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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To heal Britain’s cracks, it’s time for us northern graduates in London to return home

Isn’t it time for people like me, who’ve had privileges and experiences not open to everyone, to start heading back to our local communities, rather than reinforcing London’s suffocating dominance?

I’m from Warrington. The least cultured town in the UK. My town.

I moved to London almost exactly five years ago. Not because I particularly wanted to. Not because I wanted to depart the raucous northern town that I still call home. Because it was my only choice, really. I’d done my stint in the call centres and had some fun. But that couldn’t, surely, be my lot?

After university, I’d already started feeling a little weird and out of place back in Wazza. There were fewer and fewer people who didn’t look at me like I’d just fallen off a futuristic space flight that’d given me a different accent and lofty ideals.

Of course, that’s because most people like me had already skipped town without looking back and were all in the capital trying to strike beyond the ordinary.

The young, the cities, the metropolitan elite are still reeling after last week’s vote and wondering how people, half of our people, have got it so horribly wrong. We’re different, divided, done for.  

One thing I’ve clung onto while I’ve been in London is the fact that I’m from Warrington and proud. It might not be a cultured town, but it’s my town.

But I wasn’t proud of the outcome of the EU referendum that saw my town vote 54.3 per cent to 45.7 per cent to leave.

To be fair, even in my new “home” borough of Hackney, east London, the place with the third-largest Remain vote, one in five people voted for Brexit.

Yes, in one of London’s hottest and most international neighbourhoods, there are quite a lot of people who don’t feel like they’re being taken along to the discotheque.

Perversely, it was the poorest places in the UK that voted in largest numbers to leave the EU – that’s the same EU that provides big chunks of funding to try to save those local economies from ruin.

In many ways, of course, I understand the feelings of those people back in the place I still sometimes think of as home.

Compared to many suffering places in the UK, Warrington is a “boom town” and was one of the only places that grew during the last recession.

It’s a hub for telecoms and logistics companies, because, ironically, its good transport links make it an easy place to leave.

But there are many people who aren’t “living the dream” and, like anywhere else, they aren’t immune from the newspaper headlines that penetrate our brains with stories of strivers and scroungers.

Warrington is one of the whitest places in the UK, and I’m sure, to many locals, that means those immigrants are only a few towns away. There’s already a Polski sklep or two. And a few foreign taxi drivers. Those enterprising bastards.

We have never seriously addressed the economic imbalance in our economy. The gaping north-south divide. The post-industrial problem that politicians in Westminster have handily ignored, allowing the gap to be filled by those who find it quick and easy to blame immigrants.

When schemes like HS2, which is plotted to smash right through the place I grew up, are pushed against all of the evidence, instead of a much-needed, intercity Leeds to Liverpool investment to replace the two-carriage hourly service, it’s like positively sticking two fingers up to the north.

But I am also a big problem. People like me, who get educated and quickly head off to London when things aren’t going our way. We invested in ourselves, sometimes at state expense, and never really thought about putting that back into the places where we grew up.

There weren’t the right opportunities back home and that still stands. But, rather than doing something about that, people like me lazily joined the gravy train for London and now we’re surprised we feel more kinship with a 20-something from Norway than we do with someone who we used to knock on for when we should have been at school.

That’s not to suggest that our experiences in the capital – or mine at least – haven’t made us a thousand, million times better. 

I’ve met people who’ve lived lives I would never have known and I’m a profoundly better person for having the chance to meet people who aren’t just like me. But to take that view back home is increasingly like translating a message to someone from an entirely different world.

“You know, it’s only because you live in a country like this that a woman like you is allowed to even say things like that,” assured one of my dad’s friends down at the British Legion after we’d had a beer, and an argument or two.

Too right, pal. We live in what we all like to think is an open and tolerant and progressive society. And you’re now saying I shouldn’t use that right to call you out for your ignorance?

We’re both Warringtonians, English, British and European but I can increasingly find more agreement with a woman from Senegal who’s working in tech than I can with you.

It’s absolutely no secret that London has drained brains from the rest of the country, and even the rest of the world, to power its knowledge economy.

It’s a special place, but we have to see that there are many people clamouring for jobs they are far too qualified for, with no hope of saving for a home of their own, at the expense of the places they call home.

It’s been suggested in the past that London becomes its own city-state, now Londoners are petitioning to leave the UK.

But isn’t it time for people like me, who’ve had privileges and experiences not open to everyone, to start heading back to our local communities, rather than reinforcing London’s suffocating dominance?

We can expect local governments to do more with less, but when will we accept we need people power back in places like Warrington if we want to change the story to one of hope?

If this sounds like a patronising plan to parachute the north London intelligentsia into northern communities to ensure they don’t make the same mistake twice... Get fucked, as they say in Warrington.

It was Warrington that raised me. It’s time I gave something back.

Kirsty Styles is editor of the New Statesman's B2B tech site, NS Tech.