One of the first issues Mayor Bloomberg is going to have to reckon with if he goes public with the presidential campaign he has been nursing is why he has decided to deny for so long that he was going to run. Mr. Bloomberg himself has been truculent, even abrasive, in denying his interest in the White House. “Which letter of the word ‘No’ do you not understand?” he asked one reporter in February 2006. In August of 2006, he said, “I do not know how many times I have to say I am not going to run for president. But I’ll say it one more time. I have no plans to run for president.” In May of 2007, he said, “I’m not running for president and I’m not planning to. What else do you need? I’ve said it 1,000 times.” On New Year’s Eve, he said, “No, I will not run for president.”

On one level, this is political and personal genius. The people who have spent the last year or year and a half openly running for president, people like Mayor Giuliani and Senator Clinton, have been so overexposed at this point that the public is sick and tired of seeing them, and ready for something new, someone like Mayor Bloomberg. The national press has had a year to dig up dirt about them. The declared candidates have spent the last year eating corn in Iowa and dodging snowballs in New Hampshire, while Mr. Bloomberg has been enjoying the cultural life and cuisine of New York City.

On another level, though, it creates what might politely be called doubts. Some shrug them off; a political science professor at the University of Virginia, Larry Sabato, told our Grace Rauh for her story today, “Nobody expects politicians to be truthful all the time anyway.” Which is true in its own right, but in a way misses the unique opportunity that Mr. Bloomberg might have with his campaign.

Say the Democratic nominee is Senator Clinton, with a position on the Iraq War and on Iran that might be politely described as “evolving,” and with a family reputation for parsing the meaning of the word “is.” Say the Republican nominee is Governor Romney, who has changed his positions on gay rights and abortion and gun control. Mr. Bloomberg’s opening is to be the candidate of integrity, not the candidate who for years steered the press and the American people wrong about his intentions.

The risk is particularly great given Mr. Bloomberg’s history. He ran for mayor of New York promising not to raise taxes, and once he got into office, he raised nearly every tax he could — on property, on income, on cigarettes, on sales. This raises policy issues — would a President Bloomberg respond to a national economic downturn the same way Mayor Bloomberg responded to New York’s economic downturn, by raising taxes? As president, Mr. Bloomberg wouldn’t have anyone to bail him out with complementary tax cuts, the way President Bush did to New York. But it also raises — well, the prospect that a hardball-playing opponent of Mr. Bloomberg could come at the mayor the same way that Governor Huckabee is going at Governor Romney in the attack commercial that Mr. Huckabee showed to reporters in Iowa but did not put on the air: “If a man’s dishonest to obtain a job, he’ll be dishonest on the job,” the Huckabee attack advertisement said.

In our own dealings with the mayor we haven’t seen anything but integrity enough to suggest that the Eagle Scout adheres to the first element of the Scout Law, “A Scout is Trustworthy.” Certainly Mr. Bloomberg is so rich that a lot of the integrity issues that normally crop up with politicians — taking money for self-enrichment, doing favors for rich campaign contributors politicians hope to work for later on — do not apply.

If the mayor does run, he may say he genuinely was not planning to run and just changed his mind when he saw the Republican Party’s turn toward anti-immigrant demagoguery and the Democratic Party’s turn toward foreign policy defeatism. Maybe he will say he was genuinely not planning to run and only changed his mind when he was urged on by a distinguished group of bipartisan elders — Senators McCain and Lieberman, Vice President Gore, Secretary of State Kissinger, Peter Peterson, Senators Nunn and Hegel and Boren, Governor Schwarzenegger, Governor Jeb Bush — along with the press elite of Barbara Walters, Lally Weymouth, Rupert Murdoch, and Mortimer Zuckerman.

Maybe he can blame the whole thing on The New York Sun and say he was just ground down into entering the race by the constant drumbeat of editorials in this space urging him to enter the campaign. Maybe he will offer himself up to the Democrats or the Republicans if those parties are unable to reach consensus on a nominee through their primary and convention process. What is certain is that one way or another, if Mr. Bloomberg does run, one of his first tests will be finding a way to explain his denials.