From Alaska to New York City, ranked-choice voting has gained traction in a handful of states and dozens of municipalities.

A coalition of voter advocacy groups and some elected officials, including Rep. Mickey Dollens, D-Oklahoma City, and Stillwater mayor Will Joyce say the preference-based voting system helps reduce negative campaigning and gives a greater voice to third-party and independent voters. But several Republican lawmakers, concerned about a potential switchover being costly and confusing to voters, remain skeptical.

Five Republican-led states have banned municipalities from...