What do Davos, the annual gathering of the world's power elite, and Radio 4's Today programme have in common? One is a security-slanketted talkfest in a remote mountain resort while the other contents itself with setting the domestic agenda in the UK. Both aim to gather leaders to talk and in both cases the number of women participating adds up to about 17% of the total.

Those suspicious of the motivations of the Conservative culture minister and MPs criticising Today and the BBC for a "culture of sexism" point out that David Cameron's government fares no better. Of 121 government ministers, including the cabinet, whips, lords and 13 unpaid positions, just 17% are women.

Is 17% some sort of magic number? Why does it so often mark the headway women have made in the upper echelons or business, politics and society?

I got the chance to ask a lot of people that question in Davos. The most common answer is that high-level gatherings of top people (Davos, radio news programmes) simply reflect the failure of women to reach the top jobs.

Not only are women a minority in many governments but they make up just 3% of the chief executives running Fortune 500 companies in the US and 15% of UK board members, for example.

One banker said he needed people with MBAs (which "women don't study") while another chairman said "support" was an issue where mothers found it harder, for example, to drop everything and fly off to South Africa to deal with a management crisis.

One of the most interesting answers came from Sheryl Sandberg, the chief operating officer of Facebook. Yes, there are barriers and yes, all employees with children need support at home, but there was, she said, something in the way we raise girls that also made a difference – something she called the "girl effect". Sandberg said that boys are taught to be leaders as early as the age of four, while girls are encouraged to stay in the background. "Little girls are called bossy," she said, while boys rarely are. "Success and likability are positively correlated for men and negatively correlated for women." The impact of this is that only the girls who "don't mind being called bossy" push on through the other obstacles.

Both sexes should be allowed to choose where they wish to thrive. Her call for "girls to be ambitious at work and men to be ambitious at home" got a cheer.