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.

Photo: Getty
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How the row over Jackie Walker triggered a full-blown war in Momentum

Jon Lansman, the organisation's founder, is coming under attack. 

The battle for control within Momentum, which has been brewing for some time, has begun in earnest.

In a sign of the growing unrest within the organisation – established as the continuation of Jeremy Corbyn’s first successful leadership bid, and instrumental in delivering in his re-election -  a critical pamphlet by the Alliance for Workers’ Liberty (AWL), a Trotskyite grouping, has made its way into the pages of the Times, with the “unelected” chiefs of Momentum slated for turning the organisation into a “bland blur”.

The issue of contention: between those who see Momentum as an organisation to engage new members of the Labour party, who have been motivated by Jeremy Corbyn but are not yet Corbynites.

One trade unionist from that tendency described what they see the problem as like this: “you have people who have joined to vote for Jeremy, they’re going to meetings, but they’re voting for the Progress candidates in selections, they’re voting for Eddie Izzard [who stood as an independent but Corbynsceptic candidate] in the NEC”.  

On the other are those who see a fightback by Labour’s right and centre as inevitable, and who are trying to actively create a party within a party for what they see as an inevitable purge. One activist of that opinion wryly described Momentum as “Noah’s Ark”.

For both sides, Momentum, now financially stable thanks to its membership, which now stands at over 20,000, is a great prize. And in the firing line for those who want to turn Momentum into a parallel line is Jon Lansman, the organisation’s founder.

Lansman, who came into politics as an aide to Tony Benn, is a figure of suspicion on parts of the broad left due to his decades-long commitment to the Labour party. His major opposition within Momentum and on its ruling executive comes from the AWL.

The removal of Jackie Walker as a vice-chair of Momentum after she said that Holocaust Memorial Day belittled victims of other genocides has boosted the AWL, although the AWL's Jill Mountford, who sits on Momentum's ruling executive, voted to remove Walker as vice-chair. (Walker remains on the NEC, as she has been elected by members). But despite that, the AWL, who have been critical of the process whereby Walker lost her post, have felt the benefit across the country.

Why? Because that battle has triggered a series of serious splits, not only in Momentum’s executive but its grassroots. A raft of local groups have thrown out the local leadership, mostly veterans of Corbyn’s campaign for the leadership, for what the friend of one defeated representative described as “people who believe the Canary [a pro-Corbyn politics website that is regularly accused of indulging and promoting conspiracy theories]”.

In a further series of reverses for the Lansmanite caucus, the North West, a Momentum stronghold since the organisation was founded just under a year ago, is slipping away from old allies of Lansman and towards the “new” left. As one insider put it, the transition is from longstanding members towards people who had been kicked out in the late 1980s and early 1990s by Neil Kinnock. The constituency party of Wallasey in particular is giving senior figures in Momentum headaches just as it is their opponents on the right of the party, with one lamenting that they have “lost control” of the group.

It now means that planned changes to Momentum’s structure, which the leadership had hoped to be rubberstamped by members, now face a fraught path to passage.

Adding to the organisation’s difficulties is the expected capture of James Schneider by the leader’s office. Schneider, who appears widely on television and radio as the public face of Momentum and is well-liked by journalists, has an offer on the table to join Jeremy Corbyn’s team at Westminster as a junior to Seumas Milne.

The move, while a coup for Corbyn, is one that Momentum – and some of Corbyn’s allies in the trade union movement – are keen to resist. Taking a job in the leader’s office would reduce still further the numbers of TV-friendly loyalists who can go on the airwaves and defend the leadership. There is frustration among the leader’s office that as well as Diane Abbott and John McDonnell, who are both considered to be both polished media performers and loyalists, TV bookers turn to Ken Livingstone, who is retired and unreliable, and Paul Mason, about whom opinions are divided within Momentum. Some regard Mason as a box office performer who needs a bigger role, others as a liability.

But all are agreed that Schneider’s expected departure will weaken the media presence of Corbyn loyalists and also damage Momentum. Schneider has spent much of his time not wrangling journalists but mediating in local branches and is regarded as instrumental in the places “where Momentum is working well” in the words of one trade unionist. (Cornwall is regarded as a particular example of what the organisation should be aiming towards)

It comes at a time when Momentum’s leadership is keen to focus both on its external campaigns but the struggle for control in the Labour party. Although Corbyn has never been stronger within the party, no Corbynite candidate has yet prevailed in a by-election, with the lack of available candidates at a council level regarded as part of the problem. Councilors face mandatory reselection as a matter of course, and the hope is that a bumper crop of pro-Corbyn local politicians will go on to form the bulk of the talent pool for vacant seats in future by-elections and in marginal seats at the general election.

But at present, a draining internal battle is sapping Momentum of much of its vitality. But Lansman retains two trump cards. The first is that as well as being the founder of the organisation, he is its de facto owner: the data from Jeremy Corbyn’s leadership campaigns, without which much of the organisation could not properly run, is owned by a limited company of which he is sole director. But “rolling it up and starting again” is very much the nuclear option, that would further delay the left’s hopes of consolidating its power base in the party.

The second trump card, however, is the tribalism of many of the key players at a local level, who will resist infiltration by groups to Labour’s left just as fiercely as many on the right. As one veteran of both Corbyn’s campaigns reflected: “If those who have spent 20 years attacking our party think they have waiting allies in the left of Labour, they are woefully mistaken”. 

Stephen Bush is special correspondent at the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to British politics.