The tax, imposed only on expensive second homes, is not a new idea. In New York, its advocates began pushing for it more than a dozen years ago. The city of Vancouver, British Columbia, enacted its version, known as the Empty Homes Tax, in 2017. Toronto, Montana and Rhode Island followed in the last several years, with Rhode Island’s version known as the Taylor Swift tax, after her mansion on the state’s coast. Singapore and Paris have had such taxes for even longer.

In New York, the tax applies to homes that are not the owner’s primary residence and are worth about $5 million and above. Part of the rationale is that the owners of these homes often do not have to pay the city’s income tax, which applies only to people who spend at least 184 days a year in the city. As a result, these part-timers benefit from New York’s services and infrastructure — garbage collection, snow plowing, public transportation, policing and so on — without paying their fair share.

The tax addresses a pernicious form of tax avoidance. Many top earners carefully structure their lives to spend fewer than 184 days in New York while basing much of their activity here. The new tax tells them they can no longer have it both ways. It also takes a small step toward reducing the city’s vast income inequality.

The tax will be assessed annually, and by the second half of 2028 it will impose a rate of 0.8 percent on homes with a sales value between $5 million and $15 million. Somebody who owns a $10 million second home, for example, will face an annual bill of $80,000, on top of the existing property tax rate. The new rate will rise to a maximum of 1.3 percent a year, for homes worth more than $25 million.

The most notorious home involved in the debate is the 24,000-square-foot apartment on Central Park South that Ken Griffin, the hedge fund manager, bought for $238 million in 2019, the most expensive home sold in the United States. Mr. Mamdani singled out the apartment in a video about the pied-à-terre tax, infuriating Mr. Griffin. When added to Mr. Griffin’s current property tax bill, the new tax means that he will pay a total property rate of about 1.7 percent, which is only slightly above the city average for apartments. Until now, because the property tax system has been too lenient for expensive homes, Mr. Griffin has paid far below the average rate.