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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"We repealed, then forgot": the long shadow of Section 28 homophobia

Why are deeply conservative views about the "promotion" of homosexuality still being reiterated to Scottish school pupils? 

Grim stories of LGBTI children being bullied in school are all too common. But one which emerged over the weekend garnered particular attention - because of the echoes of the infamous Section 28, nearly two decades after it was scrapped.

A 16-year-old pupil of a West Lothian school, who does not wish to be named, told Pink News that staff asked him to remove his small rainbow pride badge because, though they had "no problem" with his sexuality, it was not appropriate to "promote it" in school. It's a blast from the past - the rules against "promoting" homosexuality were repealed in 2000 in Scotland, but the long legacy of Section 28 seems hard to shake off. 

The local authority responsible said in a statement that non-school related badges are not permitted on uniforms, and says it is "committed to equal rights for LGBT people". 

The small badge depicted a rainbow-striped heart, which the pupil said he had brought back from the Edinburgh Pride march the previous weekend. He reportedly "no longer feels comfortable going to school", and said homophobia from staff members felt "much more scar[y] than when I encountered the same from other pupils". 

At a time when four Scottish party leaders are gay, and the new Westminster parliament included a record number of LGBTQ MPs, the political world is making progress in promoting equality. But education, it seems, has not kept up. According to research from LGBT rights campaigners Stonewall, 40 per cent of LGBT pupils across the UK reported being taught nothing about LGBT issues at school. Among trans students, 44 per cent said school staff didn’t know what "trans" even means.

The need for teacher training and curriculum reform is at the top of campaigners' agendas. "We're disappointed but not surprised by this example," says Jordan Daly, the co-founder of Time for Inclusive Education [TIE]. His grassroots campaign focuses on making politicians and wider society aware of the reality LGBTI school students in Scotland face. "We're in schools on a monthly basis, so we know this is by no means an isolated incident." 

Studies have repeatedly shown a startling level of self-harm and mental illness reported by LGBTI school students. Trans students are particularly at risk. In 2015, Daly and colleagues began a tour of schools. Shocking stories included one in which a teacher singled out a trans pupils for ridicule in front of the class. More commonly, though, staff told them the same story: we just don't know what we're allowed to say about gay relationships. 

This is the point, according to Daly - retraining, or rather the lack of it. For some of those teachers trained during the 1980s and 1990s, when Section 28 prevented local authorities from "promoting homosexuality", confusion still reigns about what they can and cannot teach - or even mention in front of their pupils. 

The infamous clause was specific in its homophobia: the "acceptability of homosexuality as a pretended family relationship" could not be mentioned in schools. But it's been 17 years since the clause was repealed in Scotland - indeed, it was one of the very first acts of the new Scottish Parliament (the rest of the UK followed suit three years later). Why are we still hearing this archaic language? 

"We repealed, we clapped and cheered, and then we just forgot," Daly says. After the bitter campaign in Scotland, in which an alliance of churches led by millionaire businessman Brian Souter poured money into "Keeping the Clause", the government was pleased with its victory, which seemed to establish Holyrood as a progressive political space early on in the life of the parliament. But without updating the curriculum or retraining teaching staff, Daly argues, it left a "massive vacuum" of uncertainty. 

The Stonewall research suggests a similar confusion is likely across the UK. Daly doesn't believe the situation in Scotland is notably worse than in England, and disputes the oft-cited allegation that the issue is somehow worse in Scotland's denominational schools. Homophobia may be "wrapped up in the language of religious belief" in certain schools, he says, but it's "just as much of a problem elsewhere. The TIE campaign doesn't have different strategies for different schools." 

After initial disappointments - their thousands-strong petition to change the curriculum was thrown out by parliament in 2016 - the campaign has won the support of leaders such as Nicola Sturgeon and Kezia Dugdale, and recently, the backing of a majority of MSPs. The Scottish government has set up a working group, and promised a national strategy. 

But for Daly, who himself struggled at a young age with his sexuality and society's failure to accept it, the matter remains an urgent one.  At just 21, he can reel off countless painful stories of young LGBTI students - some of which end in tragedy. One of the saddest elements of the story from St Kentigern's is that the pupil claimed his school was the safest place he had to express his identity, because he was not out at home. Perhaps for a gay pupil in ten years time, that will be a guarantee. 

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