A Massachusetts ballot measure that would cut the amount of land required to build a single-family house was running dead even with voters a week before the election, at 41 percent in favor and 41 percent opposed in a Suffolk University/Boston Globe poll released this week.

The proposal, Question 7, would impose the state’s first statewide minimum lot-size rule. It would override local zoning to allow a single-family home on any residentially zoned parcel of 5,000 square feet or more, so long as the lot connects to water and sewer service and runs at least 50 feet along a road. On a full acre, an owner could in some cases build four homes instead of one, though only single-family houses, not townhouses or apartment buildings. Towns could still set some dimensional requirements of their own.

Governor Maura Healey and Mayor Michelle Wu of Boston back the measure. Its only major organized opponent is the Massachusetts Municipal Association, the trade group for cities and towns, which says it would erode local control over land use. Some suburban voters tell pollsters they worry it will densify their neighborhoods.

Andrew Mikula, the chief housing economist at the Pioneer Institute and the question’s author, frames it as a way to restore a kind of house Massachusetts has mostly stopped building. “The starter home used to be an anchor to the region for the middle class,” he said. “If we want to bring back that kind of housing, we need to make it legal to build it.”

Such homes went up in abundance after World War II, until suburban towns in the 1960s began passing zoning rules to slow growth. Minimum lot sizes were the main tool. Today, some neighborhoods in more than half of Eastern Massachusetts communities demand a full acre, a bit smaller than a football field, for one house. As buildable land grew scarce, builders bought up the old small houses, knocked them down and put up far bigger ones. On one Beethoven Avenue lot, a bungalow valued at $1.5 million in 2025 was recently replaced by a house of nearly 5,500 square feet, listed at $4.3 million.

Paul McGovern, owner of a Needham homebuilding firm, laid out the arithmetic. A buildable lot there runs about $1.2 million, and construction costs another $1 million or so, he said, so a house priced at $2.4 million makes no business sense. Builders aim for houses that sell for $3 million to $4 million instead. “You’re basically taking a bunch of lots across the state that it didn’t make sense to build on before and making them developable,” said Jeff Brem, president of a Westford land surveying firm. The result, he added, would be “not necessarily affordable, but cheaper.”

How many homes would actually get built is disputed. The campaign estimates 2,200 to 5,700 net new homes a year. The Center for State Policy Analysis at Tufts University puts the figure far lower, at 350 to 1,200 a year.

Susan Murphy, a land-use lawyer, objects to calling it a starter-home question at all, arguing it may hasten the teardown of older, cheaper houses. “I agree that we need to make it far more affordable to buy a starter home here,” she said. “But you’re not going to get affordable prices on a 5,000 square-foot lot inside Route 128.” Mr. McGovern said two new houses on a lot near Boston that once held one would still sell for $1.5 million each or more.

Deborah Crossley, a former Newton city councilor who led its zoning and planning committee, sees limits but also point. “It’s a bit of a sledgehammer on a problem that requires a nuanced approach,” she said, “but more housing is more housing.”