remote. For one thing, you can’t just walk down the street and whistle for one much as one would hail a cab, although my daughter is often baffled by my ability to attract females, and suspects I have some kind of “mind ray”. Well, if I ever did it’s on the blink now, and not only that – right now, I’m not even particularly bothered that it’s on the blink. Because, for another thing, I would frankly not care to inflict myself upon anyone else at the moment.

It was all a bit of a giggle eight years ago, when I was wheeled out of the family home and left to my own devices. Of course, when I say “a bit of a giggle”, I mean “terrifying and miserable”, but I had rather fewer miles on the clock than I do now, and a man can, I think, get away with a little bit more scampish behaviour, and entertain a few more illusions about the future and his own plausibility as a character, when he is squarely in his mid-forties than when he is approaching, at speed, his middle fifties.

Death has rather a lot to do with it, I suppose. I had not actually seen, or touched, a dead body until I saw, and touched, my own father’s a few weeks ago. That’s what turns an abstract into a concrete reality. You finally put that to one side and gird up your loins – and then bloody David Bowie snuffs it, and you find yourself watching the videos for “Blackstar” and “Lazarus” over and over again, and reach the inescapable conclusion that death is not only incredibly unpleasant, it is also remorseless and very much nearer than you think.

And would you, dear reader, want to be involved with anyone who kept thinking along those lines? I mean, even if he learned how to fold his undercrackers into an upright cylinder, like a napkin at a fancy restaurant, before putting them in his drawer? When he doesn’t even have a drawer?

Nicholas Lezard is a literary critic for the Guardian and also writes for the Independent. He writes the Down and Out in London column for the New Statesman.

This article first appeared in the 05 February 2015 issue of the New Statesman, Putin's war