WASHINGTON, DC • Before the United States and the world settle in firmly to the new Donald Trump-based reality, let's take a little trip down the road not taken.

Suppose we had woken up on Nov 9 to a President-elect Hillary Clinton. And let's say that, instead of former Portuguese prime minister Antonio Guterres, New Zealand's Ms Helen Clark or Bulgaria's Ms Kristalina Georgieva had been picked to succeed Mr Ban Ki Moon as United Nations secretary-general.

Mrs Clinton would have joined British Prime Minister Theresa May and German Chancellor Angela Merkel, helping to achieve critical mass in the Group of Seven. And a female UN chief would have placed women at the helm of two of the world's three biggest international organisations (France's Ms Christine Lagarde already runs the International Monetary Fund).

With so many women leaders, we would have begun to answer the question: What happens when women run the world? Would the world be better for women? Would it even be different?

According to sociologists, women leaders are of two schools - "queen bees", who are less likely to help other women advance, and "righteous women", who make the advancement of other women a priority. Most early pioneers, such as former Britain's Mrs Margaret Thatcher, India's Mrs Indira Gandhi, and Israel's Ms Golda Meir were queen bees; all of them eschewed feminism. More recently, righteous women have prevailed.

Leaders like Argentina's Ms Cristina Kirchner, Brazil's Ms Dilma Rousseff, and Iceland's Ms Johanna Siguroardottir have all sought, in one way or another, to empower women and help them advance in their countries.

Dr Merkel and Ms May have tended to be more like queen bees, while Mrs Clinton, Ms Lagarde, Ms Clark, and Ms Georgieva are more like righteous women.

To be fair, the first woman leader in a male-dominated culture must often "outman" the men. Seeking to advance other women can highlight her own womanhood and, thereby, weaken her.

Mrs Clinton, for example, was the third woman US Secretary of State but the first who felt secure enough to be able to champion the cause of women and girls worldwide.

As president, she pledged, half her Cabinet would be filled by women, and she would further the State Department initiatives launched during her tenure.

Yes, she also would have been careful to avoid being defined as a woman president. Still, just the presence of a plurality of women has an impact. For example, studies of US courts with multiple judges show that male judges are more willing to hear bias cases when one woman is on the bench, and significantly more willing when a second woman is added. "Each of us," said Ms Sandra Day O'Connor, the first female member of the US Supreme Court, who was renowned for not wanting to be perceived as a "female" justice, "brings to our job, whatever it is, our lifetime of experience and our values." In other words, women bring a fresh perspective, heard clearly only when a critical mass of them is present in any institution.

Consider a woman's perspective on conflict. Evidence does not support the stereotype that women are more pacifist than men - the peacemakers and settlers of male disputes. Women can be Amazons; recall Mrs Thatcher's prosecution of the Falklands War and her admonition to former US President George H.W. Bush not to "go wobbly" in the run-up to the first Gulf War.

On the other hand, when men see wars, they naturally imagine the world of the warriors, whereas women see themselves in the women who must try to shelter their families from forces they cannot control. That is precisely the diversity of perspective that is vital to decision-making. And indeed, the Institute for Inclusive Security at Harvard's Kennedy School has tracked the differences women make as part of peace negotiations.

An acute awareness of the magnitude of civilian suffering in conflicts such as the Syrian civil war or the ongoing horrors in the Congo Basin, and an appreciation of how cycles of violence perpetuate themselves over generations, can actually make women much more likely to urge the use of force in interventions. Former US Secretary of State Madeleine Albright famously chided her successor, Mr Colin Powell, for his reluctance to involve the US military in the Balkans in the 1990s, in part because of her own family's experience as Czech refugees from Communism.

Overall, a woman leader's decisions are no more predictable than a male leader's. Women are not monolithic - they have various ideological backgrounds and diverse governing styles. But when the world finally reaches the point when women are not a rarity at the tables of power, when their numbers reach a tipping point, their voices will be heard differently, and their opinions will hold more weight with the men around them.

Women came closer this year than in any other era to reaching that tipping point. But we may still have to wait decades to find out what will happen when we finally do.

• Anne-Marie Slaughter is president and CEO of New America. Jay Newton-Small is a correspondent for Time and author of Broad Influence: How Women Are Changing the Way America Works.