Voters keep voicing their frustration with the politically fraught way that state lawmakers redraw congressional districts every 10 years, and have approved ways to outsource the work with hopes of making fairer maps.

Colorado and Michigan approved ballot measures in November to create independent redistricting commissions to prevent one party from carving up a state in such a way as to entrench itself in office. Missouri approved a plan in which a state demographer and a statistical test will help determine lines. Utah approved the creation of an advisory commission.

“This is an exciting day for Utah,” the leaders of Better Boundaries, a group that pushed for Proposition 4, announced in a press release election night. “The voice of the people will once again be heard in drawing legislative lines — making sure Utahans choose their representatives and not the other way around.”

But the ultimate success of those commissions, as well as lawsuits to combat partisan gerrymandering, could hinge almost entirely on the views of one person — newly confirmed Supreme Court Justice Brett M. Kavanaugh.

Kavanaugh will be the center of attention when the Supreme Court hears oral arguments in March about congressional maps in North Carolina and Maryland. He is expected to have the pivotal vote in the cases that could curtail how states use politics to draw legislative and congressional districts — or leave them free to be even more partisan in the future.