The prospect that New York City Mayor Michael Bloomberg might enter the presidential race as an independent says much about the sad condition of our two-party system. A billionaire five times over, Mayor Bloomberg doesn’t need the Democratic or Republican fundraising machine. He could, of course, finance his own campaign, and that raises other questions.

Mr. Bloomberg, who last month changed from Republican to independent, is a success in business and a success as New York’s mayor. He’s not much into losing, so any run for president would indicate that he has studied the matter and concluded that Americans are finally ready to look beyond the Republican and Democratic parties for their commander-in-chief. Even as he announced that he was not a candidate (yet), he was giving campaign-like speeches about Washington’s inability to solve problems — and his aides were reportedly interviewing experts on presidential politics.

History has not been kind to third-party presidential candidates. Theodore Roosevelt couldn’t pull it off in 1912, even though he had already been president. He won 27 percent of the vote. The next-best independent showing was Ross Perot’s in 1992, with 19 percent.

But a recent Rasmussen poll suggests that the “bloc” of independent voters now rivals that of the two parties. It found that 31.3 percent of Americans refuse to identify with a party, putting independents almost even with Republicans (31.5 percent) and not far behind Democrats (37.2 percent).

Mr. Bloomberg recently shared the cover of Time magazine with California Gov. Arnold Schwarzenegger, another pragmatic, socially liberal Republican. The cover story was about local politicians who actually solve problems. It was called “Who Needs Washington?”

Mr. Bloomberg became mayor only about four months after the 9/11 attacks, which caused a national economic downturn and threatened a near-meltdown in the home of the Twin Towers. To fill a growing budget hole, he raised property taxes, unleashing scorn from conservatives who had backed his election. They had wanted him to slash the municipal workforce instead.

The problem in doing that was twofold: The previous, and also very competent, administration of Rudolph Giuliani had already made cuts, and lifting New York back on its feet was as much a psychological as economic challenge — and harder to achieve with demoralizing layoffs and underfunded public services.

Under Mayor Bloomberg the city has done very well. Serious crime has plummeted 30 percent, schools have improved, and the welfare caseload has fallen. Eventually, the budget went into surplus, and the city has earned a sterling AA bond-rating.

Mr. Bloomberg’s competence is not in doubt, but his ability to fund his own campaign is troubling. He had written a $73 million check for his first mayoral race, outspending Democrat Mark Green five to one. Another example of a self-funding candidate would be New Jersey Gov. Jon Corzine, who spent $73 million of his Goldman Sachs fortune running for the U.S. Senate in 2000. He won, of course.

Such extraordinary spending by a candidate has never been done on the presidential level. We have to question the health of a democracy in which less wealthy candidates have to undertake the humiliation of fundraising, while the tycoons just write their own checks. Wouldn’t it be better to have limited, public funding of races that gives all viable candidates the same opportunity to serve the country? Americans need to have a lively discussion of that — starting now.

If Mayor Bloomberg decides he wants to be President Bloomberg, these issues will have to be discussed.