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 the 1980s, I went to a rally where Labour Party speakers shared the stage with men in balaclavas

The links between the Labour left and Irish republicanism are worth investigating.

A spat between Jeremy Corbyn’s henchfolk and Conor McGinn, the MP for St Helens North, caught my ear the other evening. McGinn was a guest on BBC Radio 4’s Westminster Hour, and he obligingly revisited the brouhaha for the listeners at home. Apparently, following an interview in May, in which McGinn called for Corbyn to “reach out beyond his comfort zone”, he was first threatened obliquely with the sack, then asked for a retraction (which he refused to give) and finally learned – from someone in the whips’ office – that his party leader was considering phoning up McGinn’s father to whip the errant whipper-in into line. On the programme, McGinn said: “The modus operandi that he [Corbyn] and the people around him were trying to do [sic], involving my family, was to isolate and ostracise me from them and from the community I am very proud to come from – which is an Irish nationalist community in south Armagh.”

Needless to say, the Labour leader’s office has continued to deny any such thing, but while we may nurture some suspicions about his behaviour, McGinn was also indulging in a little airbrushing when he described south Armagh as an “Irish ­nationalist community”. In the most recent elections, Newry and Armagh returned three Sinn Fein members to the Northern Ireland Assembly (as against one Social Democratic and Labour Party member) and one Sinn Fein MP to Westminster. When I last looked, Sinn Fein was still a republican, rather than a nationalist, party – something that McGinn should only be too well aware of, as the paternal hand that was putatively to have been lain on him belongs to Pat McGinn, the former Sinn Fein mayor of Newry and Armagh.

According to the Irish News, a “close friend” of the McGinns poured this cold water on the mini-conflagration: “Anybody who knows the McGinn family knows that Pat is very proud of Conor and that they remain very close.” The friend went on to opine: “He [Pat McGinn] found the whole notion of Corbyn phoning him totally ridiculous – as if Pat is going to criticise his son to save Jeremy Corbyn’s face. They would laugh about it were it not so sinister.”

“Sinister” does seem the mot juste. McGinn, Jr grew up in Bessbrook during the Troubles. I visited the village in the early 1990s on assignment. The skies were full of the chattering of British army Chinooks, and there were fake road signs in the hedgerows bearing pictograms of rifles and captioned: “Sniper at work”. South Armagh had been known for years as “bandit country”. There were army watchtowers standing sentinel in the dinky, green fields and checkpoints everywhere, manned by some of the thousands of the troops who had been deployed to fight what was, in effect, a low-level counter-insurgency war. Nationalist community, my foot.

What lies beneath the Corbyn-McGinn spat is the queered problematics of the ­relationship between the far left wing of the Labour Party and physical-force Irish republicanism. I also recall, during the hunger strikes of the early 1980s, going to a “Smash the H-Blocks” rally in Kilburn, north London, at which Labour Party speakers shared the stage with representatives from Sinn Fein, some of whom wore balaclavas and dark glasses to evade the telephoto lenses of the Met’s anti-terrorist squad.

The shape-shifting relationship between the “political wing” of the IRA and the men with sniper rifles in the south Armagh bocage was always of the essence of the conflict, allowing both sides a convenient fiction around which to posture publicly and privately negotiate. In choosing to appear on platforms with people who might or might not be terrorists, Labour leftists also sprinkled a little of their stardust on themselves: the “stardust” being the implication that they, too, under the right circumstances, might be capable of violence in pursuit of their political ends.

On the far right of British politics, Her Majesty’s Government and its apparatus are referred to derisively as “state”. There were various attempts in the 1970s and 1980s by far-right groupuscules to link up with the Ulster Freedom Fighters and other loyalist paramilitary organisations in their battle against “state”. All foundered on the obvious incompetence of the fascists. The situation on the far left was different. The socialist credentials of Sinn Fein/IRA were too threadbare for genuine expressions of solidarity, but there was a sort of tacit confidence-and-supply arrangement between these factions. The Labour far left provided the republicans with the confidence that, should an appropriately radical government be elected to Westminster, “state” would withdraw from Northern Ireland. What the republicans did for the mainland militants was to cloak them in their penumbra of darkness: without needing to call down on themselves the armed might of “state”, they could imply that they were willing to take it on, should the opportunity arise.

I don’t for a second believe that Corbyn was summoning up these ghosts of the insurrectionary dead when he either did or did not threaten to phone McGinn, Sr. But his supporters need to ask themselves what they’re getting into. Their leader, if he was to have remained true to the positions that he has espoused over many years, should have refused to sit as privy counsellor upon assuming his party office, and refused all the other mummery associated with the monarchical “state”. That he didn’t do so was surely a strategic decision. Such a position would make him utterly unelectable.

The snipers may not be at work in south Armagh just now – but there are rifles out there that could yet be dug up. I wouldn’t be surprised if some in Sinn Fein knew where they are, but one thing’s for certain: Corbyn hasn’t got a clue, bloody or otherwise. 

Will Self is an author and journalist. His books include Umbrella, Shark, The Book of Dave and The Butt. He writes the Madness of Crowds and Real Meals columns for the New Statesman.

This article first appeared in the 25 August 2016 issue of the New Statesman, Cameron: the legacy of a loser