Elizabeth Warren isn't winning the Democratic race so far, but she's winning the intellectual primary. If the last three decades are any indication, that's a valuable asset to have.

The party's last six presidential nominees had one thing in common: All were perceived as the cerebral heavyweight in their race, and all six went to either Harvard or Yale.

Of the Democratic Party's four leading 2020 candidates, only Warren has an Ivy League university on her resume - not as a student but as a Harvard Law professor. She has branded herself a candidate with "a plan" for everything by offering a flood of policy papers, packed with numbers and statistics, along with wonky proposals to expand the economic safety net.

It's paying off. Many surveys show her leading the pack with liberals and college-educated white voters, who have boosted her to the top three in the national contest and within striking distance in early primary states.

"She's the brainiac in the room," said Randi Weingarten, president of the influential American Federation of Teachers and a Democratic National Committee member. "But I think what she's offering up is more than being the brainiac in the room - she's also found a way to be feisty fighter that connects with people."

It may not be enough: Joe Biden, a graduate of the University of Delaware, has a strong lead among non-white, lower-income and less-educated voters, who identify with his folksy and often unpolished style.

Warren and Biden shared the debate stage for the first time on Thursday, when she showcased her cerebral approach to issues ranging from trade and health care to foreign policy and climate change. "I know what's broken," she insisted. "I know how to fix it."

Some Biden backers and establishment Democrats are concerned Warren's left-wing platform will be poison in a general election, while others doubt Americans are ready to elect a woman. And she faces competition from Bernie Sanders for young and left-wing voters who wonder if she's serious about upending the system.

Still, five months before voting begins, history is on Warren's side in one way: Brainiacs, whether they're insurgents or establishment figures, have a way of winning the Democratic nominations.

In 2016, Hillary Clinton (Yale '73) was widely seen as the cerebral candidate in the primaries, emphasizing the point with an array of position papers and boasting that "I sweat the details of policy."

The 2008 winner, Barack Obama (Harvard '91) was a former senior lecturer at the University of Chicago Law School and adored by intellectuals for his brand of aspirational liberalism. Previous nominees John Kerry (Yale '66) in 2004, Al Gore (Harvard '69) in 2000, Bill Clinton (Yale '73) in 1992 and Michael Dukakis (Harvard '60) in 1988 were all favorites of left-leaning bookworms.

Republicans have also picked plenty of Ivy League nominees - including the party's last three presidents Donald Trump (Wharton '68), George W. Bush (Yale '68) and George H.W. Bush (Yale '48). Trump and the younger Bush were distrusted by intellectual elites but won ion anyway.

Warren's rallies are full of passionate liberals, with her largest crowds coming in majority-white and relatively upper-income metropolitan areas like Seattle and Minneapolis. Her supporters frequently say they're attracted to her intellect.

"I love that she's so smart," said Judy Mitchell, a retiree who came to see Warren in Seattle.

In a CBS News battleground poll of 18 early states, 42% of Democrats said Warren was the "most knowledgeable" candidate - well ahead of Biden and Sanders, her two main rivals, who each scored 24% on that question.

And an August Fox News poll of Democrats found Warren leading by 4 points among white college graduates, but trailing Biden by 11 points overall.

Warren has impressed some supporters of her rivals, too.

"She has an answer for everything. She's well-prepared," said Debby Fisher of Richmond, California, who plans to vote for Sanders.

Others view her skeptically.

"I don't really trust her," said Hugh O'Connell, a graphic designer who attended a Sanders rally in San Francisco, and expressed concern that she would govern like Obama, and be too compromising with the establishment.

Some Democrats are also intrigued by the erudite demeanor of Harvard-educated Pete Buttigieg, who is polling in a distant fifth but has raised plenty of money to stay in the race.

Even though it is clearly a plus in the Democratic primary, the cerebral brand can cut both ways in a general election - Kerry and Dukakis, also from Massachusetts, like Warren, were tarred as out-of-touch eggheads and lost. Obama and Bill Clinton - who despite his Ivy League bona fides campaigned as a product of Hope, Arkansas - were able to inspire voters and win.

Warren's advisers worry about her being painted as a disconnected elitist and are trying to ensure the Oklahoma-born senator has a populist touch. She has sworn off high-dollar cocktail receptions and instead spends hours on the rope line taking selfies and photos with her fans and talking about her childhood struggles after her father's heart attack.

"You really want to change something? Then you better have a plan to get it done," Warren told a cheering crowd last Saturday at the New Hampshire Democratic convention, where her campaign lined the halls with enthusiastic fans who greeted her with a standing ovation.

"I don't go behind closed doors to fancy fundraisers with corporate CEOs and millionaires," she said. "Instead, I spend time with you - and have fun."

This article was written by Sahil Kapur, a reporter for The Washington Post.