“The truth is, I don’t have an answer to that question,” said Farida Jalalzai, a political science professor at Oklahoma State who has studied women in political leadership. There simply haven’t been enough women leading states in the modern era to yield clear data on the question. Last year, the Pew Research Center noted that the number of female national leaders globally had doubled in the decade since 2005—to a whopping 18, meaning that less than 10 percent of UN member states are headed by women.

“You’re going to be able to cherry-pick either way,” Jalalzai said. “Even if we were to take a Margaret Thatcher, for example, we could say, ok, so she did go to war over the Falkland Islands. At the same time you could say, well, Ellen Johnson Sirleaf has kept Liberia peaceful,” when the country was formerly wracked by two civil wars spanning more than a decade. For that matter, where a female head of state’s term coincides with a period of peace, how much can be attributed to distinctly “feminine” leadership qualities, versus that particular woman’s partisan preferences, or even the conditions under which she rose to power? If the assumption that women are more peaceful makes voters consider them unqualified to lead in wartime, women would be more likely to get into leadership positions under peaceful conditions in the first place.

Most of the real foreign-policy effects of having women run countries, if indeed there are any, won’t really be known until more women do it. In the meantime, we can speculate about indirect benefits based on what we do know. For example, Valerie Hudson of Texas A&M University, along with her coauthors, has shown that “the best predictor of a state’s peacefulness is how its women are treated,” which could suggest that, to the extent women are more likely to prioritize the treatment of other women around the world (as both Wallström and Clinton have), they may also be contributing to peace. There’s also evidence that peace settlements women are involved in tend to be more durable. On the other hand, female leaders could just as easily have different foreign-policy priorities—like, say, European integration, or the migrant crisis, or green energy.

A telling moment came in the aftermath of the U.K.’s vote to leave the European Union, when David Cameron lost his job as prime minister and was replaced by Theresa May. There were the ritual Margaret Thatcher comparisons, as well as another ritual that may grow more common in the coming years: the celebration of a woman swooping in to clean up her male predecessor’s mess. But Jalazai wonders whether expectations like these may hurt women in the end. In the United States, for example, the Pew Research Center last year found that adult respondents, by a margin of 34 percent to 9 percent, thought female politicians were better than male ones at compromise; 34 percent thought women were more honest and ethical, versus 3 percent who thought men were.