Washington (CNN) Listen to the majority of candidates running for the Democratic presidential nomination or scroll through Twitter and you will rapidly conclude that the Democratic Party is dominated by liberals.

You would be wrong.

According to the new CNN-SSRS national poll , self-identifying liberals make up less than half of all Democrats: 42%. The rest of the party calls itself either "moderate" (43%) or conservative (11%).

Which is interesting!

What's also interesting is just how much the 2020 Democratic race is developing as a battle between its liberal and moderate wings. Among people who describe themselves as liberal, Sen. Elizabeth Warren (Massachusetts) takes 23% of the national Democratic vote in the CNN-SSRS poll while Sen. Bernie Sanders (Vermont) and former Vice President Joe Biden each take 22%. Among "moderates" and "conservatives," however, the story is very different. Biden is at 34%, compared with 9% for Sanders, 7% for Warren and 7% for South Bend, Indiana, Mayor Pete Buttigieg.

What all of these data points say is that while the most liberal elements within the party -- which tend to spend lots and lots of time online and on Twitter -- are the loudest, they are not nearly as dominant a voice within the party as they (and the candidates vying for their votes) would have you believe.

To be clear: There is absolutely a constituency within the current Democratic Party for ideas like "Medicare for All," which would end private insurance entirely, and the decriminalization of illegal immigration. But it is just as clear -- from the CNN poll and others -- that this is not the only, or even the majority, voting bloc among Democrats. There's a considerable chunk of Democrats who are in favor of more pragmatic solutions, like, say, amending and extending the Affordable Care Act rather than doing away with it.