THE heavily Democratic city of New York has had three Republican mayors in the last 68 years, and though they served for only 28 years, compared to the 40 years by five Democratic mayors, they have decisively shaped the life of their city and Ameriean cities generally. The first of them, Fiorello LaGuardia, made New York the showcase of the New Deal, building public-housing projects, a sparkling new airport, subways, and, working with Robert Moses, bridges and parks. When LaGuardia left office in December 1945, New York was the premier city in the world, widely hailed as a model for all to follow. The most recent of these Republican mayors, Rudolph Giuliani, left office only weeks ago but it is not too early to assess his record. He cut crime by more than half, reduced welfare dependency by almost as much, and lowered New York’s ruinously high taxes at least a little. He also won the admiration of the world in the days after the attacks of September 11. He has set an example for policy innovation which has been followed widely elsewhere, and has already established himself as the most constructive public official at the state or local level of the last half-century.