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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The EU-Turkey refugee deal only succeeded in one thing

It swept the humanitarian crisis under the carpet.

The Greek island of Chios is a picturesque holiday resort, and home to some 50,000 Greek residents. The occasional cruise boat moors alongside the fishing boats which populate the main harbour of the island. Tourism and fisheries make up the majority of the island’s economy.  A 7km stretch of sea separates Chios from Turkey. It is so close that you can look across the water and see the lights come on in houses in Çeşme as night falls. This beautiful island is also one of the scene of an unfolding and largely untold humanitarian disaster. It is evidence that the EU-Turkey deal in March, intended to stem the flow of refugees, has failed. 

Chios is home to more than 3,000 asylum seekers. Refugees, mostly from Syria and Afghanistan, make the perilous crossing from Turkey every day. Smugglers launch tiny rubber boats in the middle of the night, over capacity to a dangerous level, to attempt the crossing. One Syrian boy told us that the smuggler on the boat counted down from 10 to calculate when the best time was to purposefully puncture the side of the boat in order to escape the Turkish coastguard, but be rescued from drowning by the Greeks.

As a result of these cavalier strategies, this scenic stretch of water has become the grave of thousands. Those who are rescued by the Turkish authorities rather than Greece are often detained. Such high stakes has not deterred the refugees - one family we knew of had tried 17 times to get to Chios from Turkey. 

The main camp on Chios, "Vial", is at the end of a dusty track and is housed in a disused aluminium factory surrounded by barbed wire. G4S, the private security firm, guards the entrance to the European Asylum Support Office compound. It looks more like a prison than a place of refuge. The majority of the refugees live in metal containers. The camp was constructed to hold 1,100 and now holds approximately twice as many.

Most of the migrants and refugees who arrived in Greece before the EU-Turkey deal have been moved to the mainland, nominally in the hope of relocation elsewhere in Europe. More recent arrivals on Chios (and those simply left behind) have been subject to the hastily-adopted Greek Law 4375/2015, which allows for the lengthy detention of asylum seekers on arrival.

While camps on other Greek islands operate as de facto prisons, on Chios, the police allow refugees to travel around (but not leave) the island. A bus service is provided between Vial and the island’s main city, to allow those housed in unofficial camps to come to Vial for appointments. This is a tacit acknowledgement that makeshift camps are needed for those who cannot be accommodated in Vial’s limited facilities. Thus, the entire island is turned into an open prison camp, with asylum seekers unable to leave until their claims are determined, a process taking upwards of six months. During that time refugees, many of whom have fled from unimaginable horror, are left in an endless waiting game.

In May 2016, a Human Rights Watch report called the refugee “hotspots” on the Greek islands, such as Vial, “unsanitary and unsafe” . By September, when we arrived, the situation had not improved. The conditions in the camps around Chios were shocking. Violence was a daily event - both between asylum seekers and from the frustrated local population. Children, at risk of sexual exploitation and abuse, would simply disappear. We would spend hours searching the camps, armed with lists of unaccompanied minors, asking everyone we saw if they had seen this or that child. Some had already become desperate enough to risk their lives in the hands of human traffickers, in order to escape from the very place where they initially sought sanctuary. Shortly after we left Chios we heard that seven people had suffocated to death in a fridge trying to reach the mainland. Isis were known to be recruiting in the camps. 

Unaccompanied children were left to live together in overcrowded containers, often without enough beds. They would take it in turns to stay awake on guard. Food was often inedible. Access to medical treatment was limited. In Vial, the medical facilities were located inside the disused aluminium factory. To be able to speak to a doctor, you first had to get the permission of the police officers manning the entrance gate. People were sometimes left waiting there for days in the baking heat of summer.

It is no surprise that most of the refugees we met were self-harming, severely depressed and suicidal. It is also no exaggeration to say that everyone we interviewed said they would rather be dead than live in this limbo on Chios. Many of the refugees who arrive in Greece are already seriously traumatised. Large numbers of them are victims of torture, or bereaved or wounded by the Syrian war. Almost all have been forced to flee their homelands because of incomprehensible suffering. The reception they receive in Europe only reinforces their trauma. “I didn’t expect Europe to be like this," a Kurdish Syrian refugee aged 18 told us. His entire family (26 members) had been killed in one bomb blast and he had been subjected to horrific torture under the Assad regime.

We volunteered in the camps on Chios providing legal aid. Any hopes we had on arrival of facilitating the speedy settlement of refugees in Europe were quickly dispelled. The structures in place on Chios for the processing of asylum applications were at breaking point. A tiny team of under-resourced and overworked staff from the Greek Asylum Service and European Asylum Support Organisation try to work through the mammoth backlog of cases, but with officers only conducting two asylum interviews per day each, the process moved at a glacial pace. Every day of infuriating bureaucracy is another day vulnerable people are left in appalling conditions. During this indeterminate period of delay in an individual’s protection claim being processed, the authorities failed to take any steps to disseminate information or timescales which would have minimised the psychological harm caused by the never-ending uncertainty.

So what can be done? A French legal NGO collected the accounts of 51 residents in the camps and applied to the European Court of Human Rights (ECtHR) to oblige Greece to take interim measures to safeguard the refugees from the risk of serious and irreversible harm. This application was quickly dismissed, with the residents being asked to wait (yet again) and abide by the usual procedures (yet again). The case of Raoufi and others v Greece, brought on behalf of several asylum seekers challenging their detention in camps in Greece, is pending before the ECtHR and doesn’t look likely to change the position for refugees in Europe any time soon. 

Some have placed their hopes in the controversial agreement between the European Union and Turkey, signed in March of this year. The heart of the EU-Turkey deal is the return of so-called "irregular migrants" to Turkey. Syrian refugees who reach Turkey are expected to make their asylum claims there and await relocation to Europe. Turkey will then, on a one-for-one basis, take migrants from Europe who have not patiently waited their turn. The supposed lawfulness of such a deal comes from the suggestion that Turkey is a "safe third country" to which to remove refugees. 

The attractiveness of this agreement to the EU, which comes at a cost of several billion euros, is that it may deter refugees from undertaking the dangerous (and politically inconvenient) crossing into Europe. While the European Commission has insisted that the numbers of refugee arrivals has fallen, their assertions are contradicted by aid agencies who point out that the temporary drop in arrivals following the EU-Turkey deal was short-lived. Refugees continue to arrive in large numbers on Chios, to face appalling conditions on reception. Few are returned to Turkey and the promised funding has not yet been provided to Turkey’s satisfaction.

Our experience on Chios was that the EU-Turkey deal is not only not working, it is fundamentally unworkable. Most of the refugees with whom we worked had passed through Turkey on their way to Greece. Almost all had stories of mistreatment in Turkey. In particular, we were told of guards on the Syrian border shooting and wounding at desperate people – including women and small children – attempting to cross into Turkey. Once in Turkey, arbitrary arrest and detention was the norm. Those migrants most likely to be returned to Turkey (because they cannot be returned to their country of origin) are Syrians, for whom Turkey is clearly not a "safe third country". Turkey’s systematic refusal to allow refugees fleeing Syria to cross its border is a clear breach of international law mandating the reception of refugees. Those refugees who manage to slip through into Turkey are left without meaningful protection or support. Kurds are systematically mistreated by the Turkish state while migrants in general face abuse by police, army officials and criminals. Turkey simply is not a safe third country for refugees, as is underlined by the tiny numbers of people found appropriate for return. 

The EU is seeking to resolve its refugee crisis by returning vulnerable people to inhuman conditions in breach of EU member states’ obligations under international law. The assessments as to whether the refugees are returnable to Turkey, are meaningless. Thousands of refugees are waiting for months for these assessments and yet a tiny minority have been found to be appropriate for return. 

In the meantime, a humanitarian disaster unfolds. The physical and mental health of those trapped in the camps deteriorate. Children are left without schooling or proper protection. Violence breaks out. Self-harm rises. Lives are irreparably damaged. Further delay, for political, economic or legal wrangling, is not an option. As long as the European Union fails to act, it remains complicit in these human rights violations. 

Miranda Butler, Maria Moodie, Bryony Poynor and Saoirse Townshend are barristers who recently volunteered in Chios, providing legal aid to refugees.