Sex, lies and mathematics

By Burkard Polster and Marty Ross

The Age, 1 September 2008

Statistical surveys regularly report that, on average, heterosexual men have more sexual partners than heterosexual women. Consider, for example the survey included in the Sex in Australia series, published in 2003 in Australian and New Zealand Journal of Public Health. This was a very large survey, which included 9469 men and 9340 women who identified themselves as heterosexual.

The responses of the heterosexual men indicated an average of 3.9 sexual partners in the previous five years. By comparison, the responses of the heterosexual women indicated an average of only 1.9 partners, less than half that of the men. This difference is amazing. And, for Australia as a whole, it is mathematically impossible.

Let's place all the men and women in two rows and then draw lines between all the "friendly" pairs. To calculate the average number of partners for the men we sum the partners for all the men – which amounts to counting the number of connecting lines – and then divide by the number of men. Similarly, we can calculate the average number of partners for each woman.

But of course the number of connecting lines is exactly the same for both calculations. And, as the survey implies, there are about the same number of heterosexual men and heterosexual women in Australia. So the averages must be very close to identical!

The authors of Sex in Australia remark upon similar differences in surveys from around the world. A suggested explanation is that women are more accurate in the way they count partners, with (surprise, surprise?) men overestimating their partners. A related factor is the prevalence of sexual double standards: people can simply be too embarrassed (or too macho) to tell the truth.

Of course, such huge discrepancies muddy the true figures, making such reports of limited use. And the message we get is likely to be even less useful, since the media tend only to report these impossible averages.

Maths has alerted us to the problem, but how do we solve it? How can we encourage people to tell the truth in such sensitive surveys? Maths may help with a solution as well.

Suppose we are surveying a group, and we want to find out how many within the group were "friendly" with someone during the last week. Okay, so you ask the question. But, you also tell everybody to make their response dependent on tossing two coins.

The person is instructed to lie if two heads come up and otherwise to tell the truth. Then everyone can tell the embarrassing truth without anyone being sure they are doing so. Similarly, there is now little point in bragging about all your "friends". But do these coin-manipulated responses tell us anything. Yes!

Suppose there are 10000 people honestly using the coin method to respond to our question, with 6000 replying 'Yes' and the rest replying 'No'. Then some simple mathematics shows that there were about 7000 people who were "friendly" last week. We'll leave you to puzzle out why. Contact us if you get stuck.