(Cathy Lanier, left, Muriel Bowser, center, and Kaya Henderson./Bill O’Leary/Post, AP and Katherine Frey/Post.)

The nation’s capital didn’t wait for 2016 to make political history.

We started the year with three women in the District’s most high-profile jobs — mayor, police chief and schools chancellor — the only big city in the country to have such prominent female leadership.

D.C. has now caught up to Bangladesh, Liberia, Iceland and Denmark when it comes to women in charge.

Hooray for us. Rest of America? Please catch up.

As a nation, we’re still terrible at representing 51 percent of the population fairly. The numbers in this year’s Congress are historically high — and still barely a meager 20 percent.

So when D.C. Mayor Muriel Bowser (D) took office last week and announced even earlier that she’d be keeping Police Chief Cathy Lanier and Schools Chancellor Kaya Henderson in place, it was a big deal.

What will the matriarchy mean for the city? Plenty of people think D.C. will thrive with women running the show.

“Women do it Better than Men,” was the name of a leadership study published a couple of years ago in the Harvard Business Review that dissected performance evaluations of more than 7,000 leaders and concluded that women outscored men in 12 of 16 categories.

So women are more nurturing consensus builders? Are we in for a kinder, gentler D.C. government?

“What was fascinating was it’s true — they were more nurturing, on average — and yet we also found that the two competencies in which women were most ahead of men were “taking initiative” and “practicing self-development,” one of the study’s authors, Joseph Folkman, told The Washington Post’s Jena McGregor when she interviewed him in 2012 after the study was published.

Women “did particularly well on competencies like ‘driving for results.’ So this idea we have that women are just nicer [is misguided]. These women are hard driving,” Folkman said.

Not everyone believes there is a fundamental difference when women wield the power.

“I don’t think your gender really matters in this line of work,” Lanier said Sunday when the New Matriarchy — Lanier, Bowser and Henderson — appeared on “Meet the Press.” “Like most uniformed services, if you come to work and work hard every day, and you have a reputation of being a hard worker, cops really don’t care if you’re male or female or black or white, and nor does the community.”

I don’t know about that.

Crime continues to decline, highly charged political protests in a complex city cape have been welcomed and controlled without major incidents, and the police department and mayor have continued to work well together without major strife, something a lot of other big city departments run by men can’t say.

You could attribute it to the economy or the changing population of the city. But I’d like to think that Lanier’s inspiring biography — she got pregnant at 14, dropped out of high school, left an abusive husband, raised a child alone, educated herself, survived sexual harassment and departmental challenges (I hear what some of those guys say, Chief) — makes her an exceptional leader.

It’s monumental for society to see women like Lanier at work. It fundamentally changes the way others — particularly children — think when a woman is in charge at a crime scene or in a boardroom. And the sad truth is, it doesn’t happen often enough.

“Women remain hugely underrepresented at positions of power in every single sector across this country,” Barnard College President Debora Spar said at a White House conference on urban economic development last year.

“We have fallen into what I call the 16 percent ghetto, which is that if you look at any sector — be it aerospace engineering, Hollywood films, higher education, or Fortune 500 leading positions — women max out at roughly 16 percent,” Spar said. “That is a crime, and it is a waste of incredible talent.”

To take advantage of that talent, we need two things: We need boys and girls to grow up seeing that women aren’t just moms, teachers and day-care providers. Women also are mayors. Police chiefs. President?

And we need better leadership on the issues that hold women back. We need safe, affordable and effective child care. We need to change the culture of domestic violence. In 2013 in D.C. alone, police received nearly 33,000 calls reporting domestic abuse. We need to eliminate the pay gap that still exists in all too many workplaces.

Who can deliver on those issues? You already know what I’m going to say: Women.

To read previous columns, go to washingtonpost.com/dvorak.