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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From Netflix to rented homes, why are we less interested in ownership?

Instead of owning things, we are renting experiences.

In 2008 the anthropologist Daniel Miller published a book based on an intimate study of 30 households on a single street in south London. The Comfort of Things ­explored the different kinds of relationships people have with what they own.

Miller described a retired couple’s house, cluttered with furniture, framed photographs and knick-knacks accumulated over decades. Down the road, a self-employed man called Malcolm had rented a flat. Malcolm preferred a spartan existence: he kept his belongings in storage, the better to travel at short notice, and conducted as much as possible of his life online. His home was his email address. His central material possession was his laptop.

Today, we are living more like the laptop warrior than the retired couple. Increasingly, our possessions are stored in the cloud or on a distant server. Just as we had grown accustomed to the idea of owning music in the form of data, we are now getting used to not owning it at all. In television, too, we stream instead of buy the latest drama series; when people use the term “box set” they are rarely referring to a box of discs on a shelf in the living room. Everything solid is melting into wifi.

Instead of owning things, we are renting experiences. The proliferation of mobile apps enables us to source or supply whatever we want, for short periods, more easily than ever before. The “sharing economy” is not about sharing, however. I encourage my three-year-old daughter to share her toys with her little brother; I don’t suggest that she charge him an hourly fee for doing so. A better name for it is the Paygo (pay-as-you-go) economy.

The Paygo economy combines two intertwined phenomena: the rise of renting and the decline of stuff. If you are in your twenties and unburdened by wealth you may already have accepted that you will always be in hock to a landlord. If you are in the market for a car, you will probably be thinking about leasing it, or joining a car club, or waiting until Google makes car ownership obsolete. There are even apps that allow you to rent a dog rather than take on the responsibility of owning one.

A world in which we own less and rent more is not necessarily one in which consumers are empowered. You never really own the electronic versions of a book or a film – you can’t lend them to a friend or sell them on – because the publisher retains its rights over them. Even our photos aren’t ours any longer: they are owned by corporations that scrape them for data that can be sold. In a recent article, the Financial Times journalist Izabella Kaminska argued that “ownership of nothing and the rental of everything represents . . . the return of an authoritarian and feudalistic society”.

The Paygo economy is changing our relationships with each other and with ourselves. Possessions form part of what the marketing academic Russell Belk calls “the extended self”. In Daniel Miller’s book, he describes how objects, however trivial, can embody relationships. Each household’s collection of stuff – tacky souvenirs, CDs we borrowed and never gave back – forms a constellation of personal significance. Post-materialism does not equate with spiritual enrichment. “Usually the closer our relationships with objects,” Miller writes, “the closer our relationships are with people.”

Human beings have a deep-seated tendency to imbue physical items with the ­essence of their owner. Hence the market for rock-star memorabilia: an old guitar that has been played by John Lennon is more valuable, and more revered, than a new replica that has not.

We apply this intuition even to money, the units of which are, by definition, interchangeable. Psychologists who study “essentialism” have found that people are less likely to recommend that stolen or lost cash be returned when it has subsequently been deposited in a bank account, as opposed to remaining in paper notes.

When things evaporate, so does ­meaning. A fetish for owning things connects to a yearning to retain a distinct identity in the face of change. Japan has been economically stagnant for decades and, as a result (and perhaps a cause), has preserved a set of idiosyncratic social norms, at odds with the rest of the developed world. One of these is a strong preference for owning music in a physical form: 85 per cent of the music bought in this technologically advanced society is on CD or vinyl. Japan is also the last developed country to rely on fax machines. A fax, unlike an email or the past, is something you can hold on to.

One way of framing the central arguments of British politics is that they are about the rights of owners versus renters – and not just in the sense of home ownership. Long-standing Labour members believe they own the party, and are outraged both by Momentum clicktivists and £3 voters. What appals many who voted Leave in the EU referendum is the thought that migrants can, in effect, rent a livelihood from the UK, treating the country as a giant Airbnb host. They want to know if this is still their country, or if they are now merely tenants of it.

Most younger voters chose Remain, but relatively few of them voted. That was a function of their lack of home ownership as much as age: millennials who rent are nearly half as likely to vote in elections as their peers who have managed to get on to the property ladder. This is partly a product of the mundane business of spending enough time in one place to get on the electoral roll, but it nonetheless suggests that renters form weaker bonds with the society in which they live.

For centuries, what we own has been an important way of placing ourselves in relation to those around us. The 18th-century curiosity cabinet was a collection of objects used to display the erudition and refinement of its owner. In the 20th century, houses became showcases. Your curtains, your car and your choice of decor said who you were or wanted to be. This was the era of what Thorstein Veblen called “conspicuous consumption”. In the Paygo economy, we will have fewer things of our own to ­display, as our possessions dematerialise and we rent more of what we need.

Despite all this, human nature has not changed: we are still apes with status anxiety, endlessly preoccupied by our position in any given hierarchy, eager for ways to convey our aspirations and allegiances. So we find other ways to signal. Rather than deploy what we own to say who we are, we use our photo streams and status updates to show it, even going so far as to arrange our meals and holidays with the aim of generating impressive on-brand content.

The vacuum of meaning opened up by the disappearance of stuff may even have increased the stridency of our political debate. One way I can let people know who I am is by loudly asserting my membership of a political tribe.

If I can’t show off my possessions, I will show off my beliefs.

Ian Leslie is the author of “Curious: the Desire to Know and Why Your Future Depends on It” (Quercus)

Ian Leslie is a writer, author of CURIOUS: The Desire to Know and Why Your Future Depends On It, and writer/presenter of BBC R4's Before They Were Famous.

This article first appeared in the 16 February 2017 issue of the New Statesman, The New Times