Robyn Williams: But what if it's all a hoax? Space travel, I mean, going to the Moon, leaving the Earth. Some folk are sure it didn't happen, others know that aliens are here, some dressed as lizards. And what about climate change? What's the link between this sense of certainty and knowledge? Should some people, as the Chaser boys insist, not be allowed to vote. Dan Keogh investigates.

Daniel Keogh: Pittsburgh, Pennsylvania, 1995. A local man, McArthur Wheeler, walks into two banks in the middle of the day and robs them both at gunpoint. Making away with the cash, he is arrested later that evening. Back at the station police sit him down and show him footage from the banks' security cameras. Wheeler can't believe it, the cameras had somehow seen through his disguise. He was seen mumbling to himself, 'But I wore the juice.' His was no ordinary disguise; no balaclava, mask or elaborate makeup, just lemon juice, liberally applied to the face. He was certain that the squirt of citrus would render him invisible to security cameras.

This tale of overconfidence despite utter incompetence illustrates an interesting area in psychology, one so interesting that Justin Kruger and David Dunning or Cornell University used it to open their 1999 research paper 'Unskilled and Unaware of it: How difficulties in recognising one's own incompetence lead to inflated self-assessment'. The paper describes what has now become known as the Dunning-Kruger effect. You've probably met someone who personifies it. Perhaps you've been a passenger with someone who claims to be an excellent diver and yet you spend the entire trip white-knuckled gripping the seat. That's Dunning-Kruger at work. It's the idea that the worse you are at something the more likely you'll hold an inflated view of your own performance.

Dunning and Kruger have demonstrated this best through a series of experiments. They tested a group of university students, those long-suffering lab rats of psychology, for their abilities in a series of tests on grammar, humour and logic. After finishing each task the students were asked the guess how they had performed relative to their classmates.

And here's the kicker; across every test, the students at the bottom end of the bell curve held inflated opinions of their own talents, hugely inflated. In one test of logical reasoning, the lowest quartile of students estimated that their skills would put them above more than 60% of their peers when in fact they had beaten out just 12%. To put that misjudgement in perspective, it's like guessing that this piece of music [music for 5 seconds] lasted nearly half a minute.

Even more surprisingly, the Dunning-Kruger effect leads high achievers to doubt themselves, because on the other end of the bell curve the talented students consistently underestimated their performance. Again to the test of logic; those topping the class felt that they were only just beating out three-quarters of their classmates, whereas in reality they had out-performed almost 90% of them.

The verdict was in; idiots get confident while the smart get modest, an idea that was around long before Dunning and Kruger's day. Bertrand Russell once said, 'In the modern world the stupid are cocksure while the intelligent are full of doubt.' From his essay 'The Triumph of Stupidity', published in 1933.

Think back to the robber concealed in lemon juice, surprised that such an ingenious plan could fail. It's suggested that those who are incompetent lack the ability to recognise their mistakes. Dunning and Kruger demonstrated this in one of their experiments. Even when the dunces were shown how their more competent classmates had answered their exams, they didn't become aware of their own mistakes. In fact the opposite occurred; they actually increased the estimate of their own marks. Those who failed the task seemed to be completely oblivious to what a good result looks like. Context didn't make them more aware of their stupidity, it acted to reinforce their delusions.

Charles Darwin once said, 'Ignorance more frequently begets confidence than knowledge,' and Dunning and Kruger seem to have proven this point. In light of this, it suddenly becomes clear why public debate can be so excruciating. Debates on climate change, the age of the Earth or intelligent design are perfect real-life examples of the Dunning-Kruger effect. It beautifully explains the utter confidence of those who, with no expertise, remain stubborn in their views regardless of overwhelming evidence. It makes you want to shake them by the collar and scream about how stupid they are. But evidence shows that's not the best strategy.

The rather odd element of the Dunning-Kruger effect is that the incompetent don't become aware of it until they become more competent. The key is education. Extending on their earlier experiments, Dunning and Kruger took half of their volunteers and trained them in how to solve the logic puzzles. It was as though a light went on for the under achievers. For the first time out of all the tests they began to realise that they were below average. Suddenly aware of their incompetence, they readjusted their estimates to something more realistic.

For example, before being trained they had thought that they answered five out of the ten questions correctly, whereas in reality they had barely managed to score a single mark. After being trained their estimates plummeted to a more realistic score of just one out of ten. You can almost imagine them sinking their faces into their palms out of sheer embarrassment. If you've ever fancied yourself as a photographer, you might know just how this feels. It only takes a weekend workshop for you to suddenly realise that the poorly lit snaps of your cat in the backyard aren't quite the masterpieces you'd once imagined.

But the Dunning-Kruger effect isn't always as harmless as your crummy photography. We all know bosses, friends and politicians who are fully controlled by the Dunning-Kruger effect. At its extreme it lets charming and charismatic yet completely incompetent people to rise to the top and often end up being in charge. So the next time your boss button-holes you with their latest bright idea or someone knocks on your door asking for your vote, remember David Dunning and Justin Kruger and ask yourself, 'Am I staring at the embodiment of brilliance or just overconfident incompetence?'

Robyn Williams: Dan Keogh was until recently a competent member of The Hungry Beast team on ABC television. And if that puts you off elections, you'll feel even worse when you see the cover story of last week's New Scientist magazine, 'The Maths of Democracy: Why fairness is impossible'. Perhaps Plato had it right, let's just have the wise despots run everything and forget about votes for the ignorant, that's if we can find those who know what they're doing. Perhaps they'll be rendered uncertain by their superior knowledge. It's called the Jimmy Carter effect.