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; and next year the United States may elect its first woman president. 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 demeaning. 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. Some ask whether the financial crisis would have been as bad had Lehman Brothers been Lehman Sisters, given research suggesting a link between testosterone levels and risk-taking.

Supporters of this position are fond of quoting two studies by McKinsey, in 2007 and 2008, of large groups of managers in a variety of businesses. The consulting firm found that five “leadership behaviours” are seen in women more frequently than in men: people-development; setting expectations and rewards; providing role models; giving inspiration; and participative decision-making. It argued that such behaviours are particularly valuable in today’s less-hierarchical companies. By contrast, the two that men were found to adopt more often than women sound rather old-fashioned: control and corrective action; and individualistic decision-making.

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 businesses 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 styles as in the values that they bring to the job. They are much more influenced by compassion and fairness than men.

McKinsey’s studies rest on taking snapshots of managers’ opinions and scoring them. But opinions about management are in a constant flux; and managers tend to tell interviewers what they think they want to hear. The argument that women are better at managing androgynously is a bit more plausible—though the data to support this are scant. The final argument, about the human values women bring to the job of leadership, has the best supporting evidence. Around the world women are more likely to vote for parties that place a higher value on compassion than men. American private companies run by women lay off significantly fewer workers than ones run by men. Fortune 500 companies with more women on their boards donate more to charity. However, even when it resonates, the claim that women make better leaders needs to be weighed against three considerations.

The first is that lumping women bosses together obscures the huge differences between them. There are plenty of female bosses who are as hard-headed as any male. After Harriet Green took charge of Thomas Cook, a struggling travel business, she got rid of 2,500 staff and cut senior management posts by one-third. Jill Abramson, the first female editor of the New York Times, was removed for “arbitrary decision-making”, a “failure to consult” and “inadequate communication”. Even if women as a whole are more compassionate than men, that is no guarantee that a highly selected group of women, such as those who reach the top of companies, are also more compassionate.

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—Anne Grethe Solberg, a sociologist, concluded that: “Men and women don’t have different styles of leadership.”

Vive la difference?

The third, and main, problem with the argument that women do a better job in running a company is the lack of solid evidence that putting more women into senior jobs improves a business’s performance. Several early studies in this field found that companies with more women in their executive suites and on their boards had better financial outcomes. But more recent research has cast doubt on this. A study of a large sample of American firms by Renee Adams and Daniel Ferreira, two economists, found that: “The average effect of gender diversity on firm performance is negative.” A large study of the influence of diversity on group performance in companies, by Hans van Dijk, a Dutch academic, and two colleagues, found that gender diversity has no overall effect. Two studies of public companies in Norway, following legislation requiring them to give at least 40% of board seats to women, found that increasing the number of women had a negative effect on profits.

Those arguing that women leaders are different, and better, may have the best of intentions. But they are piling flimsy evidence on dubious argument to produce politically correct hokum. In some societies such claims risk reinforcing stereotypes about the sort of job that women are “good for”. The only enlightened policy for selecting leaders is to judge people purely on their individual merits. Anything else is just prejudice in disguise.