Shortly before that poll came out, Sanders’s campaign lifted up a report from Politico that seemed as though it might help explain Warren’s improved position: She was gaining support from what Sanders called “the corporate wing” of the Democratic Party. Which is to say the party’s more moderate, less progressive arm, the segment of the party that, in Sanders’s framing, will pull out all the stops to curtail his economic revolution.

It doesn’t take much reading between the lines here to understand Sanders’s argument: Centrists are circling around Warren (per Politico) because they are afraid of legitimate progressive positions like his own.

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Setting aside the question of how robustly Sanders’s big-ticket policies differ from Warren’s, there’s another, bigger problem with that argument: It’s not what polls show is happening.

Patrick Murray, who runs the Monmouth University Polling Institute, noted on Twitter that the Politico article relied on the opinions of a few people in determining that more-moderate Democrats were lining up behind Warren. One, for example, was the co-founder of a centrist think tank that, Politico’s Natasha Korecki and Charlie Mahtesian write, “is learning to live with Warren.”

Murray noted that Monmouth’s polling paints a different picture than Politico’s interviews would suggest.

And so it does. In Monmouth’s polls over the past few months, Warren’s surge has been a function of voters who identify as liberals. In April, she earned 8 percent of the vote among those who identify as liberal. In the new poll, she moved into a tie with former vice president Joe Biden.

Biden’s in the overall lead in national primary polling because he fares much better than Warren, Sanders or anyone else among more moderate Democrats. In the most recent poll, Biden gets 40 percent of the moderate vote to Sanders’s 10 percent and Warren’s 6.

Looking at the composition of the candidates’ support in Monmouth’s polling, Warren’s surge among liberal voters combined with her soft support among moderates has given her a much more heavily liberal base of support than Sanders.

That’s only one pollster, mind you. But the idea that Warren’s gains are a function of moderates viewing her as an acceptable alternative to Sanders isn’t reinforced in Quinnipiac University polling, either.

In those polls, both Sanders and Warren have gained against Biden in recent months — Sanders more so than the senator from Massachusetts.

Quinnipiac breaks respondents into three ideological groups: very liberal, somewhat liberal and moderate or conservative. Sanders’s gains have been in part a function of his gaining support among very liberal respondents in recent polls.

But in Quinnipiac’s polls, too, Sanders gets slightly more support from moderates than does Warren (though the difference is within the margin of error). Each candidate’s base shows a similar ratio of moderate-to-very-liberal support.

In Quinnipiac’s polling, Warren’s support among somewhat liberal Democratic voters trails Sanders’s support from that group by a significant margin.

A higher density of Warren’s support in these polls comes from very liberal voters than does Sanders’s.

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Sanders’s point is admittedly not entirely about moderate voters but, instead, about how moderates in the Democratic establishment may see Warren as more palatable. That fits with his long-standing rhetoric about the party and his position as an outsider.