What's the chance you've slept with a celebrity?

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was produced by the Winton programme for the public understanding of risk based in the Statistical Laboratory in the University of Cambridge. The aim was to help improve the way that uncertainty and risk are discussed in society, and show how probability and statistics can be both useful and entertaining.

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Brits three romps from celeb sex” headlined the Sun on Friday, adding that “boffins at Cambridge University have calculated every person in the UK is linked to a star through their sexual partners — with just three steps separating the average person from a steamy celeb romp”.

The boffin (actually a first year PhD student) pointed out that on average we have each slept with 7 people, so when we consider their partners and so on, by the time we reach 3 steps away we get to 7 x 7 x7 = 343 direct and indirect sexual partners. He added that "… research shows that five per cent of the population has had sex with a celeb so the chances are around 20 people within your sexual network has had sex with somebody famous." Which of course is not what the article claimed from the start.

But let’s consider these figures: people have had on average 7 partners, and yet one in 20 have apparently slept with a celebrity. These bold statistics can mean one of three things:

  1. 1 in 140 of the adult population, say 250,000 people, are considered celebrities. This seems to be pushing the definition of ‘celeb’ beyond even that of Big Brother.
  2. There are fewer celebrities, to be generous let’s say 10,000, but together they are supposed to have slept with 1 in 20 of the adult population, say 2 million people. That means that each celebrity would need to have had 200 different partners, with no overlaps allowed. While some celebs may well have achieved this dizzy pinnacle, even the most enthusiastic gossip columnist would find it hard to believe this as an average figure.
  3. The research is statistical rubbish. Some support for this hypothesis comes from noting that the ‘1 in 20’ figure is based on the sexual claims of 4000 young people surveyed for MTV’s new “Sex Degrees of Separation” programme: could these possibly be a biased and even exaggerating sample?

You can make your own mind up about this but I am plumping for the final explanation as the most plausible. But then I’m just a (different) boffin from Cambridge University,



Concerning the 7x7x7 statistic: of the second person's 7, one of those is the initial person, so this is counting some people twice. This could be illustrated on a tree diagram with each person's additional partners branching off, and those branching off ending on the third layer downwards. Links from a node (in any direction) indicate a relationship, so the total number is 7x6x6 = 252, less than 343.