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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Who is the EU's chief Brexit negotiator Michel Barnier?

The former French foreign minister has shown signs that he will play hardball in negotiations.

The European Commission’s chief Brexit negotiator today set an October 2018 deadline for the terms of Britain’s divorce from the European Union to be agreed. Michel Barnier gave his first press conference since being appointed to head up what will be tough talks between the EU and UK.

Speaking in Brussels, he warned that UK-EU relations had entered “uncharted waters”. He used the conference to effectively shorten the time period for negotiations under Article 50 of the Lisbon Treaty, the legal process to take Britain out of the EU. The article sets out a two year period for a country to leave the bloc.

But Barnier, 65, warned that the period of actual negotiations would be shorter than two years and there would be less than 18 months to agree Brexit.  If the terms were set in October 2018, there would be five months for the European Parliament, European Council and UK Parliament to approve the deal before a March 2019 Brexit.

But who is the urbane Frenchman who was handpicked by Commission President Jean-Claude Juncker to steer the talks?

A centre-right career politician, Barnier is a member of the pan-EU European People’s Party, like Juncker and German Chancellor Angela Merkel.

A committed European and architect of closer eurozone banking integration, Barnier rose to prominence after being elected aged just 27 to the French National Assembly.  He is notorious in Brussels for his repeated references to the 1992 Winter Olympics he organised in Albertville with triple Olympic ski champion Jean-Claude Killy.

He first joined the French cabinet in 1993 as minister of the environment. In 1995, Jacques Chirac made him Secretary of State for European Affairs, teeing up a long and close relationship with Brussels.

Barnier has twice served as France’s European Commissioner, under the administrations of Romano Prodi and José Manuel BarrosoMost recently he was serving as an unpaid special advisor on European Defence Policy to Juncker until the former prime minister of Luxembourg made him Brexit boss.“I wanted an experienced politician for this difficult job,” Juncker said at the time of Barnier, who has supported moves towards an EU army.

 

Barnier and the Brits

Barnier’s appointment was controversial. Under Barroso, he was Internal Market commissioner. Responsible for financial services legislation at the height of the crisis, he clashed with the City of London.

During this period he was memorably described as a man who, in a hall of mirrors, would stop and check his reflection in every one.

Although his battles with London’s bankers were often exaggerated, the choice of Barnier was described as an “act of war” by some British journalists and was greeted with undisguised glee by Brussels europhiles.

Barnier moved to calm those fears today. At the press conference, he said, “I was 20 years old, a very long time ago, when I voted for the first time and it was in the French referendum on the accession of the UK to the EU.

“That time I campaigned for a yes vote. And I still think today that I made right choice.”

But Barnier, seen by some as aloof and arrogant, also showed a mischievous side.  It was reported during Theresa May’s first visit to Brussels as prime minister that he was demanding that all the Brexit talks be conducted in French.

While Barnier does speak English, he is far more comfortable talking in his native French. But the story, since denied, was seen as a snub to the notoriously monolingual Brits.

The long lens photo of a British Brexit strategy note that warned the EU team was “very French” may also have been on his mind as he took the podium in Brussels today.

Barnier asked, “In French or in English?” to laughter from the press.

He switched between English and French in his opening remarks but only answered questions in French, using translation to ensure he understood the questions.

Since his appointment Barnier has posted a series of tweets which could be seen as poking fun at Brexit. On a tour of Croatia to discuss the negotiations, he posed outside Zagreb’s Museum of Broken Relationships asking, “Guess where we are today?”

 

 

He also tweeted a picture of himself drinking prosecco after Boris Johnson sparked ridicule by telling an Italian economics minister his country would have to offer the UK tariff-free trade to sell the drink in Britain.

But Barnier can also be tough. He forced through laws to regulate every financial sector, 40 pieces of legislation in four years, when he was internal market commissioner, in the face of sustained opposition from industry and some governments.

He warned today, "Being a member of the EU comes with rights and benefits. Third countries [the UK] can never have the same rights and benefits since they are not subject to same obligations.”

On the possibility of Britain curbing free movement of EU citizens and keeping access to the single market, he was unequivocal.

“The single market and four freedoms are indivisible. Cherry-picking is not an option,” he said.

He stressed that his priority in the Brexit negotiations would be the interests of the remaining 27 member states of the European Union, not Britain.

“Unity is the strength of the EU and President Juncker and I are determined to preserve the unity and interest of the EU-27 in the Brexit negotiations.”

In a thinly veiled swipe at the British, again greeted with laughter in the press room, he told reporters, “It is much better to show solidarity than stand alone. I repeat, it is much better to show solidarity than stand alone”.

Referring to the iconic British poster that urged Brits to "Keep Calm and Carry On” during World War Two, he today told reporters, “We are ready. Keep calm and negotiate.”

But Barnier’s calm in the face of the unprecedented challenge to the EU posed by Brexit masks a cold determination to defend the European project at any cost.

James Crisp is the news editor at EurActiv, an online EU news service.