Recent headlines bemoan the fact that, in the city of Los Angeles, only one woman — recently elected to a City Council with 14 men — holds elected office in City Hall. As for L.A. County, with 9.9 million residents, a lone woman sits on its five-member Board of Supervisors.

California is not alone. Across the United States, only 73 women hold statewide elected offices — less than a quarter of available positions. That percentage has been declining for 12 years, according to the Center for American Women and Politics at Rutgers University.

This sorry situation might be cited as an illustration of the glass ceiling, when a woman moves upward until she crashes into an unseen barrier. But new research tells us that a better image for what’s happening today is what we call the “plugged pipeline.” In the workplace, women are hitting barriers and getting tripped up all along the way, not just as they near the top.

In corporate America, the number of women promoted to board seats in Fortune 500 companies, which had steadily increased in the late 20th century, has dropped over the last three years, according to a major report in 2011 by the consulting firm McKinsey & Co. It found that the proportion of women falls quickly as you look higher in the corporate hierarchy, and overall, “this picture has not improved for years.”

Also, women’s gains in computer science and engineering have slowed or even shifted into reverse. Women make up a dismal 11 percent of tech executives. The percentage of women in computer fields has declined from nearly 40 percent in 1991 to 25 percent today, according to the U.S. Chamber of Commerce.

Women are doing well in academia, where they now earn the majority of advanced degrees. But it’s a different story in the workplace. Women are stalling out, and the higher they go, the harder it gets. Why?

The direct, in-your-face gender discrimination of the past has faded, but bias hasn’t vanished. It’s just gone underground and is growing. Under a veneer of “progress,” what we call the new soft war on women is gaining momentum, based on stubborn stereotypes about what women can’t do.

New research finds that stereotypes are now operating in surprising ways.

Too often, young men climb the ladder ahead of more seasoned female colleagues. For promising men, potential is enough, whereas women are judged on what they’ve actually done, according to research by McKinsey and the think tank Catalyst.

Women have to keep proving themselves, often fighting the stereotype that they don’t have what it takes to be real leaders.

Whoever does the work should get the credit. That’s our idea of fair play. But it doesn’t always work that way for women. Often, they do the lion’s share of the work and achieve success but men get the credit.

Professors Madeline Heilman of New York University and Michelle Haynes, now at the University of Massachusetts Lowell, have found that if it isn’t crystal clear which member of a two-member, male-female team is responsible for the team’s success, supervisors or boards of directors far more often give credit to the male team member.

Female members were seen as less competent, less influential and less likely to have played a leadership role in the job at hand. Both men and women fell into the trap of giving higher marks to the male team member.

A woman we interviewed told us: “I coordinated and ran the network depot for a nationwide network … and a young male student was given a monetary and certificate award for the work that we did, and I was not mentioned…. And then he was given the official leadership on the next project.”

We heard stories like this often from women around the country. It is an especially disturbing finding because in most cases, it isn’t conscious discrimination against women. It’s just that the stereotypes we all have in our heads about what men and women can or can’t do are incredibly deep-rooted.

And what happens when women get stuck in the pipeline? Separate studies conducted by Deloitte Consulting and McKinsey found that companies with significant numbers of women in management have a much higher return on investment than companies that lag on this front.

If women are held back in the plugged pipeline, the United States will lose its competitive edge. That is not good for women’s advancement or the pocketbooks of all Americans.