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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A swimming pool and a bleeding toe put my medical competency in doubt

Doctors are used to contending with Google. Sometimes the search engine wins. 

The brutal heatwave affecting southern Europe this summer has become known among locals as “Lucifer”. Having just returned from Italy, I fully understand the nickname. An early excursion caused the beginnings of sunstroke, so we abandoned plans to explore the cultural heritage of the Amalfi region and strayed no further than five metres from the hotel pool for the rest of the week.

The children were delighted, particularly my 12-year-old stepdaughter, Gracie, who proceeded to spend hours at a time playing in the water. Towelling herself after one long session, she noticed something odd.

“What’s happened there?” she asked, holding her foot aloft in front of my face.

I inspected the proffered appendage: on the underside of her big toe was an oblong area of glistening red flesh that looked like a chunk of raw steak.

“Did you injure it?”

She shook her head. “It doesn’t hurt at all.”

I shrugged and said she must have grazed it. She wasn’t convinced, pointing out that she would remember if she had done that. She has great faith in plasters, though, and once it was dressed she forgot all about it. I dismissed it, too, assuming it was one of those things.

By the end of the next day, the pulp on the underside of all of her toes looked the same. As the doctor in the family, I felt under some pressure to come up with an explanation. I made up something about burns from the hot paving slabs around the pool. Gracie didn’t say as much, but her look suggested a dawning scepticism over my claims to hold a medical degree.

The next day, Gracie and her new-found holiday playmate, Eve, abruptly terminated a marathon piggy-in-the-middle session in the pool with Eve’s dad. “Our feet are bleeding,” they announced, somewhat incredulously. Sure enough, bright-red blood was flowing, apparently painlessly, from the bottoms of their big toes.

Doctors are used to contending with Google. Often, what patients discover on the internet causes them undue alarm, and our role is to provide context and reassurance. But not infrequently, people come across information that outstrips our knowledge. On my return from our room with fresh supplies of plasters, my wife looked up from her sun lounger with an air of quiet amusement.

“It’s called ‘pool toe’,” she said, handing me her iPhone. The page she had tracked down described the girls’ situation exactly: friction burns, most commonly seen in children, caused by repetitive hopping about on the abrasive floors of swimming pools. Doctors practising in hot countries must see it all the time. I doubt it presents often to British GPs.

I remained puzzled about the lack of pain. The injuries looked bad, but neither Gracie nor Eve was particularly bothered. Here the internet drew a blank, but I suspect it has to do with the “pruning” of our skin that we’re all familiar with after a soak in the bath. This only occurs over the pulps of our fingers and toes. It was once thought to be caused by water diffusing into skin cells, making them swell, but the truth is far more fascinating.

The wrinkling is an active process, triggered by immersion, in which the blood supply to the pulp regions is switched off, causing the skin there to shrink and pucker. This creates the biological equivalent of tyre treads on our fingers and toes and markedly improves our grip – of great evolutionary advantage when grasping slippery fish in a river, or if trying to maintain balance on slick wet rocks.

The flip side of this is much greater friction, leading to abrasion of the skin through repeated micro-trauma. And the lack of blood flow causes nerves to shut down, depriving us of the pain that would otherwise alert us to the ongoing tissue damage. An adaptation that helped our ancestors hunt in rivers proves considerably less use on a modern summer holiday.

I may not have seen much of the local heritage, but the trip to Italy taught me something new all the same. 

This article first appeared in the 17 August 2017 issue of the New Statesman, Trump goes nuclear