# 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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# Celebrate Labour's electoral success - but don't forget the working class

The shutting down of genuine, constructive debate on the left is the great danger we face.

In the moment when the exit poll was released on 8 June, after seven weeks of slogging up and down the streets of Britain, dealing with scepticism, doubt and sometimes downright hostility, we felt a combination of relief, optimism, even euphoria.

This election broke wide open some assumptions that have constrained us on the left for too long; that the young won’t vote, that any one individual or political party is “unelectable”, that perceptions of both individuals, parties and even policies cannot change suddenly and dramatically. It reminded us that courage, ambition and hope are what’s needed and what have been missing from our politics, too often, for too long.

We have learnt to tread carefully and wear our values lightly. But in recent weeks we have remembered that our convictions can, as Jonathan Freedland once wrote, “bring hope flickering back to life” and meet the growing appetite for a politics that doesn’t simply rail against what is but aspires to build a world that is better.

In this election at least, it seems the final, anticipated fracture of Labour from its working-class base after Brexit did not materialise. Shortly before the snap election was called I wrote that while Brexit appeared to be Labour’s greatest weakness, it could just be our biggest strength, because: “consider what remain voting Tottenham and leave voting Wigan have in common: Labour… We will succeed if we seek the common ground shared by the decent, sensible majority, and more importantly, so will Britain.”

But consider this too. The Tories ran a terrible campaign. It was, without any doubt,the most inept, counter-productive campaign I’ve ever seen in British politics. The day their manifesto hit the headlines, even in our toughest neighbourhoods, we could feel change in the air. Arrogance is never rewarded by the British people and Theresa May has paid a price for it. Yet, despite a Tory manifesto that was a full, square attack on older people, the majority of over 65s still came out for the Tories.

And despite the growing relevance of freedom, internationalism and tolerance in an era characterised by Donald Trump and Vladimir Putin, the Liberal Democrats managed to become bystanders in the political debate. They stood on a platform that aimed to capture the support of those remain voters for whom Brexit is the major question, but neglected the rest. And they quite spectacularly failed to foresee that those who were intensely angered by May’s conversion to a little England, hard Brexit stance would vote tactically against the Tories. Over those seven weeks, they all but disappeared as a political force.

As Bob Dylan once said, "the times, they are a-changin" – and they will change again. The recent past has moved at extraordinary speed. The Brexit Referendum, the rise and retreat of nationalism, the election of Trump and his crushing unpopularity just a few months later, the reversal in fortunes for May and Jeremy Corbyn, the astonishing phenomenon of Emmanuel Macron and pro-European centrism, and the dramatic rise and sudden collapse of Ukip. Politics, as John Harris wrote last week, is now more fluid than ever. So now is the time, for hope yes, and for conviction too, but not for jubilation. We need some serious thinking.

We should be cautious to rush to judgment. It is only two weeks since the exit poll sent shockwaves across the country. There is no comprehensive explanation for the multitude of motivations that delivered this election result and will not be for some time. But there are some early indictors that must make us think.

After seven years of austerity, as John Curtice observes, the Tories made some of their biggest gains in some of the poorest areas of Britain. It is something I felt in all of the eight constituencies I campaigned in during the election. While the Labour vote rose significantly in towns like Wigan, so too did the Tory vote, despite little or no campaigning activity on the ground. As Rob Ford puts it, “Labour, founded as the party of the working class, and focused on redistributing resources from the rich to the poor, gained the most ground in 2017 in seats with the largest concentrations of middle-class professionals and the rich. The Conservatives, long the party of capital and the middle class, made their largest gains in the poorest seats of England and Wales… Britain’s class politics has been turned completely upside down in 2017”.

To acknowledge the growing, longstanding scepticism of many working-class men, and women, towards Labour in towns across England is not to take away from the hard work and drive of the activists, advisers and politicians that helped to fuel such a dramatic turnaround for Labour during the short campaign. To have won considerable gains in wealthier suburbs is no small achievement.

But if the future of Labour lies in a coalition between middle-class young professionals and the working class, what is the glue that binds? While there is shared agreement about investment in public services, how are those interests to be squared on areas like national security and immigration? I believe it can and must be done, but – as I said to conference when I was first elected seven years ago - it will demand that we begin with the difficult questions, not the easy ones.

Just a few days before the election, statistics were released that pointed to a collapse in trade union membership. What does the decline of an organised Labour movement mean for who we are and what we can achieve? These are not new questions. They were posed by Eric Hobsbawm in his brilliant lecture, "The Forward March of Labour Halted" in 1979 - a challenge laid down in the year I was born. Now, 37 years on, we are no further down the road to answering it.

The most dramatic finding from this election was the support Corbyn’s Labour party appears to have won from middle-class, young professionals. They said he couldn’t do it and quite stunningly it seems they were wrong. But a ComRes poll last week caught my eye – by a large margin those 30-44 year olds would favour a new centre-ground political party over the current political settlement. In an election where we returned strongly to two-party politics, it appears they moved to us. But what would a dynamic and renewed Liberal Democrat Party, or a British En Marche do to our support base?

After a hellish two years we have learnt in Labour, I hope, that unity matters. The public and private anger directed towards each other, whether the Labour leadership, the parliamentary Labour party or elected councillors, is desperately damaging and its (relative) absence in the campaign was important.

But unity is not the same as uniformity, and while two weeks ago I felt there was a real danger of historic fracture, now I believe the shutting down of genuine, constructive debate on the left is the great danger we face, and must avoid. No one person, faction or party has ever had the monopoly on wisdom. The breadth of the Labour movement was and remains our greatest strength.

Consider the Labour manifesto, which drew on every tradition across our movement and demanded that every part of the party had to compromise. Those broad traditions still matter and are still relevant because they hear and are attuned to different parts of Britain. Our country is changing and politics must catch up. The future will be negotiated, not imposed.

As we witness the age of "strong man" politics across the world, here in Britain our political culture has become angrier and more illiberal than at any time I can remember. The Brexit debate was characterised by rage, misinformation and a macho political culture that demanded that we abandon nuance and complexity, an understanding of one another and tolerance of different points of view.

But this is not where the future of Britain lies: it lies in pluralism. It lies in a politics that is nimbler, more fleet of foot, less constrained; a return to the great tradition of debate, evidence, experience and argument as a way to build broad coalitions and convince people; not shouting one another down, nor believing any of us are always right; an arena in which we listen as much as we speak; a political culture in which we are capable of forming alliances within and across party lines to achieve real, lasting change.

And ultimately that’s the prize: not just seek power but, to paraphrase a philosopher whose work inspired millions, in the end “the point is to change it”. We could sit tight in Labour and hope to see the current government fall apart. We might even inherit power, we could temporarily reverse some of the worst of the last seven years, but what then? If we have learnt anything from 13 years of Labour government it should be this: that to build lasting change is the hardest political task of all, and it requires now that we do not turn to the political culture, the tools or even the ideas of the past, but that we think hard about where the future of our movement and our country really lies. Now is not the time to sit back and celebrate. Now is the time to think.

Lisa Nandy is the MP for Wigan. She was formerly Shadow Secretary of State for Energy and Climate Change.

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