The survey of 2,672 likely voters by The Post and the Schar School at George Mason University shows that likely voters in these districts favor Democrats by a slight margin: 50 percent prefer the Democratic nominee and 46 percent prefer the Republican. By way of comparison, in 2016 these same districts favored Republican candidates over Democratic ones by 15 percentage points, 56 percent to 41 percent.

Women are driving Democratic support in the battleground districts, favoring the party’s candidates by 54 percent to 40 percent. Men in these districts favor Republicans by 51 percent to 46 percent. That gender difference continues a pattern that has been seen throughout the year in other polls and in special elections.

Of the 69 districts included in the survey, 63 are held by Republicans and six are held by Democrats. Trump carried 48 of these districts, and Hillary Clinton won the other 21. In the districts won by Trump, likely voters are split 48 percent for the Democratic candidate and 47 percent for the Republican. In the districts won by Clinton, Democrats enjoy a clear advantage, 53 percent to 43 percent.

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Democrats need to pick up a net of 23 seats to gain control of the House in November, which means they must win fewer than half of the battleground districts included in the new survey. The fact that, overall, voters in these districts are relatively evenly divided in territory that has been favorable for Republican House candidates in the past underscores why many GOP strategists are pessimistic about their prospects for holding the House.

With its focus on competitive districts, the new poll differs from many other surveys that ask what is known as a generic House vote question. In those polls, no names of candidates are included. Respondents are simply asked whether they prefer the Democrat or the Republican in their congressional districts. Those surveys also are generally made up of a sample taken from the entire nation rather than the minority of the total population living in competitive districts.

The Post-Schar School survey used the names of the two major-party candidates in each of the 69 districts. The districts included were those that as of Aug. 24 were rated as either toss-ups or leaning toward one party or the other by the independent Cook Political Report or identified by The Post’s political team as competitive. The Cook list is dynamic, given regular updates based on fresh analysis of the districts, which means the number of competitive districts can change from week to week.

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The survey also used a different sampling and interviewing approach to accurately identify voters in specific districts. Mailed invitations were sent to registered voters who were randomly selected in each district from state voter registration lists. Respondents had the option of completing the self-administered survey by computer, mobile device, tablet or phone. The margin of sampling error among likely voters is plus or minus two percentage points.

The president’s job approval rating among likely voters in these battleground districts stands at 43 percent, somewhat higher than a national rating of 38 percent among registered voters in a Post-ABC News poll taken at the end of August. In those battleground House districts that he carried, Trump’s approval is 46 percent; in the Clinton-won districts, it is 38 percent. Overall, 47 percent of voters in all the competitive districts strongly disapprove of the way he is handling his job.

A recent analysis by Public Opinion Strategies, a Republican polling firm, concluded that Republicans would need a national Trump approval rating of at least 45 percent to have a chance to maintain control of the House. In battleground districts, that number would need to be a bit higher. That suggests the current 43 percent approval in battleground districts is another sign of potential trouble for the GOP.

Trump’s approval rating remains a strong predictor of how people are likely to vote. In the survey, 91 percent of those who approve of the president’s performance also are supporting the GOP candidate in their districts. Meanwhile, 88 percent of those who disapprove of Trump’s performance are backing the Democratic candidate.

The survey also highlights the growing split between white voters with college educations and those without a college degree — something that is especially acute among women. This educational divide has been growing since Trump was elected.

White voters overall, regardless of educational achievement, are divided almost evenly in the battleground districts, with 49 percent saying they support the Republican and 47 percent saying they favor the Democrat. Among nonwhites, Democrats hold a big advantage, 64 percent to 29 percent. In these battleground districts, nonwhites make up a smaller portion of the population than they do nationally.

Looked at on the basis of educational achievement, 55 percent of white college graduates say they favor the Democratic candidate in their districts, compared with 42 percent who say they back the GOP nominee. Among whites without college degrees, the numbers are almost the opposite, with 53 percent backing the Republican candidate and 42 percent supporting the Democrat.

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The educational differences are most noticeable among women. White women with college degrees back the Democratic candidate in their districts by 62 percent to 35 percent. White women without college degrees tilt toward the Republicans running in their districts by 49 percent to 45 percent.

On another front, the new survey finds considerable optimism about the economy, with 77 percent giving the economy positive marks — 27 percent rating it “excellent” and 50 percent saying it is “good.” But when asked about the direction of the country apart from the economy, 36 percent say the country is going in the right direction and 57 percent say things are headed in the wrong direction.

More than one-third of likely voters say their families are getting ahead financially, and Republican candidates receive 74 percent support from this group. But nearly half of voters say they have “just enough to maintain their standard of living,” and Democrats garner a 61 percent majority of their support. Democrats fare even better among the 15 percent of voters who say they are falling behind financially.

Voters rated eight issues from “extremely important” to “very important” to “somewhat important” to “not so important.” The issue that drew the most “extremely important” rating, at 64 percent, was the Supreme Court and judicial nominations, the issue that dominated the news during the time the survey was conducted. Second in the “extremely important” ranking was Trump, at 60 percent.

A 57 percent majority rated health care as extremely important, with 55 percent rating the economy as extremely important and 52 percent saying the same for immigration. Issues that ranked lowest were special counsel Robert S. Mueller III’s investigation into Russian interference in the 2016 election, as well as gun violence and international trade.

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When pushed as to the single most important issue influencing their vote, a different order of significance emerged. In that case, Trump led the list, with 26 percent saying he was the most important of all the issues or factors, followed by the economy at 19 percent and the Supreme Court and other judicial nominations at 16 percent.

At this point, Trump appears to be more of a motivating factor in the voting decisions of Democrats than Republicans in these battleground districts. Among self-identified Democrats and independents who lean to the Democrats, 40 percent say Trump is the single most important issue in their vote this fall, followed by health care at 20 percent. Among Republicans and Republican-leaning independents, however, 29 percent say the economy tops their list, with 24 percent naming judicial nominations, 17 percent saying immigration and 15 percent citing Trump.

Among those who cite judicial nominations as extremely important, 50 percent are backing the Democrat in their districts and 47 percent are backing the Republican. That finding is certain to be closely watched in the wake of the fight over Brett M. Kavanaugh’s Supreme Court nomination, as a measure of energy and intensity ahead of the midterms.