Biden is the leader among Democrats in two separate measures, the first when those surveyed were asked to volunteer the name of a candidate they would support at this point as well as in a more traditional question that identifies the list of those running and asks respondents to select from among them. The former vice president’s position is buoyed by perceptions that he is the most electable Democrat in a general election and by his support among African American and older Democrats.

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When Democrats and Democratic-leaning independents are asked to identify their preferred candidate, without being prompted with a list of names, 21 percent cite Biden, a gain of eight points since late April. Sanders runs second at 13 percent, up four points since April. Harris and Sen. Elizabeth Warren (Mass.) are tied at 7 percent, both up three points.

Among the others, only South Bend, Ind., Mayor Pete Buttigieg, named by 3 percent, gets above 1 percent in this ranking. Meanwhile, 41 percent of Democrats did not volunteer a preferred candidate, down from 54 percent in April.

When the names of 22 Democrats running for the nomination are presented, Biden is slightly favored at 29 percent to Sanders’s 23 percent. Harris and Warren are again tied, at 11 percent. Buttigieg runs fifth, with 4 percent, and is tied with former housing secretary Julián Castro, who staked out a position calling for decriminalization of the border that framed the discussion of the immigration issue in both debates.

When second-choice preferences are added to first-choice selections, Biden remains atop the field, with 50 percent of Democrats saying he is either their first or second choice. Sanders stands at 40 percent in the combined ranking, followed by Warren at 25 percent and Harris at 24 percent.

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The Post-ABC survey shows a clear stratification of the large Democratic field, based on a combination of first and second choices. In that grouping, four candidates — Biden, Sanders, Warren and Harris — are chosen by at least 20 percent as the first or second choice of Democrats and Democratic-leaning independents.

No other candidate tops 10 percent when combining first and second choices. Buttigieg comes closest, with a combined 9 percent. Thirteen candidates register at 2 percent or lower in the combined first and second choices.

The event in Miami was the first time Americans could see nearly the entire Democratic field onstage together, albeit in an appearance split over two nights. Harris’s attack on Biden over his past position on school busing and his comments about working in the Senate with segregationist senators provided the most electric moment of either night and gave the campaign of the senator from California a jolt of energy in the aftermath.

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Biden in recent days has sought to recover from his performance in Miami, where he was also challenged to yield to a younger generation and struggled at other times. During an event before the Rev. Jesse L. Jackson’s Rainbow PUSH organization in Chicago on Friday, Biden offered a vigorous defense of his overall civil rights record of more than four decades while arguing that the nomination battle should not be about the past.

Other national polls taken after the debate show Biden with a more tenuous advantage. A CNN poll released Monday showed him with the support of 22 percent of Democratic or Democratic-leaning voters, closely followed by 17 percent who backed Harris, 15 percent for Warren and 14 percent for Sanders. The survey found that Biden’s support had fallen 10 points since May, while Harris had gained nine points. A Quinnipiac University poll showed similar overall results.

The Post-ABC poll underscores what has been the case from the time Biden entered the race in April: While he is the leader in the Democratic field, he is by no means a commanding front-runner. There are also signs in the poll that those who watched either of the two nights of debating came away with impressions of the candidates that were different from those Democrats who watched neither night.

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Health care stands out as a key issue for Democrats, with 29 percent saying it is one of the most important factors in their 2020 general election vote. But climate change (25 percent), immigration (24 percent) and gun violence (23 percent) also rank high.

Meanwhile, 20 percent of Democratic-leaning adults say issues of special importance to women are a top concern, with 18 percent saying the same of both the economy and abortion. Fewer say foreign policy (12 percent) and taxes (10 percent) are important factors.

One fault line among the candidates during the debates emerged on the issue of whether the party should replace the Affordable Care Act enacted during the administration of President Barack Obama with a government-run health system similar to Medicare.

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The new survey finds strong support among Democrats for a government-run plan, with about 3 in 4 saying that is their preference. Two in 3 Democrats say they would support such a system even if it meant an end to private insurance.

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Sanders long has advocated moving to a Medicare-for-all system and has been joined by others in the field. But Biden and other more moderate candidates have resisted embracing Medicare-for-all, preferring instead to add a public option to the Affordable Care Act. Sanders and Biden rank first and second as the candidates most trusted to deal with the issue of health care.

Warren has staked her candidacy in part on a flurry of policy initiatives. She and Sanders are tied on the question of which candidate has the most new ideas (27 percent each), with 26 percent saying the same of Harris. Biden, Buttigieg and Castro follow those three.

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The competition for the Democratic nomination remains fluid.

Biden’s biggest advantage is on the question of who can beat Trump in the general election. Forty-five percent of Democrats and Democratic-leaning independents name Biden as the candidate best positioned to do that. Sanders runs a distant second at 18 percent, followed by Harris at 9 percent and Warren at 7 percent. No other candidate gets above 2 percent on the electability question.

Whatever Biden’s standing overall, his debate performance did not impress Democrats as much as did that of two other candidates. Harris was the standout, with 41 percent saying she did an especially good job in Miami. Next is Warren, at 26 percent. Biden, meanwhile, is cited by 21 percent, Sanders by 19 percent, Buttigieg by 13 percent, Castro by 12 percent and Sen. Cory Booker (N.J.) by 10 percent.

Biden’s primary support is relatively stable among those who watched at least one of the debates and those who watched neither. But Harris runs stronger among those who watched the debates than among those who did not. She is favored by 17 percent who watched but by just 5 percent of those who did not. Warren runs six points better in the candidate preference question among those who watched at least one debate.

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African Americans are the most loyal constituency in the Democratic Party and a key to the nomination contest. Currently, Biden maintains a plurality advantage, supported by about 41 percent of black Democrats. Sanders runs second at 23 percent, followed by Harris with 11 percent. Warren trails significantly with this voting bloc, with just 4 percent support, the same as Booker.

Given the discussion about busing and race that swelled during the debate, the preferences among black Democrats will be closely watched, as Harris and other rivals to Biden try to cut into the advantage he enjoys.

Biden’s support among African Americans is all the more important because preferences among white Democrats are more divided. Biden leads among white Democrats with 26 percent, followed by Sanders at 18, Warren at 17 and Harris at 14.

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Sanders holds a lead among Democrats age 18 to 39, with 37 percent. Biden, at 21 percent, is the only other candidate to top double digits with these younger Democrats. But the former vice president holds an even bigger advantage among Democrats age 65 and older. Forty-four percent of those Democrats prefer Biden, with Harris and Warren getting 14 percent apiece. Sanders, who at 77 is a year older than Biden, gets the support of just 7 percent of older Democrats.

Warren does far better among Democrats with college degrees than those without. Her 21 percent support among college graduates is nearly as big as Biden’s 23 percent. But she gets a much smaller 6 percent of those without college degrees, far behind Biden (31 percent) and Sanders (27 percent). Harris gets 10 percent of non-college-educated Democrats and 13 percent of those with college degrees.

Although moderate and conservative Democrats make up a larger share of the party overall, liberals have made up the majority of Democratic voters in past primaries and caucuses. There is spirited competition for their support.

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Sanders is favored by 24 percent of liberal Democrats, Biden by 23 percent, Warren by 17 percent and Harris by 14 percent. Among moderate and conservative Democrats, Biden stands at 33 percent, Sanders at 24 percent, and Warren and Harris in single digits among these Democrats.

This Washington Post-ABC News poll was conducted by telephone from June 28 through July 1 among a random national sample of 1,008 adults, with 65 percent reached on cellphones and 35 percent on landlines. The margin of sampling error among the sample of 460 Democrats and Democratic-leaning independents is plus or minus 5.5 percentage points.