Now, those who are seeking to deny President Trump a second term say their mission is not only replacing him in the Oval Office but also leading Americans back from their own baser instincts.

Joe Biden said he is engaged in a “battle for the soul of this nation.”

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And Sen. Kamala D. Harris (D-Calif.) said Trump “isn’t trying to make America great; he’s trying to make America hate.”

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Has he succeeded?

A new study by researchers at the University of Pennsylvania suggests there is room for doubt, despite rising incidents of hate crimes, notably in the very counties that hosted a Trump rally in 2016.

Racial prejudice has not increased among white Americans since the explosive 2016 election, argues political scientist Daniel J. Hopkins. It has actually decreased by some measures, he found, possibly as a reaction to Trump’s unexpected ascension to the White House.

Hopkins told The Washington Post that the results initially surprised him. Upon reflection, however, “it’s quite conceivable that Trump has simultaneously galvanized a small number of highly prejudiced white Americans while also pushing millions more to affirm that they are not as prejudiced,” he argued.

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In other words, Hopkins believes the study provides evidence that the racially incendiary rhetoric and policies issuing from Trump’s White House have pushed the majority of Americans in the opposite direction.

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The specialist in race and political behavior acknowledged that his findings speak only to professed bias and not to concrete behavior, such as whether Americans are moving into heterogeneous neighborhoods.

The study, currently under review but posted on the Social Science Research Network on Thursday, starts from an unambiguous premise: “As a political leader, Donald Trump has used racist rhetoric to build political support.”

Hopkins and an undergraduate student, Samantha Washington, set out to determine what effect that rhetoric was having on white Americans, 57 percent of whom voted for Trump in 2016, according to exit polling. Among white men, that figure was 62 percent.

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Most think the president is motivating his racist supporters to declare their bigoted views. A Quinnipiac University poll last summer found that 55 percent of voters believed that Trump was emboldening people who hold racist beliefs to state them outright.

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There are two ways that effect might play out, the study observes. One is normalization, whereby members of the public would feel more comfortable expressing racist beliefs that they always harbored but once felt were outside the mainstream. The other is so-called opinion leadership, whereby the public would be moved to adopt racist positions advanced by political elites.

Instead, the authors found evidence of an altogether different effect — people actually moving away from the positions embraced by those in power.

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“Our findings contradict both hypotheses, as we primarily find declining prejudice and racial resentment, and certainly no increases,” the paper states.

The data was drawn from a nationally representative sample of about 20,000 people, interviewed five times between 2007 and 2008. Subsets of the sample submitted to eight further interviews, most recently in November 2018.

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Prejudice was assessed based on the credence that white Americans gave to stereotypes. Specifically, they were asked to rank different racial groups on scales of trustworthiness and work ethic. Respondents also weighed in on race-related policies, such as whether the government should make special provisions for black Americans or whether minority populations should fend for themselves.

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Across the roughly 12-year period covered by the data, anti-black prejudice declined based on these metrics, with an especially marked drop between November 2016 and November 2018. The effect was only slightly more pronounced among Democrats than among Republicans. Education was not a decisive factor.

“The decline was apparently not driven by Trump’s candidacy — or by white Americans’ reactions to his campaign rhetoric in 2015 and 2016 — but instead by their reactions to his presidency itself,” the paper claims.

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Anti-Hispanic prejudice showed a similar decline between Trump’s election and the fall of 2018, but the shift in this case was driven by people who identified as Democrats. There was a small increase in professed anti-Hispanic sentiment among Republicans between 2012 and 2018.

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A poll by the Pew Research Center published in January found record-high support among Republicans for Trump’s proposed wall along the southern border. A majority of the country nevertheless opposed the president’s emergency declaration over the situation at the U.S.-Mexico frontier, according to polling.

The study allows that factors beyond Trump’s rise — such as the election of the nation’s first black president and the spotlight cast on police-involved shootings — may have contributed to changes in expressed prejudice.

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“It is also possible that Trump’s rhetoric clarified anti-racist norms,” the study notes, pointing to the pronounced decline in certain measures of bias in the period after Trump’s election as evidence that his presidency in particular has “pushed public opinion in the opposite direction.”

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Whether the shift discovered by researchers has actually “shaped social behaviors” — rather than being empty value statements or even cover for discriminatory conduct — “is another critical question for future work,” the study suggests. But it casts into doubt whether hate crimes that rose 17 percent in 2017 reflect deepening hatred across the board.

Instead, the political scientist points to the increasing isolation of an extremist minority whose prejudices have intensified in the face of a broader shift away from the sort of opinions aired in Trump’s White House and on his Twitter feed.

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Although he was surprised by the results, Hopkins said his discovery is not out of step with other assessments. In fact, his conclusions are in line with recent scholarship suggesting that bias, both implicit and explicit, has declined when it comes to race and sexual orientation, though prejudice has remained steady regarding people with disabilities and actually increased regarding obesity.

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Other studies have tracked opinions of race relations, rather than underlying racial beliefs. For instance, a major survey published last month by Pew found that 58 percent of Americans have a negative view of race relations in the country. Nearly as many think Trump has worsened relations between the races, and about two-thirds of people said the expression of racist views has grown more common since Trump’s election.

Hopkins’s study hardly invalidates these concerns. But it questions how broad a swath of the population has imitated the president’s rhetoric. It does not explain the rationale of those who sanctioned his conduct at the voting booth but profess not to embrace it personally.