With the ashes of September 11 still smoldering, Michael Bloomberg won his first New York mayoral term largely because city voters assumed that he would stick with Rudolph Giuliani’s most successful policies. So how’s he doing? Based on the broad quality-of-life indicators highlighted here, the answer remains decidedly mixed. In some respects, the former media magnate has succeeded in building on Giuliani’s legacy. In others, Bloomberg has parted company with his predecessor, squandering hard-won gains. All this has left New Yorkers almost evenly divided on what the future will bring.

The details:

Bloomberg promised in his 2001 inaugural address to “work tirelessly to provide safe streets and homes for all New Yorkers,” to “go forward” and “never go back” to the high crime–ridden days of the not-so-distant past. So far, he is keeping the promise. Crime in New York fell again in 2004, the third full year of Bloomberg’s mayoralty, although the rate of decrease has slowed, as illustrated in the chart. Considering all the challenges facing a shrunken NYPD in the post-9/11 world, this is a solid accomplishment.

After an upward blip in the headcount during several months in late 2003, the welfare rolls are also shrinking again. As of April 2005, the number of public assistance recipients had fallen to 419,000—down about 4 percent since Bloomberg took office. But the Medicaid caseload is up another 100,000 in the past year, reaching a new high of nearly 2.6 million (around one in three city residents), putting more pressure on the fastest-growing portions of the city budget.

Three years after gaining control of the public school system—a goal that eluded Giuliani—the mayor can point to signs of progress in improving educational outcomes. In addition to the elementary school test-score gains touted by the mayor, the ultimate outcome measure—high school completion rates—also continued to inch up last year. Just over 54 percent of the class of 2004 graduated on time, up a percentage point from 2003, and four percentage points from the 50 percent average of the 1990s. It’s still a whopping 17 points below the national average, however. The number attaining a more academically challenging Regents diploma dropped for a second consecutive year, moreover, and completion rates remained significantly lower for blacks and Hispanics.

Thanks to a record 18 percent property-tax increase, followed by city income- and sales-tax hikes in 2003, Gotham’s overall local tax bite has risen to $87 per $1,000 of personal income as of fiscal 2005—the highest since the economically disastrous mayoralty of David Dinkins. The relative tax burden is projected to decline again in the year ahead, in part reflecting a slowdown in taxes generated by a slightly less superheated real-estate market, but city taxes will remain significantly above the Giuliani-era average. In fact, hoping to curry favor with the left-wing Working Families Party, Bloomberg has already signaled his willingness to raise taxes again to close next year’s enormous projected city budget gap—a far cry from the approach of his predecessor, who in late 2001 memorably and rightly declared that further tax hikes in the nation’s most heavily taxed big city would be “dumb, stupid, idiotic, and moronic.”

How do New Yorkers feel about these developments? According to periodic New York Times surveys, the percentage of city residents who’d prefer to be living somewhere else in four years remained slightly higher in the early summer of 2005 than in the halcyon late summer days of 2001, immediately before the World Trade Center attack. As for the long-range view, the percentage expecting the city to be “better” in ten to 15 years slightly exceeds the percentage expecting it to be “worse.” If past Times polls are any guide, that rough parity in the optimism/pessimism quotient probably reflects economic uncertainty as much as anything else.

What it means for Bloomberg will be clearer soon enough—after the poll that really counts in November.