Conservatives generally lined up in favor of the constitutional amendment, which proposed having members of the court vote for the chief justice, rather than automatically installing the longest-serving judge in that position. The practical effect will most likely be the demotion of Chief Justice Shirley S. Abrahamson, 81, who has served on the court since 1976 and is viewed as part of its liberal minority.

The court’s composition has garnered more interest in recent years as judges have decided a series of politically charged cases. Justices are now preparing to decide whether an investigation can proceed into the possible coordination in 2011 and 2012 between the campaign of Gov. Scott Walker and outside conservative groups. Justice Bradley, who won re-election on Tuesday, has recused herself from the case. Mr. Walker, a Republican, is flirting with a run for president in 2016.

Proponents said having judges vote for the chief justice would be a more democratic approach, and supportive outside groups bought television advertisements promoting that view. But liberals and some government watchdog groups came out against the measure.

“People walking into the voting booth might not know what’s behind it, that it’s a vendetta against Chief Justice Shirley Abrahamson,” said Matthew Rothschild, the executive director of the Wisconsin Democracy Campaign, a group that monitors campaigns in the state and came out against the amendment.

In many ways, the question about who will lead the Supreme Court overshadowed the race for who will serve on the court. But even without the high-drama campaigning seen in some recent Supreme Court elections in Wisconsin, Justice Bradley and her opponent, Judge Daley, took turns calling each other partisans beholden to political interests as they both portrayed themselves as reformers.