In the glow of Zohran Mamdani’s convincing win in the Democratic mayoral primary in New York City, a common narrative has emerged to explain his ascendence. He was a master of social media; he was charming, attractive and well spoken; he and his team simply outworked everyone.

But the emphasis on Mr. Mamdani’s style overlooks the substance of his progressive message and how the city’s voters came to embrace it, much as voters did in Boston in 2021 and in Chicago two years later.

Those elections, along with recent polling on issues like rent control, wealth taxes and the burden of child care, suggest that many voters, particularly those in large Democratic-leaning cities, have become more receptive to progressive agendas.

Mr. Mamdani, a state assemblyman and democratic socialist, adhered to a simple message in his primary campaign. New York, he said, was in the throes of an affordability crisis, and he had three main proposals to help: make city buses free, expand free child care and freeze the rent for stabilized apartments.

The financial burden of paying for these policies, he suggested, would largely fall on wealthy taxpayers and businesses — a stance that has put Mr. Mamdani at odds with many mainstream Democrats, including Gov. Kathy Hochul. But the size of his victory has forced some in his party to grapple with his ascension and whether to adopt some of his messaging in next year’s critical midterm elections.

“People are hungry for government to work and to get things done that matter and that will make a difference in their lives,” said Mayor Michelle Wu of Boston, who in 2021 became the city’s youngest mayor in a century by pushing a similar slate of proposals.