Voters in four states appear likely to approve ballot measures that would legalize marijuana for recreational purposes, according to recent surveys, while voters are split on the question in a fifth state.

The polls, taken over the last few weeks, demonstrate a seismic shift in the politics of pot. Even a decade ago, voters rewarded politicians who promised to redouble the war on drugs. After November’s elections, nearly a quarter of Americans could live in states where marijuana consumption is legal.

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But proponents and opponents alike say that polls taken before Election Day often overstate support for legal marijuana measures.

“If the pro-legalization side is not at 55 percent at this point, it will likely lose,” said Sean Noble, an Arizona-based Republican strategist working against that state’s legalization measure, Proposition 205. “We know that polling on legalization generally overperforms actual results.”

California voters appear to be the most willing to legalize marijuana for recreational purposes. The Public Policy Institute of California and the Field Poll both show 60 percent of state voters support Proposition 64, while just 36 percent and 31 percent, respectively, oppose legalization.

California was the first state in the nation to legalize marijuana for medicinal purposes, back in 1996. Golden State voters rejected attempts to allow recreational use in 1972 and 2010. Today, majorities of voters in every region of the state and in every age and ethnic bracket support legalization.

In Maine and Massachusetts, just about half of voters support ballot measures that would allow recreational use. A MassINC poll conducted for WBUR in early September showed 50 percent of Massachusetts voters support legalization, while 53 percent said they back Question 4 in a University of Massachusetts Amherst poll conducted for WBZ-TV.

Fifty-three percent of Mainers told University of New Hampshire pollsters they back Question 1, that state’s legalization measure. Only voters over the age of 65 oppose legalizing pot. Six in 10 Maine voters said they had tried marijuana at some point in their lives.

And in Arizona, 50 percent of voters said they support Proposition 205, according to an Arizona Republic/Morrison/Cronkite News poll conducted in early September. Private polling in the state shows the measure leading by narrower margins, however.

The closest battle over legal marijuana appears to be in Nevada, where a new Bendixen & Amandi survey shows a statistical tie. Forty-seven percent of Nevada voters support Question 2, while 46 percent are opposed, according to the survey conducted last week for the Las Vegas Review-Journal.

A Suffolk University poll conducted about the same time as the Bendixen survey shows much broader support. In that survey, 57 percent of Nevada voters backed legalization, while just 33 percent were opposed.

Polls in all five states show older voters and Republicans are less likely to support legalization than younger voters, Democrats and independents. Minorities, especially Hispanic voters, are more likely to be undecided than white voters.

Marijuana legalization advocates caution that, with five weeks to go before Election Day, there’s no guarantee the initiatives will pass. And both sides warn that mounds of outside money are likely to come pouring into states in the final stretch.

“I wouldn’t be surprised if the pro-legalization side starts to dump in large amounts of special interest money in order to stop the bleeding in some of these states,” Noble said.

“While it’s good to be polling ahead right now in all the states with legalization on the ballot, the margin is a little too close for comfort in a few places, especially since the opposition hasn’t yet gone on the air with the scare-tactic-filled ads we expect from them,” said Tom Angell, founder of Marijuana Majority.

Some of those advertisements in opposition to legal pot are just beginning to hit the airwaves. In Nevada, opponents are running an advertisement focusing on edible marijuana products and highlighting an increase in emergency room visits by children in Colorado, where marijuana is legal.

“Question 2 would make recreational edible pot legal in Nevada, putting our kids at risk overnight,” the narrator says in the new spot. In Arizona, opponents are running two advertisements also highlighting edible marijuana products and government spending in Colorado.

Voters in four states — Colorado, Washington, Oregon and Alaska — and the District of Columbia have passed measures legalizing marijuana for recreational purposes. If all five states with legalization measures on the ballot this year pass, 100 of the 435 members of the House of Representatives will hail from states where marijuana is legal.