It is amazing that after four years of the Obama presidency and the Romney campaign, Americans are just beginning to find out about their personalities.

Two intriguing personal portraits are emerging.

The media says that Obama is aloof and arrogant, and Romney is secretive and vague.

Romney does not consider himself to be a strongly ideological person, unusual at a time when American politics are dominated by a deep ideological split. He sees himself as a topflight problem solver, capable of identifying what’s wrong with a matter and then marshalling the forces necessary to fix it.

A revealing look at Romney, provided by the man himself and some of his closest friends, came in the Oct. 1 issue of The New Yorker magazine. He comes across as a management expert, who can solve problems facing a president without acting out of deep political conviction.

When he was asked during his campaign four years ago how he would staff his cabinet, Romney told the Wall Street Journal, “I would probably bring in McKinsey,” referring to a leading consulting firm. For him, the cabinet is a management team, with no importance attached to its political constituencies or connections.

This orientation helps explain why Romney says he would do better than Obama but remains vague when it comes to providing specifics. He offers few solutions now, but would do whatever is necessary, generally free from ideology, to solve problems ranging from the deficit to relations with China.

In Massachusetts, he supported health care reform because health care costs were burdening the state budget. The personal mandate was what Republicans then favored, so he selected that method and made the necessary compromises with the Democratic legislature to get it passed.

He probably does not see any contradiction between adopting one health care policy in Massachusetts and rejecting the same policy on the national level. A good manager simply does whatever works and does not worry much about ideological consistency.

Romney’s approach does not fit well in a presidential race. People want to know a candidate’s positions on issues and not simply that he is a good manager.

To get the nomination in a Republican Party dominated by strong conservatives, Romney did take positions on some issues. By doing that, he took management options off the table, unless he would do a risky about-face if elected.

Another problem for Romney is that he excelled in a business aimed at promoting economic efficiency rather than fostering economic development. Its goal has been to create bigger profits not more prosperity. His management successes might come at the expense of workers whose costs blocked greater efficiency, even to the point of the outright elimination of their employer.

Voters are worried about jobs, not making the economy more efficient. This view reduces the value of Romney’s claims that his business experience enables him to bring about economic recovery.

Finally, even beyond his tax returns, Romney is secretive and conceals himself from the voters.

He may think a manager’s personality does not matter. One close Romney friend told the writer, “It’s as if Romney has never had the thought of talking about himself.”

Perhaps Americans elected a president in 2008 about whom they hardly knew much more. Obama had written about his early life, an unusual story that undoubtedly influenced the man he is. But that story turned out to tell us relatively little about the man as president.

His supposed arrogance is an aspect of ego, and no man has been president who did not have an outsized ego.

Being a loner is more of a problem. He has not connected well, we are told, with many of his main backers and, more obviously, with members of Congress, including his fellow Democrats.

He has repeatedly let Congress work on a major issue, while he remained on the sidelines. He does not wheel and deal. Still, he occasionally takes a political risk or makes a bold move, like his health care policy or reviving the auto industry.

Senate leaders are now trying to come up with a compromise to deal with the federal deficit that would be adopted right after the elections. Obama seems not to be involved.

Sen. Mitch McConnell, the Senate GOP leader and no friend of Obama, says the president can no longer be a “bystander,” because he alone can close the deal.

Given the unusual political personalities of Romney and Obama, why does Obama lead in the race for president?

The answer may be that even his laid-back performance in office impresses voters more than Romney’s promise of management competence.