FOR the last time, it appears, New York Mayor Ed Koch asked the people, ``How am I doin'?'' Just 43 percent of the voters in Tuesday's Democratic primary said okay. Not good enough, was the judgment of the 51 percent who went for Manhattan Borough President David Dinkins. So at the end of the year the flamboyant, outspoken, and, in the end, divisive Mr. Koch will end his 12-year reign in city hall. If he wins the general election in November, Mr. Dinkins will become the first black mayor in New York's history. In a city where four out of five registered voters are Democrats, Dinkins must be rated the favorite. He faces an unusually tough Republican rival, though, in Rudolph Giuliani, the former federal prosecutor who earned a Tom Dewey-like reputation as a crime buster. That could carry him far in a city disgusted by disclosures of political corruption during Koch's last term.
Race was manifestly a major factor in Dinkins's victory. He won more than 90 percent of the black vote and just 30 percent of the white vote. Blacks have long been uneasy with Koch, whom they regard as insensitive. The race issue grew more volatile after last year's presidential primary, when Koch stridently opposed Jesse Jackson, and in the wake of the recent murder of a black youth by whites in Bensonhurst.
Although both Dinkins and Mr. Giuliani characterize themselves as conciliators, race may also play a role in the November election. That would be unfortunate. Racial tensions in New York City have to be cooled, not fanned. Moreover, the nation's largest city has other enormous problems that need to be discussed probingly and intelligently in the campaign. Its infrastructure is crumbling and its poorer neighborhoods decaying, it faces crack and AIDS epidemics, it's losing manufacturing jobs, and it's increasingly becoming a city of the very rich and very poor that's inhospitable to the middle class.
May the best candidate win in November - and ``best'' should be determined without reference to the color of his skin.