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.

Photo: Getty
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The Liberal Democrats are back - and the Tories should be worried

A Liberal revival could do Theresa May real damage in the south.

There's life in the Liberal Democrats yet. The Conservative majority in Witney has been slashed, with lawyer and nominative determinism case study Robert Courts elected, but with a much reduced majority.

It's down in both absolute terms, from 25,155 to 5,702, but it's never wise to worry too much about raw numbers in by-elections. The percentages tell us a lot more, and there's considerable cause for alarm in the Tory camp as far as they are concerned: the Conservative vote down from 60 per cent to 45 per cent.

(On a side note, I wouldn’t read much of anything into the fact that Labour slipped to third. It has never been a happy hunting ground for them and their vote was squeezed less by the Liberal Democrats than you’d perhaps expect.)

And what about those Liberal Democrats, eh? They've surged from fourth place to second, a 23.5 per cent increase in their vote, a 19.3 swing from Conservative to Liberal, the biggest towards that party in two decades.

One thing is clear: the "Liberal Democrat fightback" is not just a hashtag. The party has been doing particularly well in affluent Conservative areas that voted to stay in the European Union. (It's worth noting that one seat that very much fits that profile is Theresa May's own stomping ground of Maidenhead.)

It means that if, as looks likely, Zac Goldsmith triggers a by-election over Heathrow, the Liberal Democrats will consider themselves favourites if they can find a top-tier candidate with decent local connections. They also start with their by-election machine having done very well indeed out of what you might call its “open beta” in Witney. The county council elections next year, too, should be low hanging fruit for 

As Sam Coates reports in the Times this morning, there are growing calls from MPs and ministers that May should go to the country while the going's good, calls that will only be intensified by the going-over that the PM got in Brussels last night. And now, for marginal Conservatives in the south-west especially, it's just just the pressure points of the Brexit talks that should worry them - it's that with every day between now and the next election, the Liberal Democrats may have another day to get their feet back under the table.

This originally appeared in Morning Call, my daily guide to what's going on in politics and the papers. It's free, and you can subscribe here. 

Stephen Bush is special correspondent at the New Statesman. His daily briefing, Morning Call, provides a quick and essential guide to British politics.