The mind of Mitt Romney is a supremely rational place.

Arguments are compiled and advanced on the basis of analytics, not emotion. He can offer up the gauzy bromides that are every politician’s stock in trade: “I love America! I love its freedoms!” But he is most fervent and animated in his pitch to be president when he talks about how he has fixed stuff before and he can fix stuff again. Concrete examples spill out of his mouth and accrete. He bounces on the balls of his feet, speaking quickly, enunciating carefully, never with notes.

“I love small-business people like you,” he says, pitching himself to a crowd of about 100 people — business owners, lawyers, chamber of commerce types — crammed into the atrium of a law firm in Manchester, N.H.

Romney ticks off what he says people in business understand, about the economy and job creation and making the nation hum again, that people in government do not. It’s a seven-point pitch, eminently sensible, and after each point, like the experienced corporate team-builder he is, Romney affirms the good sense of his audience: “And you understand that in the private sector.”

“Now, in government, people tend to ignore the implications of incentives,” he says. This will turn out to be a story about helping the homeless, but he will tell it through numbers, not individuals.

In Massachusetts, he explains, he inherited a projected $3 billion deficit when he became governor in 2003 and proceeded to pore over line-item budgets looking for reductions. “Now, I wasn’t going to cut homeless support. But I wanted to see if the money was well-spent,” he says, and he came upon an unexpected category: hotels.

“And they said, ‘Well, Governor, you have to understand, if someone shows up for shelter and the homeless shelter is full, we simply tell them to go check into a hotel and we’ll pick up the bill.’ And I thought to myself” — and here he pauses before his punch line — “I bet the word gets around.” His audience chuckles.

So Romney made a simple change: The newest arrival got a shelter bed, and the person there the longest went to a hotel. Before, the state was renting an average of 500 hotel rooms a night, at a cost of $20 million per year. Afterward, that line item fell to zero. “And the tens of millions of dollars we saved we were able to use to get people into permanent housing.” This did provide a pathway to a stable, independent life, homeless advocates said.

“Incentives,” Romney exclaims, “have impact.”

And that’s it.

He doesn’t conjure a vision of a child shivering under an overpass. He doesn’t declare that what drives him is the belief that in the United States, families should not sleep on the street. He doesn’t float some bold, untested idea. But those uncertain about where to locate Romney’s core convictions — or if he has any — might consider whether they are embedded in this example.

“He’s a wonk who looked at things in a cost-effective way,” said Robyn Frost, the executive director of Massachusetts’s Coalition for the Homeless, who for two decades has been working on issues affecting the poor. Frost credits Romney for not cutting the budget for the homeless and for forming public-private partnerships that made headway on an intractable decades-old problem.

“I do think he acted out of a moral compunction to make those changes,” she said, “as well as a conviction that he could.”

Mitt Romney, 64, is what used to be called — before the politics of personal confession — an upstanding citizen. He is a man with a prodigious intellect who has been married to his high school sweetheart for 42 years, donates 10 percent of his money to his church (a considerable sum, as his self-made fortune is upward of $250 million) and, those close to him to say, acts generously, earns the loyalty of his staff and drives himself relentlessly to get the job done, whatever it is.

This is the way he has lived his life, friends, family members and aides say. They argue that these traits are more revealing of his presidential timber than his adherence to ideological purity.

And, they add, obeisance to ideology would impose a rigidity that would inhibit Romney’s real talent, which is forging new ways to fix old problems. That would seem to commend him to primary- and general-election voters, disgusted as they are by politicians’ seeming inability to work together to get much done in Washington.

Instead, voters have been signaling to pollsters for months that they don’t buy what Romney, with his 25 years in the business sector, is selling. He receives low scores on authenticity — sussed out in polls on such measures as “understands the problems of people like me” and “shares my values.” Voters can’t figure out what his values are, some say, given his shifting, and sometimes diametrically opposed, positions on abortion, immigration, health care and climate change.

The disconnect is right there when Romney answers the flip-floppery charge by repeatedly asserting that he is a man of “steadiness and constancy.” It’s as though he doesn’t understand what people don’t understand about him.

The problem is that in business, there is no ideology and but one principle: making money. In government, there are dozens of each — all built upon social compacts, truths held to be self-evident, and moral consequences.

Further complicating Romney’s ability to connect is this: Unlike the best of the glad-handing retail politicians, he doesn’t seem to need the applause of strangers to lend him energy. He works rope lines with a kind of obedient enthusiasm, using a silver Sharpie marker to autograph photos people press at him, making pleasant talk. But he is executing a task to achieve a goal. He isn’t going to talk about feeling their pain. It seems he just wants to get to work relieving it.

Romney is Dudley Do-Right in a Kim Kardashian world, a man temperamentally disinclined to revel in the disorder and lack of rules in modern campaigns. He’s a man forced to submit to a chaotic process he can’t remake or control. Its demands that he summon fiery rhetoric or offer up a personal tidbit are at odds with his public comportment.

If Romney were to wake up Nov. 7 as president-elect, said Kevin Madden, his chief spokesman in 2008 and an informal adviser now, “the governor is going to go, ‘Phew. Thank gosh that’s over. Now let’s have a Cabinet meeting and actually do something.’ ”

If Romney seems aloof, or slippery, ignore it, Andy Peterson seemed to suggest when he introduced the candidate at a town hall meeting last month in Peterborough, N.H.

“Take a careful look at Mitt Romney and see if you see what I see,” said Peterson, a former state legislator who runs a real estate business. He is “a man who displays a nimble mind capable of both subtle nuance and broad understanding, combined with a principled degree of restraint in words and deeds.”

Peterson’s full-throated endorsement described what Romney struggles to convey — his motivation to service and his qualifications for office. A look of almost boyish delight — “Somebody gets me” — flickered across the candidate’s face. Then it was gone, and he embarked on his practiced pitch.

It may be hard to identify with a guy who earned his law degree and his MBA from Harvard at the same time, before he turned 30 and while he and his wife were raising two young boys born close together, and then who went on to make a fortune.

Or as Peterson’s wife told him about Romney, “He’s too rich and too good-looking” to be president. He seems too perfect and tidy, his trim hair and waistline in keeping with his disciplined mien and his formidable multi-state operation. His fastidiousness can border on the fussy.At a rally at a Polish American club in Troy, Mich., Romney mentioned how he preferred the state’s lakes to the ocean.

“There’s something special about lakes where you don’t get salt on you after you’ve been swimming . . . where’s there’s not seaweed . . . where you don’t have to worry about things eating you in the water,” he said, while the audience looked at him quizzically.

Some who worked with Romney in business and in government found him imperious and condescending, and once in a while, his discipline falters and a phrase comes out that appears dismissive. At the same event, talking about Detroit’s glory days, he gestured toward some elderly folks and said, “The wheelchair set over there, you remember.”

He is a man who measures value with an unusual yardstick. Although he’s spending $12 million to upgrade his house in La Jolla, Calif., Romney wouldn’t pay the extra 10 bucks for an early boarding pass on Southwest when he was flying coach. When his top strategist, Stuart Stevens, arrived early one morning last winter at the candidate’s suite at the Marriott Wardman Park Hotel in Woodley Park, he found Mitt and Ann Romney and a couple of McDonald’s bags on the table.

“What’s this?” Stevens asked. “Ann and I walked over to McDonald’s,” Romney said. “Have you seen how much they charge for breakfast at this hotel?”

But Romney is not unaware of his flaws as a candidate and clearly has improved his performance since 2008. Nor is he without an appreciation for the absurd. In Nashua, N.H., he cheerfully handed out breakfast sandwiches in a tiny diner. It was one of those ridiculous clown-car campaign events designed to play as a just-folks moment on the local news. Four supporters sat at the counter, and a few handfuls squeezed into four tables, all pancaked by a scrum of reporters with cameras and boom microphones.

Romney was amused. Pivoting with his tray held above his head, he said, “Look, this is me, raw and unfiltered,” a reference to a “Saturday Night Live” skit the night before that lampooned his stiffness.

His devotion to data and his businesslike reserve coexist with a capacity for empathy, those closest to him say. In Michigan, when rival Rick Perry couldn’t remember for those long seconds the third of three federal agencies he said he would cut, it was Romney who jumped in with a suggestion to try to help.

Tom Rath, a former New Hampshire attorney general and the campaign’s senior adviser in the state, remembers having to call Romney in the summer of 2010 to tell him that he had been arrested for drunken driving.

“I felt terrible,” he said. “I had embarrassed him. I had embarrassed the campaign. I knew I didn’t want to be a liability.”

He dialed, identified himself, asked to speak to Romney, and waited. “And the first thing he says is, ‘If you were Mormon, Tom, this wouldn’t have happened.’ ”

Romney chuckled. Rath started to offer to resign, “and he cut me off, and said, ‘Tom, you and I are joined at the hip.’ And that was that.”

When Romney’s brother, Scott, had cancer years ago, he “called me every night,” said Scott, 70, a Detroit lawyer. “He’d ask how I was doing and listen to my worries. And then he would present all the research on my options he had done during the day. He didn’t just check in. He acted.

“It showed how much he loved me, but that’s the approach he brings to everything.”

Romney’s urge to fix stuff is both nature and nurture, Scott Romney suggested.

“He liked fixing things. I think it was innate, probably, and then he just built on it and built on it.

It’s just how we were raised,” Scott Romney said, “to have the capacity to do things.”

Their grandfather had gone broke five times, he pointed out. Living through that prompted their father, George, to insist that Scott go to night school to learn electrical wiring even as he spent his days at the elite Cranbrook School in suburban Detroit that Mitt also attended.

“Both my mother and my father told all of us, ‘You need to know how to do things,’ ” Scott said. “The people who are important are those who get things done.”

Romney himself agreed to an interview, but his campaign did not schedule it before this article’s deadline.

Associates from business and government say Romney’s operating system goes to work on a problem like this:

Romney asks for data, and then more data. “There are answers in numbers — gold in numbers,” he wrote in “Turnaround,” his account of rescuing the 2002 Olympics in Salt Lake City. “Pile the budgets on my desk and let me wallow.”

He gathers his staff members together so they can deliver their ideas. They debate. A passionate, emotional argument is not going to have much influence on the supremely rational mind of Mitt Romney. “He requires justification,” Madden said. “Why are we going to do this?”

With his characteristic work ethic, after investing in a company as head of Bain Capital, Romney would roll up his sleeves, learn the business like an insider and re-envision it — with the imperative of increasing profitability as the guiding principle. Then he would turn to marketing, jazz up the wonk and sell it to whatever audience he needed to address.

In Massachusetts, Romney’s hunt for “efficiencies” and “incentivizations” — and the threat of losing millions in federal funding for health care from the George W. Bush administration — is what propelled him and his team to institute a universal health-care system that served as a model for the Obama administration’s plan.

Was he moved to help people, selling the plan politically as cost controls? Or was insuring the poor just a happy side effect of a better bottom line? Does it matter? The net result was the same.

“Look, he does have an overriding philosophy about caring for people,” Scott Romney said. “Government should be efficient, it needs to be there to help solve people’s problems, and we need to reduce our costs.”

And in service of these goals, Romney’s flip-floppery could be interpreted as a flexibility of thinking that might help him bust through warring ideologies in Washington — an asset, not a deficit — and fix his biggest set of problems yet.