A recent poll by the University of Akron shows voters evenly split, but if the proposal passes, Ohio will be the first state to approve marijuana for personal use without first legalizing medical marijuana. That would put Ohio, a swing state, at the forefront of the national movement to overhaul marijuana laws — just in time for the 2016 presidential campaign. Gov. John R. Kasich of Ohio, a Republican candidate for president, opposes Issue 3.

“If Ohio wins, it will be a significant step forward for the broader movement — nothing will excite attention like that,” said Ethan Nadelmann, the executive director of the Drug Policy Alliance, which has helped lead the national drive for legalization. But his group is remaining neutral rather than endorsing Issue 3, he said, “because of the problematic oligopoly provision.”

To complicate matters, the Ohio General Assembly has put a competing initiative, Issue 2, on the ballot; known as the antimonopoly amendment, it would block Issue 3 by prohibiting the granting of special rights through the State Constitution. There is certain to be a protracted legal battle if both measures pass.

The story of how Issue 3 got onto the ballot begins here in Columbus, the capital, with Ian James, a political consultant whose company, the Strategy Network, specializes in gathering signatures for ballot initiatives. In 2009, his firm helped legalize casino gambling in Ohio through a measure that amended the State Constitution and specified where casinos could be located.