FALLS CHURCH, Va.—Alongside vendors selling dumplings and pastries at a recent Vietnamese Mid-Autumn Moon celebration, the Democratic Asian Americans of Virginia offered something they hoped was equally enticing for the several hundred visitors: a chance to register to vote.

“We want Asian-Americans to be recognized because then the parties pay attention to us and our issues,” said Dewita Soeharjono, the group’s president. If these voters turn out in big numbers at the polls in November, she said, “we can make a big difference.”

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