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Mr. Cain also insisted that he’s not running for the joy of hearing a band strike up “Hail to the Chief” when he walks into a room.

“It’s not about wanting to run so much as feeling compelled to run,” he said. “This country is on the wrong track, and I have some of the skill sets and qualities to lead us back on the right track.”

As to how private-sector success qualifies someone to be president of the United States, Mr. Cain said the corporate divisions he ran faced problems as complex and severe as those facing the U.S. government. He said he can offer a long, documented record of success solving problems that other high-powered executives failed to solve.

But business acumen has not always translated directly into political success, especially in presidential politics, and Mr. Cain’s only previous bid for elective office fell short when he lost to Rep. Johnny Isakson in the 2004 Republican Senate primary in Georgia.

His response: So what?

“I had never made a pizza or even eaten a Godfather’s pizza before taking over the company,” he said. “I had never been to Omaha, Neb., before, let alone to Godfather’s headquarters there.”

He said that putting foreign and domestic policy back on the right track is no different from rescuing a national pizza chain. Executive success doesn’t require knowing dough from toppings or the difference between Shiites and Sunnis or the intricacies of retirement-benefit rules in order to craft and implement successful policies for a large, complex organization.

He achieved one of his successes after his appointment as a Pillsbury vice president charged with salvaging a woefully behind-schedule, over-budget consolidation of nearly 2,000 employees scattered in offices in Minneapolis.

“After I took over, we completed it ahead of schedule and below budget,” he said. One key to his success was his discovery that a lawyer was micromanaging the project, slowing the process and costing the company time and money.

“I went to the guy who owned the space we were renting for the consolidation and got a handshake agreement to move the project along — and if we found something missing afterward, he would fix it,” Mr. Cain said.

He said that, if called upon, he can do the same for Americans.