In a House Race With Big Names, 2 Women With Local Ties Rise

“I’m so disappointed in her,” Ms. Chin said of Ms. Niou.

“Normally I would support an Asian woman, we need more representation, but in this case,” Ms. Chin said, trailing off.

Ms. Rivera has also backed a bid to allow more density, including affordable housing, in the Manhattan neighborhoods of SoHo and NoHo, an initiative Ms. Niou says she had doubts about.

This year’s unusually messy redistricting process fundamentally reshaped the 10th District. Where the district once stretched from the Upper West Side of Manhattan to Bensonhurst Brooklyn, the new map makes it more compact, encompassing only Lower Manhattan and the northwest precincts of Brooklyn.

Jerry Nadler, the congressman now representing the district, opted to run in the 12th District against a longtime colleague, Representative Carolyn Maloney, after his Upper West Side home base was moved there. The result was a rare open seat in the heart of New York City, and a political gold rush that drew a dozen or so candidates, including Mr. Jones, the congressman who currently represents Rockland County and parts of Westchester.

Mr. Jones and Mr. Goldman are by far the race’s best-resourced candidates. At the end of June, Mr. Jones had $2.8 million to spend. Mr. Goldman had $1 million, though he also has a vast reservoir of personal wealth to draw from and told NY1 he intends to use it. He has up to $253 million in personal wealth, according to Bloomberg News.

“I am extremely grateful for the opportunities I’ve had, and that is why I’ve committed my life to public service,” Mr. Goldman said in a statement. “I’m running for Congress to continue that service, to build a better future for all of our children, and to give everyone the opportunity to succeed.”

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