Since then, Trump has repeatedly said he disavows Duke and the Klan. The problem is, that is the only thing Trump has said. He hasn't explained why the Klan's white nationalism was wrong, and his disavowals are starting to sound somewhat perfunctory.

New polling data from the American National Election Studies suggests a few reasons that Duke might see sympathy for his cause among Trump’s supporters. Some of them appear to be worried about their status and identity as white Americans, a concern that has allowed him to build a broad electoral coalition that crosses the usual demographic and ideological boundaries within the Republican Party.

Maybe that is why questions about the Klan keep coming up for Trump, and why no one in the press seems to believe his disavowals. He could easily make his stance on racism clear, but to this point, he has not done so.

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A spokeswoman for Trump did not respond to a request for comment.

Contrast Trump's words with the kind of unequivocal, impassioned condemnations of white supremacy that other Republicans have offered. Sen. Ted Cruz (R-Tex.) called the Klan "abhorrent," writing, "Racism is wrong."

"There is no room in the conservative movement and there is no room in the Republican Party for members of the Ku Klux Klan or racists like David Duke," Sen. Marco Rubio (R-Fla.) said.

"If a person wants to be the nominee of the Republican Party, there can be no evasion and no games," said Rep. Paul Ryan (R-Wis.). "They must reject any group or cause that is built on bigotry. This party does not prey on people's prejudices."

Contrast Trump with Rick Perry, the Republican former governor of Texas, who back in the summer gave a carefully considered speech on race and violence.

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Perry began with a harrowing account of a lynching in Texas in 1916. Then he said the Republican Party needed to do more to confront its historical association with racism.

"I know Republicans have much to do to earn the trust of African Americans," Perry said. "Blacks know that Republican Barry Goldwater in 1964 ran against Lyndon Johnson, who was a champion of civil rights. They know that Barry Goldwater opposed the Civil Rights Act of 1964. States supporting segregation in the South cited 'states' rights' as a justification for keeping blacks from the voting booth and the dinner table."

Contrast Trump's repeated insinuations that President Obama was not born in the United States with this line of Perry's: "I am proud to live in a country that has an African American president."

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Trump has not been able to summon up such rhetoric. All he can do, it seems, is repeat the word "disavow." His comments are worth quoting at length.

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"How many times do I have to continue to disavow people?" he said Monday on NBC. "I disavowed David Duke. Now if you look on Facebook, right after that I also disavowed David Duke. When we looked at it and looked at the question, I disavowed David Duke. So I've disavowed David Duke all weekend long."

The question came up again at Trump's press conference following his victories in primaries on Tuesday. "Look, I disavowed. I disavowed," he said before beginning to talk about the huge crowds he's getting on the campaign trail. Then he came back to the subject at hand:

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I put out a tweet and I put out on Facebook that I totally disavow. Now everybody knew I did that, but the press refused to look at that. It was right after. And I disavowed then. I disavowed today on ABC with George Stephanopoulos. I disavowed again. I mean, how many times are you supposed to disavow? But I disavow and hopefully it’s the final time I have to do it.

Maybe it is unfair to expect Trump to offer more than this -- to expect him to say a few words to the effect that racism is wrong, or to explain how he'll broaden the party's appeal to voters of color if he's nominated. After all, it's clear he doesn't take the accusation of racism seriously, so why should he bother to respond in detail?

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Yet Trump was asked to do just that in Thursday night's debate on Fox. Moderator Chris Wallace told Trump that everyone is aware that he disavows the Klan. Instead, Wallace said he wanted to know more about Trump's views on racism.

"You have repeatedly disavowed [Duke], but I'd like to go deeper than that," Wallace said. "What are your views on the Ku Klux Klan, and white supremacists?"

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Trump didn't answer the question, instead simply repeating his earlier disavowal.

"Obviously I'm going to disavow," he said. Yet that was exactly Wallace's point: Of course, anyone running for office is going to disavow the Klan. What voters still don't really know is how Trump thinks about the country's history of racial oppression.

It would be easy enough for him to clear this up, and it's no wonder that many people seem confused about where Trump stands. Recent polling data shows that Trump's support is at least partially motivated by racial anxiety.

Last week, political scientists Michael Tesler and John Sides analyzed pilot data from the American National Election Studies, a recurring survey. They noted that, among white independent and Republican supporters of Trump in the survey, one-third believe that there is "a great deal" of discrimination against white people in the United States today -- twice the share of those supporting other Republican candidates.

A majority -- 52 percent -- of Trump's supporters in the survey believe it is "extremely important" that white people work together to change laws that are unfair to people of their race, compared with 31 percent of white Republican and independent voters supporting other candidates.

Also last week, the news organizations Vox and Morning Consult released a detailed survey that shows Trump's supporters are also united by what psychologists call "authoritarianism" -- a set of related character traits including a preference for unwavering leadership, resistance to change, and aversion to cultural and racial differences.

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The connection between authoritarianism and Trump's appeal is not as pronounced as the link between the belief that white status is threatened and support for Trump. Nor are voters' general feelings about immigration or the economy as useful in predicting whether or not they stand for Trump.

That said, Trump's supporters are particularly concerned about minorities in the labor force. Among white Republican and independent respondents, 47 percent of Trump's supporters say it is at least "very likely" that many white workers are unable to get a job because businesses are hiring minorities, while just 22 percent of those supporting other candidates agree.

In all, the data suggest that Trump has created a new kind of Republican primary coalition. Many of those who support him are white voters who are uncomfortable with the way America is changing demographically, and they believe that the status of people who look like them in society is in decline.

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In the past, analysts have typically divided Republican primary voters into several groups: evangelical, moderate, secular and conservative, moderately conservative, and so on. In Trump's coalition, these divisions are secondary. For certain GOP voters, racial consciousness is more fundamental than their other commitments.

As Trump's success has shown, the faction that votes based on white racial identity -- while not a majority of the party -- can be the dominant one when there are several candidates competing for the nomination.

What Donald Trump is doing on the campaign trail share Share View Photos View Photos Next Image U.S. Republican presidential nominee Donald Trump speaks at a campaign event at Trump Doral golf course in Miami, Florida, U.S. July 27, 2016. REUTERS/Carlo Allegri (Carlo Allegri/Reuters)