ONE by one, the glittering prizes are falling to women. General Motors, IBM, PepsiCo, Lockheed Martin and DuPont are among a couple of dozen giant American companies with female bosses. Oxford University is about to follow the footsteps of Harvard and appoint its first female leader. Women still have an enormous way to go: the New York Times points out that more big American firms are run by men called John than by women. But the trend is clear: women now make up more than 50% of university graduates and of new hires by big employers.

Will this growing cadre of female bosses manage any differently from men? Forty years ago feminists would have found the very question demanding. Pioneers such as Margaret Thatcher argued that women could and would do the same job as men, if given a chance. But today some management scholars argue that women excel in the leadership qualities most valued in modern firms.

Those who say women are better suited to taking charge of today’s companies also lean on two other arguments. The first is that women are better at “androgynous” management-that is, combining supposedly “male” and “female” characteristics into a powerful mixture. This is particularly valuable in business undergoing great upheaval, which need a combination of command-and-control and caring-and-sharing. The second is that women differ from men not so much in their leadership style as in the values that they bring to the job. They are much more influenced by compassion and fairness than men.

That leads to the second consideration: that both male and female managers are perfectly capable of adapting their leadership styles to meet changing circumstances. Male managers are increasingly embracing a collaborative approach to leadership, as they adapt to a society that has become less deferential. In a 2013 study of 917 managers in Norway-a country that has led the way in female-friendly policies, from board quotas to public child care-Ann Grethe Solberb, a sociologist, concluded that: “Men and women don’t have different styles of leadership.”