New York City begins an election year this week, and the field is starting to take shape. Mayor Bloomberg won in 2001 with the backing of Mayor Giuliani at the peak of Mr. Giuliani’s post-September 11 popularity. Even then, Mr. Bloomberg only beat Mark Green, the Democrat, by about 34,000 votes in a city of 8 million.

Today Mr. Bloomberg looks stronger as a candidate than he did in 2001. Back then, he was a businessman who had built a profitable company, but had never run a government. Now Mr. Bloomberg is more of a known quantity with his share of successes. He won a signal victory for the city over Albany by gaining mayoral control of the public schools, and he has implemented a suggestion of his Republican opponent in 2001, Herman Badillo, by moving against social promotion in those schools.

Mr. Bloomberg, his criminal justice coordinator, the district attorneys, and the police commissioner, Raymond Kelly, have been winning the fight against crime. The number of homicides in the city was driven down to 571 in 2004, the fewest since 1963. On a per capita basis, New York’s homicide rate of about 7 for each 100,000 population is a tremendous achievement when compared with, say, Los Angeles, with a rate of about 12 for each 100,000,and Chicago, where the rate is about 15.

The areas on which Mr. Bloomberg is most vulnerable are spending and taxes. After a stab at austerity, the mayor has started spending with abandon. A recent report by the state comptroller found that spending by New York City had increased by 9.5% in 2004.That is too much of an increase in a city whose residents are already bearing the highest state and local tax burden in the country. The mayor says in his defense that much of the spending is on things he cannot control, such as pension obligations, debt service, and Medicaid.

But it’s rarely a good sign for a mayor of New York to complain about his powerlessness. It becomes self-fulfilling. Here the mayor could benefit by observing President Bush, who rarely carps about how hamstrung he is by entitlement legislation but often talks about his vision for changing things. New York holds much in the way of opportunity for Mr. Bloomberg to lead a drive to reform the city’s pension, debt issuance, and health-care practices so as to wring unnecessary costs from the system.

An enormous opportunity presents itself on the tax front. Mr. Bloomberg got off to a rocky start. He raised taxes on cigarettes, sales, and property. In collaboration with the state, he raised the income tax. After his approval rating plummeted, the mayor finally proposed a partial rebate of the property taxes. His approval rating has since recovered somewhat, but the damage his tax hikes did to his credibility is, in our estimation, far and away his biggest hurdle. As a candidate, after all, he campaigned against tax increases, and as mayor he could do much by reclaiming this ground.

Particularly with the Democratic alternatives. As speaker of the City Council, Gifford Miller signed off on every one of Mr. Bloomberg’s spending increases and tax increases – while pressing for even more spending. Mr. Miller claims in his own defense that he helped downsize Mr. Bloomberg’s proposed property tax increase, but he did so only by shifting the burden onto higher-income taxpayers.

Mr. Miller dealt with the terrorist threat by supporting a council resolution opposing the administration’s plan to meet the terrorists in Iraq. Mr. Miller is raising money to run for mayor, but on the basis of this record, he doesn’t even deserve to be reelected to the City Council. Fortunately, it’s a moot point, as the term limits law makes him ineligible to run this year for re-election to his seat on the Council.

C. Virginia Fields, an early backer of Senator Kerry, appears more moderate than Mr. Miller, who backed Governor Dean for president. Dr. Dean opposed the war outright and sought to roll back the entire Bush tax cut. Ms. Fields, who is the president of Manhattan, also has an inspiring personal story, having marched with Martin Luther King in Alabama.

But on taxes, Ms. Fields is certainly worse than Mr. Bloomberg. In a February 2002 speech, she called for examining the revival of a tax on the transfer of stock, which she said could bring in more than $700 million a year. In a 2003 speech, she supported bring and raised the stakes even more by supporting a $600 million increase in the income tax that the city imposes on residents. She has opposed Mr. Bloomberg’s spending cuts.

Anthony Weiner, who represents parts of Brooklyn and Queens in Congress, shows signs of centrism. He told us last year, “The people who feel most betrayed by the decisions the mayor’s made are Giuliani Democrats…they took a flier on Bloomberg in part because of the Giuliani stamp of approval.” We are admiring of the work on foreign policy that Mr. Weiner has done in Congress, where he has pressed the executive branch to obey the law recognizing Jerusalem as Israel’s capital and has fought against American funding for Saudi Arabia and the Palestinian Authority. We admire his stand against anti-Semitism at Columbia University, where the others have been silent.

But to delve into Mr. Weiner’s congressional record is to be disappointed. He voted against Mr. Bush’s tax relief for all Americans who pay taxes. He voted against Mr. Bush’s cuts to the death tax. He voted against Mr. Bush’s reduction in the marriage penalty that was part of the tax code. If Mr. Weiner is going to run as a tax-cutting Giuliani Democrat in New York, he is going to have to find a way to explain his record of opposing tax cuts when he had a chance to vote on them in Washington.

Then there is Fernando Ferrer, who served in the 1980s in the City Council and for 14 years as president of the Bronx. Mr. Ferrer has been leading Mr. Bloomberg in some recent polls. Mr. Ferrer shows signs of breaking with the liberal orthodoxy when it comes to, say, having the occasional cigar in public. But on taxing and spending, the signs aren’t good. The United Federation of Teachers and the Service Employees International Union 1199, two locals that help push state and local government spending higher in New York, have been funding Mr. Ferrer’s activities at a liberal think tank, the Drum Major Institute.

More dangerously, Mr. Ferrer is a member of the board of directors of the Campaign for Fiscal Equity, which has been suing the state for tens of billions of dollars in more spending on the city’s schools, to be funded by tax increases on New Yorkers. He has opposed vouchers that would allow students currently trapped in the government school system to attend Catholic schools like the one he attended.

One or several of the Democrats may yet challenge Mr. Bloomberg on taxes and spending, but to do so would require something of a political conversion. It wouldn’t be unprecedented – Mr. Bloomberg, a liberal, made something of a shift himself when he became a Republican. But it would require some doing. Until that happens, or until a challenger of Mr. Bloomberg emerges in his own party, the mayor looks to us to be in strong position relative to his opponents. It’s way too soon to make an endorsement. But it’s not too soon to observe that the election year ahead holds lots of opportunity for him to sketch a second-term vision.