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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Qatar is determined to stand up to its Gulf neighbours - but at what price?

The tensions date back to the maverick rule of Hamad bin Khalifa al-Thani.

For much of the two decades plus since Hamad bin Khalifa al-Thani deposed his father to become emir of Qatar, the tiny gas-rich emirate’s foreign policy has been built around two guiding principles: differentiating itself from its Gulf neighbours, particularly the regional Arab hegemon Saudi Arabia, and insulating itself from Saudi influence. Over the past two months, Hamad’s strategy has been put to the test. From a Qatari perspective it has paid off. But at what cost?

When Hamad became emir in 1995, he instantly ruffled feathers. He walked out of a meeting of the Gulf Cooperation Council (GCC) because, he believed, Saudi Arabia had jumped the queue to take on the council’s rotating presidency. Hamad also spurned the offer of mediation from the then-President of the United Arab Emirates (UAE) Sheikh Zayed bin Sultan al-Nahyan. This further angered his neighbours, who began making public overtures towards Khalifa, the deposed emir, who was soon in Abu Dhabi and promising a swift return to power in Doha. In 1996, Hamad accused Saudi Arabia, Bahrain and the UAE of sponsoring a coup attempt against Hamad, bringing GCC relations to a then-all-time low.

Read more: How to end the stand off in the Gulf

The spat was ultimately resolved, as were a series of border and territory disputes between Qatar, Bahrain and Saudi Arabia, but mistrust of Hamad - and vice versa - has lingered ever since. As crown prince, Hamad and his key ally Hamad bin Jassim al-Thani had pushed for Qatar to throw off what they saw as the yoke of Saudi dominance in the Gulf, in part by developing the country’s huge gas reserves and exporting liquefied gas on ships, rather than through pipelines that ran through neighbouring states. Doing so freed Qatar from the influence of the Organisation of Petroleum Exporting Countries, the Saudi-dominated oil cartel which sets oil output levels and tries to set oil market prices, but does not have a say on gas production. It also helped the country avoid entering into a mooted GCC-wide gas network that would have seen its neighbours control transport links or dictate the – likely low - price for its main natural resource.

Qatar has since become the richest per-capita country in the world. Hamad invested the windfall in soft power, building the Al Jazeera media network and spending freely in developing and conflict-afflicted countries. By developing its gas resources in joint venture with Western firms including the US’s Exxon Mobil and France’s Total, it has created important relationships with senior officials in those countries. Its decision to house a major US military base – the Al Udeid facility is the largest American base in the Middle East, and is crucial to US military efforts in Iraq, Syria and Afghanistan – Qatar has made itself an important partner to a major Western power. Turkey, a regional ally, has also built a military base in Qatar.

Hamad and Hamad bin Jassem also worked to place themselves as mediators in a range of conflicts in Sudan, Somalia and Yemen and beyond, and as a base for exiled dissidents. They sold Qatar as a promoter of dialogue and tolerance, although there is an open question as to whether this attitude extends to Qatar itself. The country, much like its neighbours, is still an absolute monarchy in which there is little in the way of real free speech or space for dissent. Qatar’s critics, meanwhile, argue that its claims to promote human rights and free speech really boil down to an attempt to empower the Muslim Brotherhood. Doha funded Muslim Brotherhood-linked groups during and after the Arab Spring uprisings of 2011, while Al Jazeera cheerleaded protest movements, much to the chagrin of Qatar's neighbours. They see the group as a powerful threat to their dynastic rule and argue that the Brotherhood is a “gateway drug” to jihadism. In 2013,  after Western allies became concerned that Qatar had inadvertently funded jihadist groups in Libya and Syria, Hamad was forced to step down in favour of his son Tamim. Soon, Tamim came under pressure from Qatar’s neighbours to rein in his father’s maverick policies.

Today, Qatar has a high degree of economic independence from its neighbours and powerful friends abroad. Officials in Doha reckon that this should be enough to stave off the advances of the “Quad” of countries – Bahrain, Egypt, Saudi Arabia and the UAE - that have been trying to isolate the emirate since June. They have been doing this by cutting off diplomatic and trade ties, and labelling Qatar a state sponsor of terror groups. For the Quad, the aim is to end what it sees as Qatar’s disruptive presence in the region. For officials in Doha, it is an attempt to impinge on the country’s sovereignty and turn Qatar into a vassal state. So far, the strategies put in place by Hamad to insure Qatar from regional pressure have paid off. But how long can this last?

Qatar’s Western allies are also Saudi Arabia and the UAE’s. Thus far, they have been paralysed by indecision over the standoff, and after failed mediation attempts have decided to leave the task of resolving what they see as a “family affair” to the Emir of Kuwait, Sabah al-Sabah. As long as the Quad limits itself to economic and diplomatic attacks, they are unlikely to pick a side. It is by no means clear they would side with Doha in a pinch (President Trump, in defiance of the US foreign policy establishment, has made his feelings clear on the issue). Although accusations that Qatar sponsors extremists are no more true than similar charges made against Saudi Arabia or Kuwait – sympathetic local populations and lax banking regulations tend to be the major issue – few Western politicians want to be seen backing an ally, that in turn many diplomats see as backing multiple horses.

Meanwhile, although Qatar is a rich country, the standoff is hurting its economy. Reuters reports that there are concerns that the country’s massive $300bn in foreign assets might not be as liquid as many assume. This means that although it has plenty of money abroad, it could face a cash crunch if the crisis rolls on.

Qatar might not like its neighbours, but it can’t simply cut itself off from the Gulf and float on to a new location. At some point, there will need to be a resolution. But with the Quad seemingly happy with the current status quo, and Hamad’s insurance policies paying off, a solution looks some way off.

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