No state has moved more significantly than Ohio since 2012 to take raw partisanship out of the process, said Morgan Cullen, a policy analyst at the National Conference of State Legislatures.

Jon Husted, Ohio’s secretary of state and a Republican, praised the plan as a step toward ending polarization in the General Assembly. Many members face competition only in primaries, pushing them to cater to ideological extremes.

“We elect people that get there by winning primaries, and we say, ‘Now you come together and do the people’s business,' ” Mr. Husted, a former speaker of the State House, said. “If your electoral incentive is only to care about staying loyal to the base voter in a primary election,” he added, “then your incentive to govern” is small.

Senator Nina Turner, a Democrat who unsuccessfully challenged Mr. Husted for secretary of state last month, said she thought the plan would create a more balanced General Assembly. “I always say Ohio is conservative by design and not by desire,” she said. “This really is a tremendous deal.”

But some Democrats said the change did not go far enough because it excluded congressional maps.

Republicans said that was because of the chance that the United States Supreme Court would invalidate an overhaul in a ruling expected next year. Lawmakers in Arizona are suing to reverse a ballot initiative that took the congressional map-drawing decision out of the hands of the Legislature and gave it to an independent commission.

In 37 states, legislatures now draw voting maps. The 13 others use commissions that are, in theory, less partisan. In some states, the commissions are independent, and in others, their members are politically appointed. That has been Ohio’s system since the 1970s. The Apportionment Board is composed of three elected state officials — the governor, auditor and secretary of state — and one member from each party chosen by the legislature. Republicans have controlled it for three decades.

The new plan would add two members, one from each party. And if the minority-party members did not approve of the district maps, the changes would last only four years, not the traditional 10. Partisan control of the board could seesaw in four years after statewide elections, so this would create an incentive to win the minority’s approval.