If you've got lucky, it's easy to convince people you're a sage

"Expert" predictions only need a few lucky guesses, then everyone believes them.

LSE's Nattavudh Powdthavee and Nanyang University's Yohanes E. Riyanto presented a paper last month titled Why Do People Pay for Useless Advice? (pdf) The authors demonstrate that people are prepared to pay for investment advice which they know cannot possibly be based on any real evidence – provided the advisor has got things right in the past.

Participants in the experiment were told to bet on five consecutive rounds of coin flips (they could pick the stake, provided it was higher than a minimum level and wouldn't make them lose all their money before the last round). Since they were using a fair coin, the chance of heads or tails coming up each time was 50-50, and the chance of someone calling the correct flips in all five rounds is one in thirty two. More importantly, no amount of expertise can help one predict the outcome of a sequence of coin tosses.

So when the participants were offered the chance to buy "predictions", you would expect them to ignore them. And most of them did, at least for round one (although even then, around 15 per cent of them did pay). But after the first round of tosses, everyone got to see their predictions, even those who hadn't paid. And for half the participants, those predictions were correct. Still, it's obviously just chance, right?

Apparently not so obvious. Those who got a correct "prediction" in round one were three times more likely to pay for one in round two than those who'd got an incorrect one. And by the time a subset of the group had got four correct predictions in a row, the possibility that they would buy a prediction for the fifth round had risen from 15 to 40 per cent.

In other words, just a few lucky guesses are all it takes to get people to pay for what the authors call "transparently useless advice". As they conclude:

Our experiment accurately describes how the real "false" experts typically operate in the information market, and the findings of this paper help to highlight how easy it is for an average person to form a belief in an expert when none may actually exist. 

Something worth bearing in mind next time you are looking at horse tips, stock pickers, or hedge funds, maybe.

George Bush tosses a coin. Is he an expert? 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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Brexit has opened up big rifts among the remaining EU countries

Other non-Euro countries will miss Britain's lobbying - and Germany and France won't be too keen to make up for our lost budget contributions.

Untangling 40 years of Britain at the core of the EU has been compared to putting scrambled eggs back into their shells. On the UK side, political, legal, economic, and, not least, administrative difficulties are piling up, ranging from the Great Repeal Bill to how to process lorries at customs. But what is less appreciated is that Brexit has opened some big rifts in the EU.

This is most visible in relations between euro and non-euro countries. The UK is the EU’s second biggest economy, and after its exit the combined GDP of the non-euro member states falls from 38% of the eurozone GDP to barely 16%, or 11% of EU’s total. Unsurprisingly then, non-euro countries in Eastern Europe are worried that future integration might focus exclusively on the "euro core", leaving others in a loose periphery. This is at the core of recent discussions about a multi-speed Europe.

Previously, Britain has been central to the balance between ‘ins’ and ‘outs’, often leading opposition to centralising eurozone impulses. Most recently, this was demonstrated by David Cameron’s renegotiation, in which he secured provisional guarantees for non-euro countries. British concerns were also among the reasons why the design of the European Banking Union was calibrated with the interests of the ‘outs’ in mind. Finally, the UK insisted that the euro crisis must not detract from the development of the Single Market through initiatives such as the capital markets union. With Britain gone, this relationship becomes increasingly lop-sided.

Another context in which Brexit opens a can of worms is discussions over the EU budget. For 2015, the UK’s net contribution to the EU budget, after its rebate and EU investments, accounted for about 10% of the total. Filling in this gap will require either higher contributions by other major states or cutting the benefits of recipient states. In the former scenario, this means increasing German and French contributions by roughly 2.8 and 2 billion euros respectively. In the latter, it means lower payments to net beneficiaries of EU cohesion funds - a country like Bulgaria, for example, might take a hit of up to 0.8% of GDP.

Beyond the financial impact, Brexit poses awkward questions about the strategy for EU spending in the future. The Union’s budgets are planned over seven-year timeframes, with the next cycle due to begin in 2020. This means discussions about how to compensate for the hole left by Britain will coincide with the initial discussions on the future budget framework that will start in 2018. Once again, this is particularly worrying for those receiving EU funds, which are now likely to either be cut or made conditional on what are likely to be more political requirements.

Brexit also upends the delicate institutional balance within EU structures. A lot of the most important EU decisions are taken by qualified majority voting, even if in practice unanimity is sought most of the time. Since November 2014, this has meant the support of 55% of member states representing at least 65% of the population is required to pass decisions in the Council of the EU. Britain’s exit will destroy the blocking minority of a northern liberal German-led coalition of states, and increase the potential for blocking minorities of southern Mediterranean countries. There is also the question of what to do with the 73 British MEP mandates, which currently form almost 10% of all European Parliament seats.

Finally, there is the ‘small’ matter of foreign and defence policy. Perhaps here there are more grounds for continuity given the history of ‘outsourcing’ key decisions to NATO, whose membership remains unchanged. Furthermore, Theresa May appears to have realised that turning defence cooperation into a bargaining chip to attract Eastern European countries would backfire. Yet, with Britain gone, the EU is currently abuzz with discussions about greater military cooperation, particularly in procurement and research, suggesting that Brexit can also offer opportunities for the EU.

So, whether it is the balance between euro ‘ins’ and ‘outs’, multi-speed Europe, the EU budget, voting blocs or foreign policy, Brexit is forcing EU leaders into a load of discussions that many of them would rather avoid. This helps explain why there is clear regret among countries, particularly in Eastern Europe, at seeing such a key partner leave. It also explains why the EU has turned inwards to deal with the consequences of Brexit and why, although they need to be managed, the actual negotiations with London rank fairly low on the list of priorities in Brussels. British politicians, negotiators, and the general public would do well to take note of this.

Ivaylo Iaydjiev is a former adviser to the Bulgarian government. He is currently a DPhil student at the Blavatnik School of Government at the University of Oxford

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