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Mr. Swift likened the changing attitudes on the drug to the increased support of gay marriage, which has reached “majority support in the last two years.”

Ethan Nadelmann, executive director of the nonprofit Drug Policy Alliance, which advocates for the decriminalization of responsible drug use, said the poll highlights the “absurdity and even venality of persisting with harsh prohibitionist policies.”

“No other law is enforced so harshly and pervasively yet deemed unnecessary by so many Americans,” Mr. Nadelmann said. “Spending billions of dollars and arresting 750,000 people annually for violating marijuana laws now represents not just foolish public policy but also an inappropriate and indecent use of police powers to favor one side of a cultural and political debate.”

Seth McLaughlin contributed to this report.