NORWOOD, Mass. » Donald Trump insults and exaggerates.

He dismisses the need for public policy ideas, gets confused about world affairs and sometimes says things that flat out aren’t true.

And the cheers from his supporters only grow louder.

By the standard that voters typically use to judge presidential candidates, Trump probably should not have survived his first day in the 2016 race.

Yet as the summer draws to a close and the initial votes in the nominating calendar appear on the horizon, Trump has established himself as the Republican front-runner.

Listen to these voters:

— "It’s totally refreshing. He’s not politically correct. He has a backbone and he cannot be bought," said Leigh Ann Crouse, 55, of Dubuque, Iowa.

— "This country needs a businessman just like him to put us back on track, to make us stop being the laughing stock of this world," said Ken Brand, 56, of Derry, New Hampshire.

— "He says everything that I would like to say, but I’m afraid to say. What comes out of his mouth is not what he thinks I want to hear," said Janet Boyden, 67, of Chester, Massachusetts.

They are among the dozens of voters interviewed in the past two weeks by The Associated Press to understand how Trump has defied the laws of political gravity.

Uniting them is a deep-rooted anger and frustration with the nation’s political leaders — President Barack Obama and conservative Republicans who, these voters say, haven’t sufficiently stood up to the Democratic administration.

Some haven’t voted in years, or ever, and may not next year. But at this moment, they are entranced by Trump’s combination of utter self-assurance, record of business success and a promise that his bank account is big enough to remain insulated from the forces they believe have poisoned Washington.

By the way, they say it’s not that they are willing to look past Trump’s flaws to fix what they believe ills the country. It’s that those flaws are exactly what makes him the leader America needs.

"At least we know where he stands," said Kurt Esche, 49, an independent who was at Trump’s recent rally outside Boston. "These other guys, I don’t trust anything that comes out of their mouths. They’re lying to get elected. This guy’s at least saying what he believes."

"He may have started as a joke," Esche said, "but he may be the real deal."

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Crouse is a merchandise processor at a retail distributor outside Dubuque, the Mississippi River town where Trump tossed Univision anchor Jorge Ramos from a news conference.

A political independent who has never participated in Iowa’s leadoff presidential caucuses, Crouse said she began following Trump from the moment he referred to Mexican immigrants as criminals during his campaign kickoff.

"He’s just attracting people who are frustrated, and as you can see, there are a lot of us," she said.

Illegal immigration is the perfect summation of Trump’s unorthodox campaign.

He claims it’s an issue the GOP would not be discussing if not for his presence in the race, even though the topic has been at the center of political debate for years.

It’s the only one on which he has made a concrete proposal; his rivals, by comparison, have rolled out lots of ideas on a range of issues.

Here’s Trump’s pitch: deport millions of people who are living in the United States illegally and build a border wall. Critics deride this approach as naïve, but his supporters say it’s the obvious solution.

"As crazy as it might be, I think he’s addressing something that needs to be heard," said Randy Thomas, 40, of Bedford, New Hampshire. "I think he’s saying something that everybody thinks always has to be addressed. If you have a country of laws, you have to abide by the laws."

Republican pollster Frank Luntz, who recently held a discussion with a group of nearly 30 Trump backers in Virginia, said such support is emblematic of Trump’s popularity. It stems less from their love for the candidate and more from a belief those in power have failed.

"He activates the anger and frustration they have toward Washington and Wall Street," Luntz said.

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For many, Trump’s rise is a reaction to Obama, long criticized by opponents as a weak leader who appeases America’s enemies rather than asserting U.S. dominance on the global stage.

The voters interviewed by AP said much of Trump’s appeal stems from their belief he is a decisive and forceful leader who never backs down or apologizes, even when maybe he should.

Many appear convinced that the sheer force of Trump’s personality can reverse decades of global realignment, and that his pledges to rid the country of people living in the U.S. illegally and penalize imported goods will restore manufacturing jobs lost to China and boost an economy still scarred by the recession.

"We’re just so weak. We’re not respected anymore," said Jerry Welshoff, 56, of Franklin, Massachusetts. He arrived at a recent Trump event near Boston unsure about the candidate; he emerged sold on the candidate.

"We’ve appeased everything. We can’t negotiate. I would want Donald Trump to sit across a table from (Russian President Vladimir) Putin or Iran or the Mexican prime minister to cut a deal because he’s done it his whole life," he said.

The frustration among voters isn’t limited to their feelings about Obama.

Welshoff said the Republican Party has done nothing but acquiesce to Obama despite taking control of Congress in 2014.

It’s the same complaint heard from Duane Ernster, 57, of Dubuque. He is disappointed by the few accomplishments of tea party candidates elected to Congress in 2010.

"Things just didn’t happen. It just hasn’t happened the way we’d hoped," he said. "Maybe we need a warrior instead of a politician. People compare Mr. Trump to Putin. There’s something to be said about the man, who takes care of the Russian people."

Others are simply blown away by Trump’s wealth and his promise to pay for his campaign out of his own pocket. "He won’t owe anybody," said Susan Sager, 57, of Aiken, South Carolina.

This is an important point of distinction with both Democratic front-runner Hillary Rodham Clinton and former Florida Gov. Jeb Bush, who began the campaign viewed as the GOP front-runner due in no small part to his ability to raise huge amounts of money.

"Remember this. They have total control over Jeb and Hillary and everybody else that takes that money," Trump said this past week, adding: "I will tell you this. Nobody’s putting up millions of dollars for me. I’m putting up my own money."

The argument that Trump is uncorruptible is powerful.

"I just think he’s doing it for all the right reasons," said Nancy Adam, 60, at the rally near Boston. "It’s not about the money. It’s not about the political power. He’s already got everything. He has nothing to lose by doing this."

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Trump’s uncanny ability to stumble without consequence has befuddled his rivals.

The latest misstep for Trump came Thursday. After pledging only to run as a Republican, he fumbled a series of foreign policy questions from radio host Hugh Hewitt. Trump confused the Quds Force, an elite Iranian military unit, and the Kurds, an ethnic group of more than 30 million people.

He said the line of inquiry amounted to a "gotcha question."

"I mean, you know, when you’re asking me about who’s running this, this this, that’s not, that is not," Trump said, "I will be so good at the military, your head will spin."

Such an answer would invariably be attacked as disqualifying if offered by anyone other than Trump. His rivals have yet to figure out how to challenge an unpredictable opponent who appears immune to such gaffes.

"He just keeps repeating things over and over again. And you all just accept it for the truth, and it’s not," Bush told reporters in New Hampshire on Thursday.

Indeed, Trump’s foibles often appear to make him stronger.

During his recent discussion with Trump supporters, Luntz played several video clips of the billionaire’s least flattering moments.

One was Trump’s rejection of Arizona Sen. John McCain’s status as a war hero — "I like people that weren’t captured, OK?" Another was his complimenting daughter Ivanka’s figure and saying that if she "weren’t my daughter, perhaps I’d be dating her."

Instead of being rattled, the participants ate up Trump’s comments and left the meeting feeling even more confident in their support for him than when they had arrived.

"I think the Trump candidacy is here to stay and I think Republicans need to figure out how to deal with it," Luntz said. He said there is little the party establishment, journalists or his rivals with a background in politics can do to knock Trump down, because the candidate’s supporters distrust those groups so strongly.

"In essence, he’s Teflon because the people most able to take him down can’t because of the very jobs that they do," he said.

It’s for that reason that Herman Cain, the former chief executive of Godfather’s Pizza who rose to the top of the polls in the fall of 2011, only to see his fortunes derailed by allegations of sexual harassment, said he believes that Trump can succeed.

"It is a totally new paradigm for how the race for president is unfolding," said Cain, making the case that Trump, as well as two other Republican candidates, former Hewlett-Packard chief executive Carly Fiorina and former neurosurgeon Ben Carson, had tapped into a portion of the electorate that is typically disengaged from the political process.

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Many of the Trump supporters interviewed by AP said there was a chance they might change their minds before voting next year or sit the contest out. Trump’s campaign operation lacks the sophistication of many of his rivals, who in some cases have years of experience in politics and the business of getting out the vote.

For all of Trump’s success so far, he’s yet to drive any candidate from the race.

There are several debates still to come and five months until the Iowa caucuses — enough time for a rival to build a winning coalition of voters such as Marvin Smith, a Republican from Independence, Kentucky, who said Trump "scares the hell out of me."

"He’s appealing to some base emotions. But my worry is that he splinters the Republican Party," Smith said. "He’s saying the message people want to hear, but I don’t like the way he’s saying it."

But anyone who has bet against Trump so far in this campaign has come up — as Trump would say — a loser.

Paul Demerjian, a 55-year-old small business owner from Stoneham, Massachusetts, said he isn’t much into politics. But there he was at a recent Trump rally outside Boston, mobbing Trump’s SUV as he made his exit.

"I haven’t been passionate about a politician running for office since Ronald Reagan," he said.

Associated Press writers Thomas Beaumont in Dubuque, Iowa, Bill Barrow in Greenville, South Carolina, and Julie Pace in Cincinnati contributed to this report.