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In the 18th century, the University of Basel used random selection to appoint a scholar. Three people were chosen and the final selection was made by lot

There has been a flurry of press interest about the plight of women in the workplace recently, highlighting issues such as the lack of women on boards, the gender pay gap and the dearth of female leaders. Women reading this article may think ¡°Oh no, not another piece portraying us as victims¡±, while the men may be suffering from neck ache ¨C from lowering their heads in shame.

But it is surprising that in 2015 women are still so under-represented at the top of all kinds of hierarchies, be it in corporations, universities or the public sector. Many academics will be familiar with the figures for UK higher education: 20.1 per cent of vice-chancellors and 30.5 per cent of pro vice-chancellors and deputy vice-chancellors are female. While the latter figure is encouraging, suggesting a potential pipeline for a new cohort of female vice-chancellors, change is slow and the continued dearth of women in senior leadership positions seems at odds with recent research findings.

First, diversity brings benefits to a company¡¯s bottom line. There is evidence that Fortune 500 companies with more female directors outperform those with fewer female board members on a broad range of financial indicators ¨C although these results do not tell us whether women increase a firm¡¯s performance, or whether better-performing firms select more women.

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Evidence from a field study by Cristian Dezs? at the University of Maryland and David Gaddis Ross at Columbia Business School, which controlled for many factors, concluded that female representation in top management improves the performance of companies that pursue innovative strategies. Additionally, diversity is believed to have a positive impact on a firm¡¯s performance in turbulent times, and laboratory experiments have found that the performance of a group is affected more by the proportion of women in it than by the intelligence of the group¡¯s members.

One of the most interesting findings on women and leadership, from the work of Amalia Miller at the University of Virginia, is the evidence that women are more likely to get promoted in organisations where senior executives are female. Women seem to get more out of other women. The productivity of female workers has been shown to increase under female managers and leaders. A study by Luca Flabbi and colleagues suggests that female executives are better equipped to interpret signals of productivity from female workers. (In a similar way, previous research has shown that academic leaders are better able to interpret other scholars.)

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Second, women today are better educated than men on average. The majority of university graduates in Organisation for Economic Cooperation and Development countries are now female. In the UK in 2014, 180,000 men graduated from university compared with 240,000 women. Moreover, research by Angela Duckworth and Martin Seligman of the University of Pennsylvania shows that in a wide range of settings, girls are more self-disciplined than boys. In general, this characteristic is correlated with success in the workplace ¨C but not for women.

Despite these gains in education, and the apparent benefits that female leaders bring to companies, women still have much lower promotion rates than men across all ranks, even after controlling for individual characteristics like age, education, experience and tenure. And the higher the level of business leadership, the more male-dominated it is.

Why wouldn¡¯t everyone want to benefit from the talents of women and a diversity of ideas and decision-making? Everything points to the importance of getting women into leadership positions. So why aren¡¯t there more of them there?

Research highlights several possible reasons why women become less visible in the upper echelons and why they leak out of the proverbial pipeline. Most studies focus on ¡°demand-side¡± causes ¨C in particular, discrimination against women. Demand-side factors are imposed on women externally, often because of stereotyping. Women are expected to be less ambitious, less assertive and less self-reliant, but also more caring and communally oriented. In addition, it is assumed that women will face family-work conflicts. These stereotypes clash with the stereotypes associated with leadership. Instead a ¡°too risky to promote¡± attitude emerges, regardless of whether these expectations are justified or not.

Research on ¡°supply-side¡± explanations is a more recent development. Such studies examine how women tend to impose negative stereotypes on themselves and their self-identity, for example. Women also appear to have to choose between career success and social success, and to endure extra pressures that male leaders are not exposed to. So females who adopt counter-stereotypical behaviour are sometimes viewed as ¡°out of role¡±, ¡°bitchy¡± or lacking in social skills. They may try to compensate for this by attempting to display greater sociability in a bid to be liked. However, most women conform to female stereotypes to some extent. Studies show that conforming to such stereotypes has a negative impact on their entrepreneurial intentions, leadership aspirations and interest in science, technology, engineering and maths.

Recent findings in social psychology and behavioural economics suggest that women and men often have different preferences. The differences between men and women that are highlighted most frequently are aversion to competition, risk aversion, feedback aversion and low self-confidence. These factors all help to explain the gender gap in visibility, promotions and salaries.

Evidence from field studies and experiments shows that women are more likely to opt out of contests even when they are equally, or more, qualified for the task as men. Do women retreat from competition while men pit themselves against one another too much?

These two questions are addressed in a landmark 2007 study by Muriel Niederle of Stanford University and Lise Vesterlund of the University of Pittsburgh. In an experimental setting, the authors found that among men and women of equal abilities, men chose to compete twice as often as women. A number of possible explanations for this are raised in the literature.

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First, men¡¯s preference for competition may have evolutionary roots linked to breeding, or it may result from historical parenting practices that have generally encouraged competitiveness in boys and more passive behaviour in girls.

The ¡®tournament-entry gap¡¯ between men and women is mainly driven by women¡¯s preference not to compete, and by lower levels of self-confidence

Second, research suggests that men tend to exaggerate their abilities, whereas women typically have less self-confidence, creating a ¡°confidence gap¡±. Overconfidence is more pronounced when men undertake tasks that are considered to be masculine ¨C and, arguably, leadership may be one of these. If men and women are equally confident, researchers have found that there are no gender differences in competitive entry. This has been shown in the laboratory as well as in the field.

The third explanation given in academic studies is that women are more likely than men to allow negative feedback to influence the way that they perceive themselves. Correspondingly, women are less likely than men to incorporate positive information into their self-perception; they are prone to attributing their success to luck rather than crediting their own performance. Men generally seem to be more robust in their response to criticism ¨C and more able to absorb praise.

The final explanation is that women are more risk-averse than men. However, the evidence here is very mixed. On balance, it seems that women appear to make less risky choices in certain situations ¨C for example, when making financial investments. But risk aversion is reduced as women become more experienced. According to the results of Niederle and Vesterlund¡¯s laboratory experiment, the ¡°tournament-entry gap¡± between men and women is mainly driven by women¡¯s preference not to compete, and also by lower levels of self-confidence.

If women tend to have an aversion to competition, how might their antipathy towards it be reduced?

The answer is likely to involve both cultural and institutional factors. In a patriarchal society ¨C for example the Maasai in Tanzania ¨C women are less likely to choose to enter competitions. However, in a matrilineal society ¨C such as the Khasi in India ¨C women¡¯s tendency to compete is higher than men¡¯s. Similarly, a study of Swedish schoolchildren found that boys and girls are equally likely to enter competitions, an outcome that the authors attribute to the egalitarian nature of Swedish society.

Interestingly, evidence suggests that the influence of negative stereotyping is moderated or disappears when women compete against women, in situations when the competition concerns typical female tasks, or when the task is framed as gender-neutral. In Middle Eastern countries with same-sex schooling, there is no gender gap in students¡¯ performance in maths. Also, having a female maths or science teacher seems to improve the performance of girls in the relevant subject, particularly among those who are gifted.

While culture-specific preferences are not easy to change, and single-sex competition is not usually feasible in the workplace, other institutional alterations can be made to reduce stereotyping. One set of measures open to institutions is to adopt affirmative action policies or quotas. Writing in ³ÉÈËVRÊÓƵ earlier this year, Simonetta Manfredi asked whether higher education should set a target of having women fill 40 per cent of vice-chancellor posts by 2020 (¡°Lead by example¡±, Opinion, 1 January). We know that quotas work. When quotas are adopted, more women compete and their chances of winning improve. Moreover, findings from laboratory experiments show that the strongest female candidates are more likely to compete under affirmative action and win; in contrast, the percentage of men choosing to compete falls. However, in the workplace, quotas can prompt concern that female leaders will be labelled as ¡°token women¡±. Would the effect of encouraging talented women to participate through quotas outweigh this sort of detrimental effect? Some may view affirmative action as unfair ¡°reverse discrimination¡± while others see it as a necessary measure of last resort ¨C one that should be enacted if present trends of under-representation of women in leadership roles continue.

Setting up a reward system is another way of motivating women to compete. Women may, for example, be offered cash incentives to apply for a particular job. Studies show that if the rewards are sufficiently large, women will not only choose to compete ¨C they will also be as successful as men. This measure could be expensive for universities. It may also fail to change women¡¯s general preferences and, if women are offered greater rewards than men, it could foster resentment. However, given that men are currently paid more on average than women, such a system may help to equalise pay.

What else can we do to encourage women to throw their hat into the ring? Reducing the role of competition in promotion and appointments¡¯ procedures may be one option. Competition is not always positive. Research shows that in cooperative settings, when people are working towards a common goal, the introduction of competition can be detrimental to performance because individuality is encouraged over collectivism.

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So we suggest two measures. The first is for universities to make more use of job-sharing. Sharing management jobs gives two people leadership experience. At the FTSE 100 Women on Boards meeting in February, Vince Cable, the secretary of state for Business, Innovation and Skills at the time, stated that the role of director of higher education in BIS was carried out by two women. Arguably, the job of head of department could be shared by two women, or a man and a woman.

A second, more unusual measure would be the use of random selection for mid-level management appointments. Post-holders would be picked at random from a pre-selected pool of equally capable candidates. In higher education, such an approach is not entirely alien ¨C for example, in the 18th century, the University of Basel used random selection to appoint a new professor. The top three candidates were chosen by a committee and the final selection was made by lot. Using this method of selection, the ¡°losers¡± save face and the most highly respected candidates choose to stand for office. Women who win in this type of lottery will not be exposed to the negative stereotypes that are sometimes associated with women when they outperform men. Moreover, this measure avoids homophily and fosters a more diverse applicant pool.

Universities need to do more to take advantage of the huge female talent pool and get women into leadership positions. They should take on board the evidence suggesting that women have different preferences than men. Carrying on as we are isn¡¯t good for equity or efficiency ¨C so universities need to be open to fresh and unusual ideas. At the Women on Boards meeting, Cable spoke about using quotas as sticks. One would hope that UK universities with international reputations to maintain will jump before they are pushed.