In South Dakota, Democrats allowed voters with no party affiliation to participate in their June primaries, but Republicans did not. The ballot initiative would amend the state constitution to end partisan primaries by allowing all candidates for office to run at once in what is sometimes called a “jungle primary.”

Supporters of the change argue that it would allow elections to better reflect voters’ wishes and ensure that 155,000 voters with no party affiliation can vote for their preferred candidates in a primary.

But leaders of the two major political parties have criticized the proposal, arguing that candidates from the smaller Libertarian and No Labels parties are unlikely to ever appear on the general election ballot.

In a state where the Republican Party holds nearly 90 percent of the seats in the Legislature, it is likely that in many places all general election candidates will be Republicans. Meanwhile, a broader electorate could help more moderate Republican candidates at the expense of more conservative candidates favored by party leaders.

Hanna reported from Topeka, Kansas.