Fed up with the government shutdown in 2013, Senator Susan Collins took the floor, presented a three-point plan and implored colleagues on both sides of the aisle to work with her.

As soon as she walked off, her cellphone rang. The first three senators to call her, she said, were women: Kelly Ayotte and Lisa Murkowski, fellow Republicans, and Amy Klobuchar, a Democrat.

“I’ve always thought that was significant,” said Ms. Collins, a Republican from Maine. “And indeed, we put together a plan for the reopening of government, and women led the way.”

Tuesday failed to be a ceiling-shattering day for women in government. In addition to Hillary Clinton’s loss, the number of female governors dropped to five from six, according to the Center for American Women and Politics at Rutgers. Kate Brown of Oregon was the only woman to win a governor’s race. The number of women in Congress stayed flat at 104, or 19 percent of seats (the Senate had a net gain of one woman and the House a net loss of one.) Thirteen states will send no women to the 115th Congress, including Mississippi and Vermont, which have never had a woman in Congress.

Women’s representation in government is stalled, and in some cases moving backward. Does that make a difference to the work of governing? Yes, according to decades of data from around the world.

Women govern differently than men do in some important ways. They tend to be more collaborative and bipartisan. They push for far more policies meant to support women, children, social welfare and — when they’re in executive positions — national security. But these bills are also more likely to die, largely because of gender bias, research shows.

Women in Congress sponsor and co-sponsor more bills than men do, and bring 9 percent more federal money to their home districts, according to a study in the American Journal of Political Science.

Those bills are more likely to benefit women and children or address issues like education, health and poverty. In Congress, for instance, it was women who fought for women’s health coverage in the Affordable Care Act, sexual harassment rules in the military, the inclusion of women in medical trials, and child care vouchers in welfare overhaul.

“All members of Congress have to follow their constituency, but because of their personal experiences either as women in the work force or as mothers, they might be inclined to legislate on some of these issues,” said Michele L. Swers, a professor of government at Georgetown University who studies gender and policy making.

In a new analysis of the 151,824 public bills introduced in the House between 1973 and 2014, to be published in print in Political Science Research and Methods, researchers found that women were significantly more likely than men to sponsor bills in areas like civil rights, health and education. Men were more likely to sponsor bills in agriculture, energy and macroeconomics.

An analysis of floor speeches during the 106th Congress, by political scientists at the University of Iowa and Oklahoma State University, found that women spent more time talking about policy concerns like women’s health and family issues. Another study, of state of the state speeches from 2006 to 2008 published in State and Local Government Review, found that female governors devoted much more attention to social welfare issues than male governors did, even after controlling for political and situational factors.

Women are less likely to vote for war or the death penalty. Women’s representation in legislatures is significantly correlated with the abolition of capital punishment, according to a study of 125 countries published in July by researchers at Sul Ross State University in Texas.

A higher share of female legislators correlates with less military spending and less use of force in foreign policy, even after controlling for other explanations like partisanship, according to an analysis by researchers from Texas A&M University of data from 22 established democracies from 1970 to 2000.

Yet when women are in executive positions, the opposite is true: They are more hawkish than men. The researchers said that could be in part because of a need to overcome stereotypes of women as weak. Margaret Thatcher, Golda Meir and Indira Gandhi, all of whom governed in conflicts, were described as governing like men.

Whether women’s policies become law is another question. Studies have shown they encounter more obstacles than men’s policies.

Over all, female lawmakers are just as successful as men at getting their bills passed — except when the bills are about issues affecting women, health, education and social welfare, according to the new study of four decades of House bills by Craig Volden of the University of Virginia, Alan E. Wiseman of Vanderbilt University and Dana E. Wittmer of Colorado College.

Then, only 1 percent of bills sponsored by women passed, compared with 4 percent of all bills. That has been true since 1970, even when controlling for other factors that influence bills’ success.

The researchers concluded that it was not because of a gender difference in expertise or lawmaking ability, but because of institutional bias. Bills on the issues that women dominate are often gridlocked in committee, so they never make it to a vote.

“These are highly contentious issues in the first place, and it could be because there are relatively fewer women in Congress and as committee chairs, they might have less of a built-in coalition to push these through,” Mr. Wiseman said.

Yet women also have advantages in governing — and the biggest gender differences appear during behind-the-scenes work.

A variety of research has found that women interrupt less (but are interrupted more), pay closer attention to other people’s nonverbal cues and use a more democratic leadership style compared with men’s more autocratic style. The result is that women build coalitions and reach consensus more quickly, researchers say.

“Women share their power more; men guard their power,” said Michael A. Genovese, director of the Institute for Leadership Studies at Loyola Marymount University, who has studied gender and leadership.

Senator Kirsten Gillibrand, Democrat of New York, said the data backs up her experience in the Senate. “Women tend to be less partisan, more collaborative, listen better, find common ground,” she said. “Every time I’ve had a bill that’s important to me, I’ve had strong Republican women helping me pass it.”

These days, partisanship can seem more highly valued than collaboration in Washington, and without more women entering government, their influence might be muted.

“Women have the great potential to govern differently,” said Lyn Kathlene, a political scientist who studied gender and governing and is now director of Spark Policy Institute. “But my expectation is that’s going to be less overt than behind the scenes, because the reality is you have to play the game as the game’s played.”