That essential contradiction was particularly evident in one line from the speech Hillary Clinton gave Thursday night accepting the Democratic nomination for president.

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Clinton sought to appeal to young voters by looking forward to the more equitable society she suggested they could create.

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"We have the most tolerant and generous young people we’ve ever had," the former secretary of state said.

It was unclear exactly in what sense Clinton meant that young Americans today are more tolerant and more generous, but in one important sense, there is only limited evidence that today's young people are more open-minded than their parents.

The generation commonly known as millennials are roughly as likely to hold racist stereotypes against African Americans as baby boomers, according to a recent analysis by The Washington Post using data from a major national survey.

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Participants in the study, known as the General Social Survey, were asked a long list of questions, including how hardworking they believe members of different groups are. Roughly 31 percent of white millennials rated African Americans as less hardworking than white Americans, compared to 35 percent of white baby boomers.

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Both generations were less likely to express this prejudice than the Silent Generation (those born between 1928 and 1945) — 46 percent of whom rated African Americans as less hardworking. Progress toward reduced bias seems to have slowed in recent decades, and some of the difference between the Silent Generation and the baby boomers could simply be because the younger generation grew up with different social norms around what is acceptable to say publicly and what is acceptable to tell surveyors.

Psychologists also try to measure Americans' unconscious biases, not just what they are willing to say out loud about people of different races. To do so, psychologists ask subjects to rapidly associate words with images of black faces and white faces. Many associated negative words with black faces more readily.

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Using data from another study, The Post found that 38 percent of white millennials displayed unconscious bias against black faces, compared to about 48 percent of white baby boomers.

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In terms of young people's views on specific policies designed to alleviate racial inequality, another researcher found that young people in 2008 had attitudes on race that were no more liberal than the attitudes of young people 20 years earlier.

One possible explanation for the persistence of racial antipathy across the generations is the possibility that young people receive their views on race from their parents and are unlikely to change them later in life. If so, these hostilities might persist for generations to come.

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A group of researchers recently pointed to evidence of this pattern. They used data that began half a century ago, finding that Southerners who were seniors in high school in 1965 and who had racially conservative parents were more likely to have racially conservative views throughout their adult lives — at least until their 50th birthdays.

That pattern, they argued, helped explain why the areas of the South where cotton was grown before the Civil War and where slavery was most prevalent are the areas where white Southerners are still the most racially conservative today.

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It could be that millennials are more tolerant than their parents, but to the extent that is true, the fact that millennials are a more ethnically and racially diverse group of people is probably the main reason. There is little evidence that white millennials, in particular, are much different than their parents when it comes to attitudes on race.

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Perhaps that will not matter for Clinton's efforts to turn out young voters at the polls this November. All the same, the persistence of biases among white millennials suggests the politics of race could remain bitterly divisive for decades to come.