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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In her first interview of 2017, I pressed the Prime Minister for Brexit clarity

My week, including running out of cat food, reading Madeleine Thien – oh, and interviewing Theresa May on my show.

As the countdown to going live begins in your ear, there’s always a little rush of adrenalin. Especially when you’re about to launch a new Sunday morning political programme. And especially when you’re about to conduct the Prime Minister’s first interview of 2017. When you hear the words, “Cue Sophy,” there’s a split-second intake of breath – a fleeting moment of anticipation – before you start speaking. Once the show is under way, there’s no time to step back and think; you’re focused on what’s happening right now. But for that brief flicker of time before the camera trained on you goes live, you feel the enormity of what’s happening. 

My new show, Sophy Ridge on Sunday, launched on Sky News this month. After five years as a political correspondent for the channel, I have made the leap into presenting. Having the opportunity to present my own political programme is the stuff that dreams are made of. It’s a bit like having your own train set – you can influence what stories you should be following and which people you should be talking to. As with everything in television, however, it’s all about the team, and with Toby Sculthorp, Tom Larkin and Matthew Lavender, I’m lucky enough to have a great one.

 

Mayday, mayday

The show gets off to a fantastic start with an opportunity to interview the Prime Minister. With Theresa May, there are no loose comments – she is a cautious premier who weighs up every word. She doesn’t have the breezy public school confidence of David Cameron and, unlike other politicians I’ve met, you don’t get the sense that she is looking over her shoulder to see if there is someone more important that she should be talking to.

In the interview, she spells out her vision for a “shared society” and talks about her desire to end the stigma around mental health. Despite repeated pressing, she refuses to confirm whether the UK will leave the single market as it leaves the European Union. However, when you consider her commitment to regaining control of immigration and UK borders, it’s very difficult – almost impossible – to see how Britain could remain a member. “Often people talk in terms as if somehow we are leaving the EU but we still want to kind of keep bits of membership of the EU,” she said. “We are leaving. We are coming out. We are not going to be a member of the EU any longer.” Draw your own conclusions.

 

Women on top

This is probably the kind of thing that I should remain demurely quiet about and allow other people to point out on my behalf. Well, screw that. I think it’s fantastic to see the second female prime minister deciding to give her first interview of the New Year to the first woman to front a Sunday morning political show on television. There, I said it.

 

Escaping the bubble

In my view, every journalist should make a New Year’s resolution to get out of London more. The powerful forces that led to the political earthquake of 2016 came from outside the M25. Every week, I’ll be travelling to a different part of the country to listen to people’s concerns so that I can directly put them to the politicians that I interview. This week, it was Boston in Lincolnshire, where the highest proportion of people voted to leave the European Union.

Initially, it was tricky to get people to speak on camera, but in a particularly friendly pub the Bostonians were suddenly much more forthcoming. Remain supporters (a minority, I know) who arrogantly dismiss Leave voters as a bunch of racists should listen to the concerns I heard about a race to the bottom in terms of workers’ rights. Politicians are often blamed for spending too much time in the “Westminster bubble”, but in my experience journalists are often even worse. Unless we escape the London echo chamber, we’ll have no chance of understanding what happened in 2016 – and what the consequences will be in 2017.

 

A room of one’s own

Last December, I signed a book deal to write the story of women in politics. It’s something I’m passionate about, but I’ll admit that when I pitched the idea to Hachette I had no idea that 2016 would turn out to be quite so busy. Fitting in interviews with leading female politicians and finding the time to write the damn thing hasn’t been easy. Panic-stricken after working flat out during the EU campaign and the historic weeks after, I booked myself into a cottage in Hythe, a lovely little market town on the Kent coast. Holed up for two weeks on my own, feeling a million miles away from the tumultuous Westminster, the words (finally) started pouring on to the page. Right now, I’m enjoying that blissful period between sending in the edited draft and waiting for the first proofs to arrive. It’s nice not to have that nagging guilty feeling that there’s something I ought to be doing . . .

 

It’s all over Mao

I read books to switch off and am no literary snob – I have a particular weakness for trashy crime fiction. This week, I’ve been reading a book that I’m not embarrassed to recommend. Do Not Say We Have Nothing, by the Canadian author Madeleine Thien, tells the haunting story of musicians who suffered during the Cultural Revolution in China. It’s also a chilling warning of what happens when anger towards the elite is pushed too far.

 

Political animals

However busy and exhilarating things are at work, my cat, Ned, will always give me a reality check. In the excitement of the first Sophy Ridge on Sunday, I forgot to get him any food. His disappointed look as he sits by his empty bowl brings me crashing back down to earth. A panicked dash to Sainsbury’s follows, the fuel warning light on all the way as I pray I don’t run out of petrol. Suddenly, everything is back to normal.

“Sophy Ridge on Sunday” is on Sky News on Sundays at 10am

Sophy Ridge is a political correspondent for Sky News.

This article first appeared in the 12 January 2017 issue of the New Statesman, Putin's revenge