Can Cameron survive the Late Show?

Good politicians are ardent students of the loss/gain ratio. For every situation they approach they play a little game of rational choice theory in their head. What do they have to lose? And what they have to gain?

Cameron's decision to appear on the Late Show with David Letterman is a classic example of not getting the loss-gain ratio right. It is a popular US chat show few Brits have heard of. If the interview goes well no-one in the UK – the people who will actually be asked to re-elect Cameron – will hear about it. But if it goes wrong, the video will go viral. Lots to lose, little to gain.

So why is Cameron doing it? According to Downing Street, the PM wants to use the goodwill from the Olympics to "bang the drum" for British business and, presumably, tourism. It's commendable that he would take political risks to make the most of what the Olympics offered the UK. But, in truth, a part of him must surely be attracted to the glamour of US entertainment television.

The problem is promoting British business does not make for good TV – whether it's on BBC Parliament or late night talk shows. Cameron will inevitably take several jibes from Letterman, a witty, composed and deadpan host who will be eager to keep things lively.

Even Boris Johnson, who has made a career out of being extremely clever while appearing foolish, struggled on the show. At one point he was asked how long it had been since he started cutting his own hair. The London mayor looked as if he was grasping for words. He survived the encounter pretty much unscathed, thanks to some classic Boris lines, such as suggesting America was "London's greatest creation".

But even Boris struggled. He came across as eager to please and even a little nervous. It wasn't his finest moment. Cameron has little of his wit and even less of his charm. To American eyes, Boris looks like a caricature of a lovable, hyper-intellectual Brit. Cameron looks like the villain in a Disney animation – complete with a snooty upper-class accent and barely-concealed condescension.

Furthermore, he has the burden of office. As the prime minister of Great Britain and Northern Ireland he can't afford to lack gravitas. Barack Obama, who glides through Late Show appearances without a care in the world, is adept as appearing like a regular guy while simultaneously coming across as serious and respectable. Cameron will struggle with that combination, even if he's had a bit of practise on the sofas on morning TV programmes.

The Americans admire down-to-earth charm in their elected politicians, which is why you see presidential candidates humiliate themselves with photo opportunities of them watching baseball with mysterious 'friends' or going windsurfing. British voters tend to find that toe-curling. In US elections the man most voters would like to go for a beer with invariably wins. In British elections, they rarely do.

We just have a different conception of what a good leader looks like, and it isn't connected to being likable. That distinction shows why US politicians will have much easier time on a late night talk show than Cameron will.