A dozen years ago, not a single Asian-American held elected office in New York City, even though they accounted for almost one in 10 of its residents.

Now, two Asian-Americans serve on the City Council. One, Comptroller John Liu, holds citywide office. Another, Grace Meng, holds a seat in the Assembly and won the June 26 primary for a congressional seat in Queens. She is favored to win the general election in November.

Ms....